IDOL: Meeting Diverse Distribution Shifts with Prior Physics for Tropical Cyclone Multi-Task Estimation
Authors: HantingYan
Pan Mu
Shiqi Zhang
Yuchao Zhu
jinglin zhang
Cong Bai
Venue: NeurIPS 2025 poster ()
Keywords: Tropical Cyclone Estimation
Multi-Task Learning
Physics Modeling
Distribution Shift
Primary area: machine_learning_for_sciences
TL;DR: This paper introduces an effective Ientity Distribution-Oriented Physical Invariant Learning framework to deal with distribution variability with physical invariance.

Abstract: Tropical Cyclone (TC) estimation aims to accurately estimate various TC attributes in real time. However, distribution shifts arising from the complex and dynamic nature of TC environmental fields, such as varying geographical conditions and seasonal changes, present significant challenges to reliable estimation. Most existing methods rely on multi-modal fusion for feature extraction but overlook the intrinsic distribution of feature representations, leading to poor generalization under out-of-distribution (OOD) scenarios. To address this, we propose an effective Identity Distribution-Oriented Physical Invariant Learning framework (IDOL), which imposes identity-oriented constraints to regulate the feature space under the guidance of prior physical knowledge, thereby dealing distribution variability with physical invariance. Specifically, the proposed IDOL employs the wind field model and dark correlation knowledge of TC to model task-shared and task-specific identity tokens. These tokens capture task dependencies and intrinsic physical invariances of TC, enabling robust estimation of TC wind speed, pressure, inner-core, and outer-core size under distribution shifts. Extensive experiments conducted on multiple datasets and tasks demonstrate the outperformance of the proposed IDOL, verifying that imposing identity-oriented constraints based on prior physical knowledge can effectively mitigates diverse distribution shifts in TC estimation.

IDOL: Meeting Diverse Distribution Shifts with Prior Physics for Tropical Cyclone Multi-Task Estimation
Hanting Yan', Pan Mu Shiqi Zhang', Yuchao Zhu', Jinglin Zhang", Cong B.i
CCollege of Computer Science, Zhejiang University of Technology, China
"School of Control Science and Engineering, Shandong University, China
$7hejiang Key Laboratory of Visual Information Intelligent Processing, China
Abstract
Tropical Cyclone (TC) estimation aims to accurately estimate various TC attributes in real time. However, distribution shifts arising from the complex and dynamic nature of TC environmental fields, such as varying geographical conditions and seasonal changes, present significant challenges reliable estimation. Most existing methods rely on multi-modal fusion for feature extraction but overlook the intrinsic distribution of feature representations, leading to poor generalization under ditto---dittibbtionn (OOD) scenarios. To address this, we propose an effective Identity Cetrrbutiio-OOrientt Physical Invariant Learning framework (IDOL), which imposes identity-oriented constraints to regulate the feature space under the guidance of prior physical knowledge, thereby dealing distribution variability with physical invariance. Specifically, the proposed IDOL employs the wind field model and dark correlation knowledge of TC to model task-shared and task-specific identity tokens. These tokens capture task dependencies and intrinsic physical invariances of TC, enabling robust estimation of TC wind speed. pressure, inner- core, and outer-core size under distribution shifts. Extensive experiments conducted on multiple datasets and tasks demonstrate the outperformance of the proposed IDOL, verifying that imposing identity- -rrieted constraints based on prior physical knowledge can effectively mitigates diverse distribution shifts TC estimation. Code is available at httph:tt//////
htaps:///githutt //tggttttb......
1 Introduction
As typical natural disaster, Tropical Cyclones (TCs) endanger human life and the environment each year. Accurate estimation of TC intensity and size is thus essential in the field of weather service, helps reduce casualties and property losses. Driven by the strong capability of deep learning in feature representation and nonlinear modeling, recent TC multi-task estimation methods 7 primarily em- ploy deep neural networks to jointly estimate multiple TC attributes, including intensity and size. Gen- erally speaking, deep learning models rely on the assumption that the training and test data are drawn from the same underlying distribution, referred to di-distribution [I]] to make reliable predictions. However, in weal-world scenarios, the spatiotemporal heterogeneity of TC environmental fields often gives rise to complex and diverse developmental pathways [10]. resulting in nut-of-distribution (OOD) data during inference. Consequently, ignoring the inherent distribution of network embeddings, ex- isting methods may fail learn features that capture all possible variations in TC evolution. This, in turn, severely limits the models' ability to generalize effectively when learning from previously unseen TCs. To verify the presence of OOD data, use violin plots visualize the distributions of input X and output Y across different datasets or tasks. As shown in Figure 7 in Appendix A the varying shapes and spreads of the violins reveal notable discrepancies in the TC data distributions.
"Corresponding author. Email: congbai @ zjut.edu.cn
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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These observations highlight the importance of im- proving model generalization by explicitly address- ing the OOD issue in TC estimation. Considering the spatiotemporal and multivariate correlations among multiple TC attributes, based on previous studies [3), we attribute the OOD issue in TC estimation to three types of distribution shifts. As shown in Figure |l covariate shift and label shift refer to changes in the input and output distribu- tions between the seen and unseen datasets, i.c., P(X)vs. P(X') and vsY) P(Y"), respectively. Concept shift denotes variations in the conditional probabilities P(Y) X), arising when different TC attributes follow distinct developmental patterns and data distributions. The detailed definitions and underlying causes of these shifts are provided in Ap- pendix A To cope with various distribution shifts, one important approach is invariant feature learn- ing, which aims to extract features with certain invariance across both training and other unseen domains [1]. From this perspective, two key challenges remain to be addressed. C1: What can represent the invariance in specific domain, i.e., TC multi-task estimation? C2: How can this invariance be modeled and utilized to handle the aforementioned three types of distribution shifts?
Seen (Training) Distribution
Unsoen
x
2
Estimation Network Ex-y
Yv
xx-Yy
Px-r7
Px-v
Seen
no
P ① Covariate Shift p(x) + ppx)
Unseen
@ Concept Shift p(rlx) = p(y)))
( Label Shift p(y) * pO? yo * y
1 (v.prti.ro
Distribation of
Figure I: Diverse Distribution Shifts TC Multi-Task Estimation. The v, P, ri and ro represent the wind speed, pressure, inner-core and outer-core size of TC, respectively.
Contributions. As illustrated in Figure 2 to cope with various distribution shifts, we propose a novel perspective based on Gaussian model- ing that characterizes the invariant distributions of the feature embeddings, rather than the fea- ture embeddings themselves. Although the envi- rommental fields outside TCs are highly variable, the internal physical relationships among multi- ple TC attributes [15 16] remain relatively stable and invariant. Consequently, for C1, we propose the lentity Distribution-Orienee ant Learning framework (IDOL), which imposes adentity-orienter constraints on embeddings by regulating their distributions under the guidance of prior physical knowledge. The task-shared and task-specific identity tokens derived from the proposed IDOL represent the underlying physical invariant distribution in TC multi-task estimation.
Input Data
Backbone
Embedding
Output
Prior Physics
Learning
Identity-
Oriented
Tack-Shared
Gaussian
Tack-Specific
Constraint
Identity
Modeling
Identity
Figure Solution to various distribution shifts: Regulating the feature space to task identities by prior physies.
Physical Invari-
For C2, the learned task-specific identity tokens transform the synchronous learning of conditional probabilities for multiple specific tasks Y,, E [v.p, ri, ro} into a task flow learning process, involving P(Y;) (X) and P(Y, Y1). thereby addressing concept shift through the decoupling and modeling of task dependencies. The v. P. ri, and ro represent the estimated TC attributes, namely wind speed, pressure, inner-core size, and outer-core size, respectively. Meanwhile, the task-shared identity token is employed to address covariate and label shifts by linking the input and output and maximizing their information representation. Specifically, we incorporate two types of prior physics, including TC wind field model and dark correlation knowledge, to learn the physical invariance of TC, the major contributions of the proposed IDOL are summarized as follows:
To address concept shift in multi-task learning, propose Task Dependency Flow learning module. By incorporating the prior wind field model, the conditional probabilities of multiple specific tasks are decoupled to model the dependencies among tasks, thereby facilitating the learning of distinct task-specific identities.
To address covariate and label shifts, we design a Correlation-Aware Information Bridge module. By incorporating physical correlations to regulate the latent feature distribution, the task shared identity token is modeled to serve as an information bridge that preserves the core information of both input and output in TC estimation.
Comprehensive experiments are conducted on multiple TC estimation and prediction tasks to evaluate the effectiveness of the proposed IDOL. The results demonstrate the efficacy of

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IDOL in handling diverse distribution shifts through feature space constraints informed by prior physical knowledge.
2
Related Work
TC Estimation. TC estimation is a thriving research field that aims to model and understand the intricate development dynamics in multiple attributes of TC. Since traditional methods [1 5 6
depend on the experiences of experts, numerous approaches for TC intensity estimation based on Convolutional Neural Network (CNN) [1722] have been introduced. Similarly, various CNN-based
methods have been employed to estimate multiple sizes TC [22] 23 4]. Another important direction involves leveraging multi-task learning to simultaneously capture the relationships between different TC attributes and estimate them 77 g 26 These models employ the method of hard parameter sharing to capture the commonality of different tasks, facilitating TC multi-task estimation. However, most existing TC estimation models only rely on data-driven learning, limiting their generalization across diverse data distributions.
Invariant Learning. Invariant learning is a method aimed at learning features that are consistent for a specific task, while remaining robust changes in environments domains 27 29 This approach tackles distribution shift issues, allowing models to generalize across varying conditions. One common method is partition the training data into multiple environments or domains and optimize shared objective function across these environments, ensuring that learned features are consistent across all of them [30] [3], thus mitigating distribution shifts. Another approach uses the Mixture of Experts framework, which decomposes the model into expert modules with dynamic routing mechanisms to separate comainn-specifie and
features 32
improving
cross-domain generalization.
Physics-incorporated Methods. There has been recent surge of interest in combining physics with deep learning methods for improving the interpretability. and generalization of models. According to the previous survey [35). there are three different ways to inform deep learning models with physics. The first is observational bias (3 377, which incorporates physics principles and constraints implicitly through data. The second one is learning bias approaches [38] 39] which incorporate the governing Partial Differential Equations more explicitly into the loss of training process. At last, in contrast enforcing physical constraints, inductive bias approaches 40 attempt to embed prior physics knowledge within the network design.
Since previous methods of invariant learning rely environmental constraints and insteintervnntion output distribution, they can not cover diverse shifted distributions and are not suitable for specific meteorological tasks. In this work, tackle diverse distribution shifts, we integrate observational bias and inductive bias to learn the identity distribution of tasks that represent physical invariance.
3 Preliminaries
Representation of Correlated Data: The specific semantic information of TC is captured and encoded using temporal-spatial satellite data and auxiliary physical data, collectively denoted as X. For satellite data, we use multi-channel infrared brightness temperature data, which is denoted as Xir = {X X where Xir E xexbxv at each time a three-dimensional tensor. In this representation, с represents the number of channels, h and w denotes the height and width. Moreover, combined with the previous research in TC estimation 7 42 we define the auxiliary data as Xaux (Xaev: X including developmental and correlation factors of TC. In this representation, Xāev includes the previous level and the time since the TC became a named storm in minutes. Xcor contains TC fullness, concentration ratio, energy ratio, and TC width. To ensure real-time applicability, all auxiliary data are collected from the 12 hours preceding the estimation time.
Irinnity TC Estimation. In the context of TC multi-task estimation, a common goal is to estimate multiple current attributes by leveraging task-shared features extracted from multi-modal data. As shown in Eq. ( the conventional objective is to learn feature extractor f and task estimators g that minimize the overall estimation error:
0 argmin La (x((((())))),) Y), 0= 0= (01,02)
(I)
3

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(a) Task Dependency Flow learning
Identity Token Initialization id-N(.,o)
(b) Correlation Information Bridge
Xgev Dev Enc
id
Dide
Gak
GMM
Lide
(M1-al01-2)
I-ie
( Fo) Upp Apl id
PriorApp
Cor
PriorApp
Enc
L
ld sp
sp
Zikk
id
idgh
idsh
IDttt
yv
Encoder
F
emmb
IDAtE
Identity-
Backhone
IDALL
Oriented
X1r
Xoor
Embedding
idlp
Estimator
IDAtt
Fro
Y'i
Estimation
Figure 3: The framework of the proposed IDOL, v. p. ri, and ro denote the TC wind speed. pressure. inner-core size, and outer-core size, respectively. DevEnc, CorEnc, and GMM refer to the proposed Development Encoder, Correlation Encoder, and Gaussian Mixture Model, respectively.
where La denote the error loss function for all task, X and Y denote the input data and ground truth labels, respectively. However, this objective relies on the in-distribution assumption, which often violated in practice, thereby limiting the model's 's generalization capability. To address diverse distribution shifts, we propose an ddentity-orienter TC estimation framework that captures physical invariance, formally defined in Eq. (2)
r" = argmin Le (giidep id ((X;0));62) Y) + Liw ((F(X;81)) Identity-Oriente Constraint
Estimation Loss
where idep and id refer to the proposed task-specific and task-shared identity tokens. Lide is the identity-oricntee constraint imposed on the feature distribution (X (0)). Specifically, we design the operator Osa to model task identity tokens by leveraging the internal invariant physical correlations to regulate the feature distribution, In our method, the function g refers to the proposed estimation heads based the Correlation-Awer Attention mechanism. And 6, refers to the parameters of the encoder backbone, while O2 includes the parameters of the modules illustrated in Figure 3(a-(c))
Our Approach: IDOL
This section provides an in-depth explanation of the technical details of the proposed IDOL framework. The goal of our method is to achieve identity-oriente estimation of multiple TC attributes, including wind speed, pressure, and inner- and outer-core sizes, denoted by the subscripts v, p. ri, and ro, respectively. As illustrated in Figure 3 we present a comprehensive overview of the framework. Based on the feature embedding Fanb extracted by the encoder backbone S, the identity token id, which represents the physical invariant distribution of TC, is initialized as follows:
F eab f(X;0,) id ggauseian (F eabb
Pgauessan denotes Gaussian sampling operation applied based on the mean and variance of the feature embeddings. Details of the Eq. (3) are provided in Appendix B.
Then, based the initialized identity, the proposed model consists of three main components for handling distribution shifts: (a) Task Dependency Flow Learning: To address concept shift in multi-task learning, we introduce Development Encoder and Prior-aware Approximator (PriorApp) to decouple and model task dependencies. This facilitates the learning of all task-specific identity tokens, denoted as id.p {id] sp. idp sp: id id (b) Correlation-Awes handle covariate and label shifts in the input and output, we construct a dark knowledge graph to learn latent physical correlations among TC attributes. These learned correlations are used to regulate the embedding distribution. The resulting task-shared identity, denoted as id serves between input and output by capturing their invariant physical relationships. (c) Identity- Estimation: The feature embedding, along with the task-specific and task-shared identity tokens, is fed into a multi-head self-attention mechanism impose identity-oriented constraints. Finally, four feature embedding.
Information Bridge: To
bridge
estimation heads produce the outputs based on the

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4.1 Task Dependency Flow Learning
In this section, to decouple and model task dependencies, we first assume that the development of TC in line with the prior Holland model shown in Eq. (4). In this prior model, an inherent physical dependency exists between the intensity and wind radii of TC, in which, intensity includes wind speed and pressure, and wind radii include the size of the inner and outer core. Therefore, to model the task-specific identity tokens, we decompose the task dependency flow learning into two sequential modules: Development Encoder and Prior- aworrwwwaee/ee Approximator, which are responsible for modeling the identity of TC intensity and size, respectively.
Prior Wind Field Model. To model task-specific identity tokens by the decoupling and modeling of task dependencies, we incorporate the Holland model into the framework, which is a classical TC wind field model, providing mathematical framework for describing the radial wind distribution of TC [15]. Based on quasi-statistical physical assumptions, this model assumes quasi-steady-stuue balance, where the wind field is driven by the interplay of dynamic and thermodynamic processes, reflecting a balance between pressure gradient force, centrifugal force, and Coriolis force. The formulation can be represented follows:
In((pn Pc)/(pr - Pc)l = A
where Pr is the pressure at radius r. Pe is the central pressure and Pa is the ambient pressure (theoretically at infinite radius). The A and B are scaling parameters, which allow the model to adapt to different types of TC by adjusting the steepness of the wind profile.
Development Encoder. Considering TC wind speed and pressure are highly related to the state of TC, which reflects the dynamiic development. Consequently, we design encoder explore the developmental mode from the developmental factors of TC, and use the mode features to regulate the initialized identity token (id), then obtain the task-specific identity tokens of TC wind speed and pressure (denoted as id and id The above processes can be expressed as follows:
11 0. Encaer (Xavr Oeer) id ap
11 + a. id, i {v.p)
where EnCaav denotes the proposed Development Encoder, composed of linear layers followed
by ReLU activations, with corresponding parameters Pder- The operator Ou defined in Eq. 2 implemented here via the reparameterization formulation: μ41 o2 id.
Prior-aware Approximator. Through an identical transformation of Eq. (4) we derive the transcen- dental equation in Eq. (6). with its derivation provided in Appendix B.2
1/2 ? #
r (p Po) In(pr Pc)
To encode the prior task dependency captured by Eq. (6). we propose the PriorApp, which transforms task-specific identity tokens across tasks via two key components: (i) learnable linear mappings to approximate the intermediate term y, and (ii) deep iterative algorithm that simulates the nonlinear
exponentiation, with each iteration defined in Eq. (16) of Appendix [B.2, As an illustrative example, the dependency between TC pressure and outer-core size is modeled as follows:
To p
Yoo In (Fid 0a)) - In (F, (ide 0z))
= GConv((U,, U Un], E.): 0.)
id = H = PriorApp"(H** U, Tro; Ostor), s.t. 5(H', (H'HH'H")) <T
where In(-) denotes the natural logarithm; F, and Fr are linear layers with learnable parameters 6, and 85; and a a learnable scaling factor. U, represents the learnable node embeddings, and E, is their edge connectivity matrix, where an edge exists if two nodes are adjacent. The GConv here refer to the Graph Convolutional Layer, which is introduced to supplement the prior equation by modeling the additional latent interactions through U. The deep iterative algorithm terminates either upon reaching a predefined maximum number of iterations or when the difference 8(H', Ht-1) falls below threshold T.
5

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4.2 Correlation-Aware Information Bridge
To address covariate and label shifts in the input and output, we propose modeling the task-shared identity token idga. which acts as an information bridge between them by capturing invariant physical relationships. Inspired by the concept of dark knowledge proposed LoCa 44], which encompasses multi-task information, we first construct dark knowledge graph Gax to uncover latent physical correlations among TC attributes and input data. Details of the construction of Gax are provided in Appendix B.3 Then, to model the task-shared identity token grounded in these correlations, we use the learned graph to inform the regulation of feature distribution. Specifically, the proposed module comprises two components: (i) a correlation encoder (CorEnc) using stacked GConv layers to capture latent correlations, and (ii) a self-adaptive Gaussian Mixture Model (GMM) with correlation-awant weighting. The GMM flexibly combines latent distributions to effectively capture shared identity features across tasks. The learning process is formulated as follows:
Zak Encear (Gaz; faxx) at = Soft
idah - alah Aggregatel (da ..., dx|j = 0, 1, ...,. k:)) dl M4 a0
Here, Enccor denotes the Correlation Encoder with parameters 0ak- The GMM contains & learnable components {d,}ī=o- each constructed from a parameter pair (Kz,
4.3
Identity-Oriented Estimation
To enable odintity-oriented TC estimation, we design four estimation heads based on correlation- aware attention 45) to output all TC attributes. These heads are collectively referred to as the IDAtt Estimator in Figure 3 The estimation process and final loss based on Mcan Absolute
Error (MAE, denoted as LYAE) and identity-oriented constraint Lide are given by Eq. (
y1 = 2 (Pear (idti) idan F Fent); 0z), E (i,
Le = Σ LHAR Lido (id, Luaz (id id y y")
(9)
Ltotal =La + X (idaa Y) Σ Lide y:))
where Dig consists of a transformer encoder with correlation-aware attention, followed by three linear layers with ReLU activations. Y.. y: and Y denote the estimated value, the ground-truth value the specific task, and the concatenation of ground-truth values across all TC attributes, respectively. The Lise encourages alignment between the intra-sample correlations the learned identity and those of the corresponding ground-truth labels.
5 Experiments
In this section, we first illustrate the datasets and experiments settings of this paper. Then, compre- hensive experiments, including comparison experiments, ablation experiments, and the analytical experiments were conducted to answer the following questions. Q1: How does the proposed IDOL framework perform in TC estimation and even forecasting tasks? Q2: Do the learned identity tokens effectively capture the physical invariance of TCs? Specifically, does identity-orienter estimation enhance both the accuracy and the distribution alignment of TC attribute estimations by addressing all types of distribution shifts? Q3: How does the proposed IDOL framework address concept, covariate, and label shifts using task-shared and task-specific identity tokens?
5.1 Experimental Setup
Datasets. To evaluate how well the proposed model performs in TC estimation, our newly constructed Physical Dynamic TC datasets (PDTC) and the Digital TC datasets [46] are used. These datasets include records of 303 TCs from 2015 to 2023 over the Western North Pacific, containing various TC-related information, such position, age, and corresponding satellite cloud images. Notably, the PDTC dataset incorporates additional TC correlation factors, e.g. TC fullness, to better capture the dynamic development of TC. Details of the datasets are provided in Appendix C.I
Metrics. To assess the performance of the model in both TC estimation and prediction, including trajectory (distance, km), wind radii (nmi), pressure (hPa), and wind speed (m/s), we employ two

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Table 1: Comparison of TC multi-task estimation methods on the Physical Dynamic TC datasets.
Comparison Methods
Wind Speed
Pressure
Inner-Core Size
Outer-Core Size
Categories
MAE RMSE STD TAARMMESTDDMARREE STD MAERMSE STD
ADT
11.2
14.2
8
10.2
Traditional
MTCSWA
11.7
18.2
26.4
33
STIA
10.7
14.41
9.67
Multi-
NS
10.5
15.51
11.4426.35
36.12 24.71
Modal
TC-MTLNet
13.82
18.06
11.62
12
15,46
9.79
31.49
42.83 29.14
Fusion
DeepTNNet
8.84
11.76
7.76
8.13
10.42
5.31 8.09
13.71
11,2525,86
33,49 21.29
PeRCNN
10.04
13.23
8.61
6.99
8.78
6.52 8.56
14.13
11.2524.97
32.94
21.48
IRM
9.54
12.93
8.71
7.71
10.06
6.47 8.12
13.7
11.06 25.6
34.7 23.37
V-Rex
10
13.29
8.76
8.13
10.48
6.6 8.21
13.7
10.94 25.4
34
22.59
Invariant
SADE
10.01
13.47
8.66
8.09
10.55
6.76 8.23
13.41
10.5925.95
34.19
22.26
Learning
DirMixE
9.93
13.27
8.8
7.92
10.27
6.54 8.47
14.2
11.37 25.5
34.3 23.02
IDOL
5.93
7.6
4.75
5.77
7.15
4.23 6.24
12.06
10.31 17.06 23.26 15.8
widely-used evaluation metries: Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE). The lower values of these metrics indicate better performance. Moreover, the standard deviation (STD) of error on test sets selected as an additional metric to measure the stability and generalization ability of the model.
Baselines. To evaluate the effectiveness of the proposed, we compare our IDOL with several representative SOTA methods, which can be divided into three groups:
Traditional Methods. ADT and Multiplatform Tropical Cyclone Surface Wind Analysis technique (MTCSWA) are typical methods for using satellite infrared data estimate TC intensity and wind radii respectively 53 6)
Multi-Modal Fusion Methods. We select several typical TC estimation methods based on
multi-modal data understanding. including single-task [1 23 and multi-task estimation [8] 7.5.. Additionally, PeRCNN is a physical method that models polynomial correlations, which can be adapted for TC estimation. Specifically, following the correlation modeling method in Phy-CoCo (55), we use PeRCNN to transform the task-specific identities of TC attributes, which are then compared in subsequent analysis experiments of task-specific identity distributions.
Invariant Learning Methods. Invariant learning methods, including standard IRM [3)]
V-REx 31 and MoB based methods SADE and DirMixF [32 33
5.2 Overall Performance (for Q1)
Table and Table 5 reports the overall performance of all the methods PDTC datasets and Digital TC datasets respectively, where the best is shown in bold. Among the SOTA methods, Deep based observational bias, and PeRCNN, based inductive bias, generally perform well. This suggests that leveraging the physical relationships among multiple TC attributes can effectively improve TC estimation. However, general invariant learning methods perform poorly, primarily due to the lack of domain-specific knowledge integration. In contrast, the proposed IDOL incorporates prior knowledge into the feature distribution to model identity tokens with physical invariance, achieving the best performance among all SOTA methods. Additionally, Figures I and TO in Appendix C.2 further illustrate the robust estimation results across TC categories on unseen TCs in both the PDTC and Digital TC datasets. Specifically, for estimating wind speed, pressure, inner-core size, and outer-core size on the PDTC dataset, IDOL outperforms the previous best method, Deep by 32.9%, 29%, 22.9%, and 34% in MAE, respectively.
The above experimental results highlight the importance of modeling task identity tokens with physical invariance, as it enables the model to generalize effectively to previously unseen TC. As shown in Table in Appendix C.2 our model achieves the best estimation performance without increasing model parameters or inference time. Moreover, as shown in Table in in the Appendix C.2 the improvement in TC forecasting accuracy with the proposed method further proves the ability of our IDOL to handle distribution shifts, which are also inevitable in TC forecasting.
5.3 Identity-Oriented Performance (for Q2)
Ablation Study. In this section, as shown in Table 2 we conduct an ablation study to investigate the contributions of physical identity tokens in the proposed IDOL. First, observe that the model with
7

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Table 2: Ablation experiments. y refers the encoder backbone f. idep and id represent task-specific and task-shared identity tokens with physical invariance, addressing concept shift and covariate/label shifts, respectively.
Wind Speed
Pressure
Inner-Core Size
Outer-Core Size
5et, id ad
MAE RMSE STD MAE
RMSE STD MAE RMSE STD MAE RMSE STD
10.13
13.25
8.54
7.79
10.13
6.47
8.32
13.87
11.1 28.58 37.66 24.52
7.24
9.13
5.55
6.66
8.27
4.97
7.37
13.24
10.99 24.91 33.28
22.07
5.93 7.6
4.75
5.77
7.15
4.23
6.24 12.06 10.31 17.06 23.26 15.8
the proposed identity tokens derived from prior physical knowledge, significantly improve both the accuracy and stability of the model across the four estimation tasks. Secondly, as shown in Table in Appendix C.3] the model with task-specific identity tokens learned by the prior Holland model outperforms those learned by a noisy prior or linear layers. This further validates the importance of incorporating effective prior knowledge. Since the test and training datasets are completely non- overlapping in the temporal domain, meaning the test set comprises entirely unseen TCs, which effectively represents unknown data distribution. Therefore, in addition evaluating estimation accuracy, we also visualize the distributions of ground-truth and estimated results on the test set using kernel density estimation (KDE). As shown in Figure 4 a). the distributions of TC attributes estimated by our IDOL are closer to the true distributions compared to baseline models such as DeepTCNeet and PeRCNN. This demonstrates that the learned physical identity tokens enable the accurate estimations in terms of both error and distribution alignment.
Distribution Comparison
Varfance of BaselineF and OurlD
1.6-
40
1.2
20
Veriance
1.0-
HDv
PiTp
0.8
(131)
0
0.6-
MM3r
PDsh
0.4
-20
022
-40
0.0
2015
2016
2017
2018
2019
2020
2021
2022
2023
-60
-20
(a)
(b)
Figure 4: (a) Distribution visualization of test set estimation results based on KDE. (b) Variance comparison between physical identity (PID) tokens and the features extracted by DeepTCNet.
Moreover, to explore how different degrees of parameter sharing affect model size and multi-task performance, conducted ablation experiments by varying the parameter ratios between task-shared and sasc-spe identity tokens. Specifically, we define the ratio based on the dimensional size the corresponding identity token, with configurations including 1:1, 1:2, 1:3, 2:1, and 3:1. For example, ratio 1:2 means that the task-shared identity token has half the dimensionality of the task-specific identity token. The results are presented in Table 3
Table Additional ablation experiments on the ratios between mask-shared and task-specific identity tokens. Bold indicates the best result, and underline denotes the second best.
Ratio Settings
Wind Speed
Pressure
Inner-Core Size
Outer-Core Size
(id id
MAE
RMSE
STD
MAE
RMSE STD
MAE RMSE
STD MAE RMSE STD
1:2
5.75
7.46
4.76
5.78
7.17
4.25
6.36
12.24
10.45
17.95
24.74 17.02
1:3
6.1
7.85
4.95
5.95
7.36
4.33
6.3
12.07
10.29
18.11 24.52
16.53
2:1
5.91
7.58
4.75
5.9
7.33
4.35
6.32
12.03
10.24
17.94
24.52
16.72
3:1
5.93
7.69
4.89
5.79
7.14
4.17
6.13
11.81
10.09
18.79 25.34
17
1:1 5.93
7.6
4.75
5.77
7.15
4.23
6.24
12.06
10.31 17.06 23.26
15.8
As shown in Table 3 under the given model design and experimental settings, varying the parameter ratio between task-shared and task-specific identity tokens has slight impact on model size and overall estimation performance. This is mainly because the proposed identity tokens, even with lightweight configurations, are sufficient to impose physical constraints on the feature distributions, thereby guiding the model to effectively capture the intrinsic characteristics required for multi-task
8

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HSLP Distrcutiona SHANUN
CutA--ove Care Size Distribttirn of KHAAUN
975.5 hpa
966.8 B hpa
966.1 hpa
975.4 hpa
76.6 nmi
122 nmi
86.1 nmi
98.1 nmi
KSLP of CHAMIUN
Dutencrre Saw KIMALU
Esrradio Emw
977 hpa
961 hpa
83.7 nml
83.3 nm
Time Stepps
Streph
SSSP DiSt Bution SAOLA
Cuoor care Size Dccrisudin SAOLA
971
hpa
961 hpa
952.9 hpo
81.3 mumel
63.6 nmi
86.3 ami
106.9 nmi
SACIA
CUCA SAOLA
1500 10 Emo
Devortt mose
968.1 hps 22.5
0 IDOL
DOL
Timee Stepes
Tirr Steps
(a) Sample pairs with Shifted X
(b) Sample pairs with Shifled Y
Figure 5: Estimation performance of pressure and outer-core size on test samples under distribution
shifts: (a) Estimation results under covariate shift and (b) Mean absolute errors under label and concept shifts across different TCs and output attributes. Each vertical red box indicates a pair of samples exhibiting distribution shift.
learning. Increasing the dimensionality of specific identity token primarily enables more fine- grained representation learning, which may lead to slight variations in task-wise performance, but does not result in significant overall performance gains. This further confirms the effectiveness and efficiency of the proposed identity token design in ensuring consistent and robust multi-task learning.
Invariant Learning. To answer Q2, we visualize the statistical variance of the proposed physical identity tokens and DCep features in (tg to assess whether the learned identities capture TC invariance. In invariant learning, features from different domains should be close to each other, which means they will have similar variances. Supposed the model extracts physically invariant identity tokens across time domains, their statistical variance should remain consistent. From Fig compared to TCNet features, our physical identity tokens exhibit smaller variance across domains, indicating stronger robustness to domain shifts. This improvement supports our assumption: by leveraging physical correlations to constrain feature distributions, the learned identities capture the intrinsic physical invariance of TCs. In other words, incorporating prior physics enables the model to better understand the internal TC dynamics and generalize to unseen, variable environments.
Moreover, to evaluate the model's 's robustness under distribution shifts, we screen out and visualize specific sample pairs from the test set that exhibit distribution shifts in both input and output. Following the task dependencies in the prior Holland model, pressure and outer-core size are treated
as a correlated task group, their shifted sample results shown in Figure 5
Similarly, the results for
wind speed and inner-core size are presented in Figure 13 in Appendix C.4 The details of the selected
shifted sample pairs are also provided in Appendix C.4 In Figure 5 three types of distribution shifts
illustrated: covariate shift, referring difference in TC structures seen in the input; label shift, referring to distribution differences of the same output attribute across different TCs; and concept shift, referring to distribution differences across different output TC attributes. Compared with SOTA method DCepT'NNet in Figure 5ja), the estimations of our IDOL (green boxes with underlines) noticeably closer the ground truth (red boxes), even under covariate shift. Meanwhile, in IDOL also achieves lower estimation error across different TC: instances and attributes with varying distributions, showing its effectiveness under label and concept shifts. These results collectively demonstrate IDOL's robustness to various distribution shifts, validating its capability in physical invariance learning.
5.4 Analysis of Physical Identity (for Q3)
To address Q3, we conduct analytical experiments on the learned task-specific and task-shared identity tokens. First, assuming that concept shift in multi-task estimation can be mitigated by decoupling

---

and modeling inter-task dependencies (i.e., the v-ri and p-ro relationships in the Holland model), we compute the mutual information (MI) between each true TC attribute and its corresponding task- specific identity token to quantify the adequacy of dependency modeling. As shown in (a)-()) a)-(b), the MI between task-specific identity tokens is even higher than that of between the ground-truth attributes themselves, on both seen (training) and unseen datasets. This indicates that the learned physical identities effectively model prior task dependencies, i.c., P(Y, | Y)), as higher MI indicates stronger inter-variabl variable correlations. Moreover, since task dependency flows are grounded in learning P(Y, | X), where E (v. p), we further compute the MI between the output attribute and its corresponding identity token for tasks and p quantify the adequacy of correlation modeling. Figure 12 (Appendix c.5) presents this result, where the x-axis represents the degree of concept shift relative to the training set, and the y-axis shows the corresponding MI. The figure reveals that MI remains consistently high across varying shift degrees, with the average MI even higher on the test set than the training set. This confirms that task-specific identities successfully preserve essential information for estimating v and p.
Task Dependency Validation
Task Dependency Validation
Scatter plot MK(PID, F)
Scatter plot MKPID, Y)
+ NoDEx MDHI MXY.r0
1.1
1.7
1.7
E 0.8
t39
1.0
MIRIDA
MIPID,
1.4
0g
0.79
ua
0.8
0.5
0.6
0.09
0.8
Samples
Meantti 1.376
0.8-
Toinset
Samples
Tmnn
valid
Test
Train
Valid
0.58
0.60
0.62
0.64
0.56 0.56..58 0. 0.62 0.64 0.66 Degree of Label Shift
Dataset
Dataset
Degree of Covariate Shift
(2)
(b)
(c)
(d)
Figure 6: (a) Adequacy of modeling the task dependency between and ri. (b) Adequacy of
modeling the task dependency between p and ro. (c) Adequacy of correlation modeling between the learned task-shared identity token and input features on the test set. (d) Adequacy of correlation modeling between the learned task-shared identity token and output attributes Y on the test set. PID and Y denote the proposed physical identity tokens and ground-truth TC attributes, respectively.
Second, to evaluate whether covariate and label shifts are mitigated by using the task-shared identity as a bridge between inputs and outputs, we compute the MI between the task-shared identity and both the input features and the output attributes, respectively. As shown in Figure ((c)-(d), the MI remains high across varying degrees of shift, and the average MI on the test set is higher than that on the training set. This demonstrates that the task-shared identity effectively acts as robust bridge, capturing consistent information under covariate and label shifts. Further evidence is provided in Figure IT (Appendix C.5). where the estimation performance using real and randomized dark knowledge graphs is compared. The negligible difference in MAE and STD indicates that the proposed correlation-awar mechanism successfully captures meaningful physical invariances of TC.
6 Conclusions
This paper addresses the challenge of diverse distribution shifts to improve model robustness in TC estimation. The core idea is to learn invariant identity tokens that represent different task distributions by leveraging prior physics to constrain feature embeddings. Various distribution shifts are tackled by modeling prior task dependencies and latent physical correlations. Comprehensive experiments show that IDOL outperforms previous state-of-the--e art methods, underscoring the effecctiveness of prior physics modeling in handling unknown data distributions for TC estimation.
Acknowledgments and Disclosure of Funding
This work is partially supported by Zhejiang Provincial Natural Science Foundation of China under Grant No. LRG25F020002, Distinguished Young Scholar of Shandong Province under Grant 7R2023JQ025 and Natural Science Foundation of China under Grant No. U24A20221 and No. 62202429.
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IDOL
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A Distribution Shifts in TC.
To verify distribution shifts across different TC attributes, we use violin plots to visualize the distributions of input X and output Y across datasets or tasks. Using a standard normal distribution as reference, we compute the distributions across datasets. The JSD values for each data batch are shown in the violin plots in Figure a) and (b). The varying shapes of the violins in Figures and (b) indicate clear differences in the distributions of X and Y. confirming the presence of covariate and label shifts. Furthermore, Figure (c) presents the variance of ground-truth values across batches for each task, where the differences among tasks illustrate the existence of concept shift. These findings underscore the necessity of introducing physical invariant learning to model task-specific identity tokens, enabling the model to handle distribution shifts effectively and enhancing generalization.
Shannon divergence (ISD) between the input, output, and contrast
Vii' Not Duss Decrout on Detaset
Volio Fot Ci cotutiin DICAAIES
Viiie Pot Derruut on Tidks
6.2
(h)
Gc)
Figure 7: (a)-(b): Violin plots of ISD between input/output and contrast distributions across datasets, indicating covariate and label shifts. (c): Violin plots of real variance across batches for each task, indicating concept shift.
To explain the aforementioned distribution shifts, we summarize their definitions and underlying causes as follows:
Label shift. The distribution of labels P(Y) changes between the training and testing datasets, even the conditional distribution P(X YY) remains unchanged. i.e. Due to climate change, including global warming and rising sea levels, the intensity and frequency of may change over time, leading to label shifts.
Covariate shift. The distribution of input P(X) changes, while the conditional distribution P(Y (X) remains unchanged. i.e. TC shapes may vary significantly due to geographical differences, reflected in brightness gradients and structural complexity, indicating a shift in the input distribution. However, the conditional distribution P(Y X), mapping cloud images to TC attributes, remains consistent.
Concept Theft.The conditional probability P(Y X) varies across different tasks. That is, influenced by distinct factors such as sea surface temperature or vertical wind shear, different TC attributes may follow distinct distributions and correlations. Thus, rules learned for one attribute (e.g., intensity) may not generalize to others, leading to concept shift.
B More details of IDOL
B.1 Encoder Backbone
This section details the encoder backbone architecture employed in our framework. To enable identity-oriented estimation, it is essential to thoroughly analyze sequential satellite data and provide well-informed initializations for the identity tokens. To achieve this, our backbone is designed as peatio-temporal semantic fusion network, comprising three main components: (i) Infrared Encoder: This module effecttivlyy captures features that are sensitive to both channel-wise and spatial variations by processing multi-channel infrared satellite data. (ii) Spatio-Temport Semantic Fusion: This component introduces correlation-await attention to guide the integration of features across time steps. It captures the interdependencies between temporal sequences and physical auxiliary inputs, enhancing the semantic richness of the learned representations. (iii) Gaussian Distribution Sampling: To initialize the identity tokens, we employ Gaussian distribution sampling based on the fused representations.
Infrared Encoders. VGG13 efficiently extracts multi-scale features through its convolutional layers, with initial layers capturing low-level features and deeper layers capturing complex semantics. Given
22

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its suitability for capturing both local and global image features, we use VGG13 A7 as the encoder (Encιa) for satellite infrared data. The process of the proposed infrared encoders for satellite data shown as follows:
F
EnCIR
to 6ER F
F
EncIr (X:: fi)
to
(10)
Fie OP cat
(F tar
FT)
where oi and O are the parameters of encoders. F.a E Rexexaxx, where represents the number of time series.
Spatio-Temporal Semantic Fusion. Based on the multi-scale features Fie extracted by the infrared encoders, we perform spatio-temporal semantic fusion to enhance the representation of TC dynamics. First, linear transformation layer, denoted as Linear, is applied to extract features corresponding to TC-related correlation factors. To effectively integrate these with the infrared features, we adopt Self- Attention ConvLSTM [48), which is well-suited for capturing global spatio-temporal dependencies. This module enables the model to retain and propagate both spatial and temporal context across frames, thereby enriching the fused representation with deeper semantic information. The overall fusion process can be summarized as follows:
F cor -Lincar (aaccar(Xcoriii fcor)
(11)
F emb =Fusste (Peat (F Fcor);
where Fussta denotes the ConVLSTM with Self-Attention and Ost represents its parameters. Se- mantic fusion is achieved by introducing physical features at each step of temporal fusion through concatenation. Here, F; E {F J. and enb IRexa, where n the feature dimension.
Gaussian Distribution Sampling. Based on semantic features after spatio-temporal semantic Fusion, good initial distribution is generated by Gaussian sampling. Specific sampling operations are as follows:
μ Pa(F emb: di):o Pa d,)
(12)
id =P PPganasian (1,
where Pa and Pe are operations of taking the mean and variance, the subscript of d; represents specific dimension. Pgeuessan denotes a Gaussian sampling operation, which draws samples from normal distribution using the mean and variance of the feature embeddings, In implementation, this corresponds to the torch.normal function in Py' PyTooch.
B.2 Task Dependency Flow Learning
Holland Model. The Holland model is widely used empirical model in meteorology for representing the wind field of TCs [5), which can be used for estimating the wind speed profile of TC. The wind profile in the Holland model is assumed to decrease radially outward from the center of the TC. The model assumes a smooth, continuous decrease in wind speed with increasing distance from the center.
Proof of Formula. To incorporate the prior model for learning task identity, we make the following identical transformation the original Holland equation.
B In((pa Pc)/(p (pr -Pe)l = A r
In In po)/(pt - -Po]] =
(13)
In Inr = =lnn
Inr ln
Er +
Based on the Holland model, we substitute the inner and outer-core size into Eq. 13 shown below:
A
TO poVer -ro
In Pc)/ (Pro Pc)]
(14)
ri 7
pow.i
Yri
In[(P= - PcP) (pts -P))
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PriorApp for TC Wind Speed. Corresponding to Eq. inner-core size is formulated as:
14
the prior constraint from wind speed to
Tr In (id 0n)) In Fr (id'))) 0z))
(15)
U GConv( ((UU, U2 Ua) Ex); 0u)
id sp
Iteration (H*-1, U, Yroi Oster) HJ 8(H
(H"HH"" <
where In(.) denotes the natural logarithm; F, and Fr are linear layers with learnable parameters On and 0r: and 0. a learnable scaling factor. U₁ represents the learnable node embeddings, and E, is their edge con- nectivity matrix, where an edge exists two nodes are adjacent. The GConv here refer to the Graph Convolu- tional Layer, which introduced to supplement the prior equation by modeling the additional latent interactions through U. The deep iterative algorithm terminates ei- ther upon reaching a predefined maximum number of iterations or when the difference 5(H', H²-1) falls be- low threshold T.
GConv
id
Figure 8: The framework of the proposed PriorAP.
Details of PriorApp. Inspired by the gating mecha- nisms in the Long Short- Term Memory (LSTM) architecture [43, to approximate the power operation in a deep and dynamic manner. Specifically, we introduce a forget gate (Feg), input gate (Fin), and output gate (Fou), which collaboratively regulate the information flow across iterations, analogous to the memory cell updates in LSTM. As illustrated in Figure the module refines its internal state over maximum of R iterations, until convergence reached, which is defined as the output fluctuation falling below a predefined threshold т. At each step, all relevant nodes are jointly considered inputs for associative modeling. This iterative simulation allows the module to capture higher-order interdependencies among tasks, going beyond the expressiveness of the original power operation formulation. The internal states are updated at each iteration as follows:
design gated iterative module
fgg -0 (Ftg( Yra, U}; Org))
f, =0 (Fin([[ (H, /rol: [ 0m))) tanh(F.((H, Trol; 0c))
fou =a (F [H, 7oo, U]: (ou))
(16)
Č C frg + fin H tanh (Ö) fou
id s.t. 8(H)- <T
Here, H and C denote the hidden state and cell state, respectively, both of which are iteratively updated via gated operations. The forget gate fig determines how much of the previous memory C should be retained. The input gate fin incorporates new information into the memory by modulating candidate state. The output gate fou controls the extent which the updated cell state propagated to the output. The functions Fig. Fiu. Fou. and F. are linear transformations, each parameterized by learnable weights lzg. l... fau. and fc. respectively. The functions (-)) and tanh(-) denote the sigmoid and hyperbolic tangent activations, respectively. The iterative process terminates when the change the hidden state, measured by 8HH), falls below a predefined threshold T.
B.3 Correlation-Aware Information Bridge
Dark Knowledge Graph. The graph G comprises node features extracted from Xcor and edge index matrix defining connections between nodes. An edge is established between nodes i and j if M 1. Specifically, d refer correlation matrix, where the nodes correspond correlation factors and TC attributes. An entry M = indicates that the i-th correlation factor is related the j-th attribute. For example, the factor tcf (TC fullness) is related to TC. size attributes such as ri and ro, resulting in M02dk M03dk factors, the initial matrix 4 is defined follows:
Based on prior physical knowledge of TC correlation

---

P
tcf
0
1 0
M
tcc
1
0
1
tce
1
0
tcW
0
1
0 1
Here, tcf, tcc, tce, and tcw denote TC fullness, concentration ratio, energy ratio, and TC width, respectively. To address covariate and label shifts in both the input and output domains, M is then used to construct the dark knowledge graph. Through the learning process, this graph captures latent physical correlations and leverages them to bridge the input-output gap via a taskeshared identity token, denoted id
C
Experiments
C.1 Experiment Settings.
Datasets. To evaluate the performance of the proposed model TC estimation, we use the Physical Dynamic TC datasets and the Digital TC datasets [46]. For constructing the Physical Dynamic TC datasets, we collected rich meteorological data from the IBTrACS [49] and satellite data from Himawari 8 [50] of TCs from the year 2015 and 2023. Since the infrared data of channels 7, 8, 13 and 15 are beneficial to TC estimation [2]. we downloaded the brightness temperature data from these four IR channels which normally used monitor clouds and water vapor. The observation area is 60S-6ON, 80F-160W, providing data at temporal and spatial resolutions of 10 min and 5 km, respectively. The satellite data were first linearly transformed the interval [0, 1] using Min-Max Normalization. Then, the data were divided by year, with training data from 2015 to 2021. The training data were augmented by rotating the images by 90" 180%, and 270" clockwise and flipping them horizontally and vertically. The data for 2022 and 2023 were used for validation and testing. Table [ the number of samples in the training, validation, and test sets.
Table 4: Number of training, validation and test data.
Dataset
Train
Valid
Test
Total
TC Num
235
36
32
303
File Num
10099
1244
1245
12588
Moreover, to help model capture information of TC physical development, we matched the time dimension to obtain the developmental and correlation factors, including the category, the time since the TC became a named storm in minutes, the fullness, concentration ratio, energy ratio and width of TC. Among them, TC categories include tropical storm and hurricanes of grades to 5.
For Digital TC datasets, we use the same ground data set, i.c. International Best Track Archive for Climate Stewardship (IBTrACS) 49 to match it, and crop the satellite data size to 156 x 156 too. What's more, to conduct migration experiments on TC multi-task forecasting, we use the datasets used in MGTCF and TC-Diffuser [5l 52). which encompassing all the 1722 TCs data from 1950 to 2021 over the Western North Pacific.
Experiment Settings. To estimate multiple attributes of TC, we implemented the IDOL and all the Ota (SOTA) methods with the Pytorch toolkit on an NVIDIA RTX A6000 GPU. In our experiments, we employ the Adam optimization algorithm with an initial learning rate of 0.0001. The model is trained for 200 epochs with a batch size of 48. In addition, for fair comparison, all experiments are performed on the same datasets, which will be publicly released.
C.2 Performance Comparison.
The inference speed on the test datasets and model size of different methods are summarized in T which shows that IDOL is comparable to previous methods in terms of both model size and inference speed. Moreover, to better understand the model complexity, we analyze the parameter sizes of the proposed identity modeling modules and the feature extraction backbone (two VGG13
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Table 5: Comparisons of TC multi-task estimation with previous methods on the Digital TC dataset.
Comparison
Wind Speed
Pressure
Inner-Core Size
Outer-Core Size
Categories
Methods
MAE RMSE STD MAERMSESTI
STD MAERMSE STD
ADT
11.2
14.2
10.2
Traditional
MTCSWA
11.7
18.2
26.4
33
STIA
9.79
12.39
7.59
Multi-
NS
10.09
15.52
11.79
33.48
42.53
26.23
Modal
TC-MTLNet
13.14
16.7
10.31
11.5
14.04
8.1
35.61
44.34
26.42
Fusion
DeepTCNet
9.15
11.87
7.56
8.02
9.91
5.82
7.99
11.76
8.62
28.91
36.11
21.63
PeRCNN
6.51
8.54
5.53
6.89
8.57
5.09
7.88
11.57
8.48
28.17
34.9
20.59
IRM
9.3
11.81
7.28
7.65
9.44
5.53
8.07
12.4
9.41
28.6
34.7
19.57
V-Rex
9.54
12.13
7.49
8.23
10.03
5.75
8.13
12.4
9.37
28.6
34.3
19.03
Invariant
SADE
9.55
11.93
7.15
8.33
10.22
5,93
7.77
11.8
8,91
28.5
34.2
18.88
Learning
DirMixE
9.24
11.8
7.33
7.54
9.31
5.47
7.83
11.7
8.65
27.1
32.73
18.36
IDLL
5.82
7.45
4.66
6.08
7.54
4.45
7.07
10.81
8.17
24.74
30.33
17.55
networks) in IDOL. The parameter sizes are 9.78M and 266.1 respectively. This indicates that the identity Dustribtioon-oriente learning module itself is lightweight. To further investigate the trade-off between accuracy and efficiency, replaced the VGG13 backbone with significantly simpler CNN architecture and retrained the model on the same dataset. The comparative results are presented in Table 7
Table 6: Comparisons of model size and inference time.
Methods
DeepTCNet IDOL(ours)
Size(M) 270.42
275.89
Inference time(s) 4.88
3.18
Table 7: Comparisons of model size and inference time with different feature extraction backhone in IDOL,, including two VGG13 networks and two CNN.
Wind Speed
Pressure
Inner-Cone Size
Outer-Core Size
Model Size(M)
Time(s)
MAE
RMSE
MAE
RMSE
MAE
RMSE
MAE
RMSE
Deep
270.42
4.88
8.84
11.76
8.13
10.42
8.09
13.71
25.86
33.49
VGG-IDOL
275.89
3.18
5,93
7.60
5.77
7.15
6.24
12.06
17.06
23.26
CNN-IDOL 12.88
2.52
6.32
8.27
6.08
7.62
6.00
10.75
16.79
23.66
In summary, shown in the table, replacing the backbone with lightweight CNN architecture has slight impact on overall estimation performance. This demonstrates that the proposed identity distribution-orientee physical -nvvaial-ivvaiiantt learning framework is not only effective and lightweight, but also robust to changes in the feature extraction backbone, making it highly adaptable and scalable for practical deployment.
TC Multi-task Estimation. Table 5 reports the overall performance of all the methods on Digital Typhoon dataset (46), where the best is shown in bold. The experimental results show that the proposed IDOL has the best performance in all tasks, including estimation error and model stability, even on the dataset with poor estimation performance. This further prove that the observational bias and inductive bias are potential in physical invariant learning. Moreover, we present the estimation performance for each TC. category on the test set in Figure 9 and Figure TO The consistently lower mean absolute error (MAE) and standard deviation (STD) across different TC categories demonstrate that method exhibits stronger generalization and more robust learning capability when handling previously unseen TCs.
TC Multi-task Forecasting, MGTCF 51 and TC-Diffuser 52 are state-of-the-ar methods for TC multi-task forecasting, based on Generative Adversarial Networks (GANs) and diffusion models, respectively. Therefore, these two models were selected for migration experiments. By integrating task-shared and task-specific identity tokens, which are guided by prior physical knowledge, into their original architectures, we observe notable improvements in both prediction accuracy and stability, as summarized in Table 9 Moreover, to further compare the performance of our approach with foundation weather model, selected the publicly available Pangu model representative baseline.
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1666 for Cach TE Category
Mil for Farh Catrgey
N65 for Farth Categery
MAl tor Facth Calmaay
1442
Colepayy
407
20
2
Catngery
Ceregory
Categery
Category
Figure 9: Visualization of estimation results across TC categories PDTC dataset. From left to right: estimated wind speed, pressure, inner-core size, and outer-core size.
Each Categery
Catagery
Sach Cetegery
'or Catapery
0.2
1922
3d
Cabegory
Caragory
Cabegory
10 Catagory
STD for Dach TE. Eateerry
ST3 Each Conegery
CTD Se Farh Cateeary
STD for tach TE. Category
10-
65
(1) prosumm
633 Dinere doe
(iraaee dan
Figure 10: Visualization of estimation results across TC categories on the DigitalTC dataset. From left to right: estimated wind speed, pressure, inner-core size, and outer-core size.
To ensure fairness, we evaluated Pangu on the same datasets and reported its test results following the settings in TC-Diffuser [52]. These results demonstrate the effectiveness and generalizability of our physically invariant learning framework in the context of TC forecasting.
C.3 Ablation Study.
To further validate the contribution of the Holland model modeling task-specific identity tokens, we conducted additional experiments in which the Holland model was replaced with learnable linear layers or with intentionally perturbed priors (i.e. Linear id and Noisy id.p). Specifically, in the Noisy id.p setting, we injected additional task correlations into the Holland model that are not physically supported in prior research, such as introducing an artificial dependency between inner-core size and outer-core size.
As shown in Table the performance the model with task-specific identities learned by Holland is better than that of the model with task-specific identities learned by Linear layers noisy priors. It's because informing prior can help the model better capture the physical relationships among tasks and the development mechanism of tropical cyclones. Besides, from the table, we can also observe that the model with task-specific identities learned by Linear layers still performs better than the one without task-specific identity modeling, which demonstrates that even without prior knowledge, constraining the feature distribution to model task-specific identities is still effective for mitigating distribution shifts, thus improving the estimation accuracy of tropical cyclones.
27

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Table 8: Additional Ablation experiments. id.p represents task-specific and task-shared identity
tokens.
Wind Speed
Pressure
Inner-Coue Core Size
Outer-Core Size
Settings
MAE
RMSE
STD
MAE
RMSE STD
MAE
RMSE
STD
MAE RMSE
STD
Encoder Backbone
10.13
13.25
8.54
7.79
10.13
6,47
8.32
13.87
11.1
28.58 37.66 24.52
w/ /innear idsp
w
8.75
11.48
7.43
7.83
10.25
6.61
7.68
13.29
10.85 25.49 33.79
22.18
w
Noisy idap
8.54
11.33
7.44
7.58
9.88
6.34
8.1
13.95
11.36
25.84
33.84
21.84
w/ Holland idge
7.24
9.13
5.55
6.66
8.27
4.97
7.37
13.24
10.99
24.91
33.28
22.07
Methee Orth TC Coteggy Meton orion
IMd to Exth DANEEY
MAC Py CAS CongSTy
H4t for Evch CRlger
Band 200000
135
1.00
444
10
④1 Categgry
6
Lattegrry
Cateoory
Categooyy
Figure 11: Visualization of estimation results using random dark knowledge (DK) graph during testing. From left to right: estimated wind speed, pressure, inner-core size, and outer-core size.
C.4 Analysis of Invariant learning
Details of Shifted Sample Pairs. To evaluate the model's robustness under distribution shifts, screen out and visualize specific sample pairs from the test set that exhibit distribution shifts in both input and output. Following the task dependencies in the prior Holland model, pressure and outer-core size are treated as a correlated task group, with their shifted sample results shown in Figure 5 Three types of distribution shifts are illustrated in figure: covariate shift, referring to difference in TC structures as seen in the input; label shift, referring to distribution differences of the same output attribute across different TCs; and concept shift, referring to distribution differences across different output TC attributes. Similarly, the results for wind speed and inner-core size are presented in Figure 13
To identify samples exhibiting covariate shift, we first compare the structural shapes and ground-truth values of TCs in the test dataset. A sample pair is considered to exhibit covariate shift if there is a substantial difference in TC structure (e.g., spatial pattern or appearance), while the difference in their GT values remains within predefined threshold. Moreover, for detecting label shift and concept shift, we visualize the ground-truth distributions of each attribute across different TCs in the test set using kernel density estimation. A pair is considered to exhibit label shift if the dis- tributions of the same attribute differ significantly across TCs. Similarly, a pair is considered to exhibit concept shift if the distributions of different TC attributes vary notably across instances. Specifically, the sample pairs exhibiting covariate shift in Figure 5 are drawn from the following TCs: [LAN-202 NMM--222308918, Figure [3] and MASWAR-2023022122 variate shift are shown in Figure 14 where the selected sample pairs are from the fol- lowing TC instances: (HAIKUI- 2023090212, LAN-2023081009) (HAIKUT-2023090318,, and
and NDNN-2023010000 the covariate shift sample pairs are from HAMMRY-2002308271
220X0000222000033 In SITRGII-202008111 MAWAR-20280 2023053015.. Additional estimation results under co-
LAN-2023081000), (LAN-2023080918, KOINU- 1020000003100300) Additional results under label shift and concept shift are provided in Figure 15
28

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Table 9: Experimental results of method migration verify the ability to handle distribution shifts in TC multi-task forecasting.
Trajectory (km)
Pressure
(hpa)
Wind Speed (m/s)
Methods
Metrics
6h
12h
18h
24h
6h
12h
18h
24h
6h
12h
18h 24h
Pangu
MAE
42.8
44.75 50.85 65.68 16 16.5 16.7 16.9
MGTCF
24.21
44.99 69.2 96.77
1.41
2.14 2.77 3.25 0.79 1.2 1.57 1.88
MAE
MGTCF w/ IDOL
24.21 44.23 68.4 95.81 1.31 1,95
2.38 2.82 0.74
1.14 1,42 1.64
MGTCF
20.31 36.79 55.27 81.87 2.25 3,01
3.81
4.35 1.17 1.58 1.89 2.14
STD
MGTCF w/ IDOL
19.48 33.99 49.77 73.99 1.96 2.52
3
3.4 1.04 1.42 1.69 1.85
TC-Diffuser
T9.39 20.83 41.82 77.41 1.24 0.84 1.85 2.81 0.75 0.43 0.93 1.38
MAE
TC-Diffuser w/ IDOL.
18.73 19.53 40.82 74.21 1,21 0.81 1.66 2.47 0.73 0.37 0.91 1.31
TC-Diffuser
21.16 25.15 44.47 73.78
1.83 1.35 2.88 4.31 0.96 0.7 1.46 2.2I
STD
TC-Diffuser w/ IDOL
20.55 22.29 39.35 65.85
1.81 1.16 2.44 3.69 0.99 0.57 1.42 2.02
Scatter plot of MI(PIDv, Yv)
Scatter plot of MI(PIDp, Yp)
1.5
1.6
Test Samples
Trainset MeanMI 0.721
1.3
1.4
Testset MeanMI = 0.958
MI(PIDv. Yv)
MI(PIDp, Yp)
1.1
1.2
0.9
1.0
Test Samples
0.7
0.8
Trainset MeanMI 0.753
Testset MeanMI 1.247
0.5
0.6
0.40
0.45
0.50
0.55
0.40 0.45
0.50 0.55 0.60
Degree of Concept Shift (task v)
Degree of Concept Shift (task p)
a
(b)
Figure 12:
Validation of task dependency modeling for (a) PID.-Y, and (b) PID,-Yp: Scatter plots of mutual information (MI) used to quantify the adequacy of correlation modeling.
Performance of Invariant learning. Compared with SOTA method DeepTCNet, Figure 5 a)
and [33aa), the estimations of our IDOL (green boxes with underlines) are noticeably closer to the ground truth (red boxes), even under covariate shift. Meanwhile, in Figure (5bb) and 13 b).
IDOL also achieves lower estimation error across different TC instances and attributes with varying distributions, showing its effectiveness under label and concept shifts. These results collectively demonstrate IDOL's robustness to various distribution shifts, validating its capability in physical invariance learning.
C.5 Analysis of Physical Identity
The visualizations and additional analysis results discussed in Subsection 5.4 are provided below:
Figure 12
Scatter plot showing MI vs. concept shift magnitude.
Figure Comparison between real and random dark knowledge graphs on model perfor-
mance (MAE and STD).
Definition Shift Degree. quantitatively measure degree of distribution shift between training and test sets, we define the shift magnitude using the Jensen-Shannon divergence (JSD) between the attribute distributions. Specifically, each TC attributes, we estimate empirical probability density on the training set and the test set via kernel density estimation. The JSD

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M/SV Disviibution K-AANUN
Iree -coe Size D siributice KHAAAA
k3.9
45 kts
71.4
nm
32.1 nm)
19,6 nmi
14.4 nmi
Iroeenzee KIMAUN
EsPrato Lmn
20 nmi
25 mmi
CT
BoOL
Stepps
Tire Stegs
43
HEW DicoRoution SAQUA
Imner oa Size Distnbbu on SAGLA
33.3
nml
SAOLA
BITNFGOTN SAGIA
ER Earaaie
DeeettiCee Mape
25.5 kts
60.4 kts
BDL
IDX
Stepes
5tmps
(a) Sample pairs with Shifted X
(b) Sample pairs with Shifted Y
Figure 13: Estimation performance of wind speed and inner-core size test samples under distribu- tion shifts: (a) Estimation results under covariate shift and (b) Mean absolute errors under label and concept shifts across different TCs and output attributes. Each vertical red box indicates a pair of samples exhibiting distribution shift.
963 hpa
961.9 hpa
977.8
987.1 hpa
62.2
69.8 kts
97.2 kts
34.3
93.8 nm)
89,7 nm
20.5 nm
16.6
hpm
DT
hpa
86.3 nmi
O
81.3 mmi
CompTiMer
25 nmi
12 nmi
DeepiCter
86.5 nmn
hpa
950.9 hpa
86.3
968 hpe
956.5 hpa
6B kts
71.1 kts
105 ktss
94.4
18.7
963 3 hpa
AT O DesSTOke
970.8 hps
104.5
GT DespTCler
CevpTMMe
19.9 nml
14.6 nmi
Sample poirs with Shifted X for
(b) Sumple paits with Shifted X for Y-11
Figure 14: Estimation performance under covariate shift for (a) pressure and outer-core size (p-ro) and (b) wind speed and inner-core size (v-ri). Each vertical red box indicates a pair of samples exhibiting distribution shift.
between the two distributions is then computed and used as scalar measure of the distribution shift:
1
1 (
JSD(P || Q) KL M) KL(Q) M), where M =
(17)
denotes the Kullback- divergence, and P, Q are the estimated distributions for training and test sets, respectively. JSD symmetric and bounded measure, which provides stable metric for quantifying both covariate and label shift degree.
Here, KL( 1)
30

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NEW Disiibution of MiNiOR
MSLP INStribution of WWWA
Irnenge Sie Distrbbution of Mirwook
Outercore Siee strteaggs MWWAA
VSW MANWAA
NAWAR
Soe VANING
Cutenss Size NowtoR
(O0)
Edimuttonn ETTE
Edivation
180
40
120
40
300
49
soriuttion ROINU
HGLP Dicribution KDBUU
Innrccore care Shee Destrizution ADUU
core Size Dietr bution KOBUU
MEDYY HOYNL
KELP
NORMU
DUSE IOIN
Edinatn Err
BOCK
20
19
69
23
60
Figure 15: Estimation performance under label shift and concept shift. Each vertical red box indicates pair of samples exhibiting distribution shift.
D Limitations and Future Work
Despite the promising performance of IDOL., our exploration of physical invariance in the embedding space remains at a preliminary stage. The prior wind field model (e.g., the Holland model) incorpo- rated into the framework has inherent statistical simplifications and limitations. While the proposed correlation-awart information bridge helps compensate for physical correlations not captured by the Holland model, the overall robustness of the model can still be improved. Future work may explore constraining the feature space using more comprehensive and generalizable physical mechanisms, such fundamental dynamical or thermodynamic equations. Incorporating such principles has the potential to further enhance model generalization under diverse and complex distribution shifts.
31


Reviews:
[{"review_id": "PZc94guG6t", "reviewer": "Reviewer_46TP", "summary": "The paper introduces the deep learning model \"IDOL\" to reliably estimate parameters of tropical cyclones (TCs) under domain shift (Fig. 1, out-of-distribution predictions). An CNN-based encoder generates a feature vector from timeseries of infrared satellite imagery which serves as an initial estimator of a multi-variate Gaussian distribution (Fig. 3). This distribution is subsequently adjusted by side-information such as the severity level of the TC (Fig. 3 (a)). Further adjustments stem from a knowledge graph correlating the TC's physical properties such as the fullness, energy ratio, etc. to parameters such as wind speed and pressure information (Fig. 3 (b)). All these \"identity tokens\" model distribution shifts due to shifts in the input imagery and shifts of TC attributes from one TC event to another. The manuscript draws conclusions on the IDOL methodology from experiments with a TC dataset based on \"Digital TC\" with additional extension resulting in a total of 303 cyclone events - each of which  tracked by approx. 80 timestamps over the Western North Pacific (Tab. 3 & Figs. 5/11/12).", "questions": "- The code is not available under https://anonymous.4open.science/r/IDOL-898 as you cited in Question 5, is it?\n- How does your approach compare to predicting TCs from state-of-the-art weather foundation models such as Google's GenCast, IBM's PrithviWxC, or Microsoft's Aurora?\n- Eq. (2): addtional details on $g$ and $\\mathcal{O}_\\text{id}$ in supplementary material, please\n- Question 10: of course, your work may have significant positive impact on society when accurately predicting cyclone attributes for early warning systems! \n- Question 12: Your code will get released under which license?\n- Question 13: In l246-l247 you state: \"the Physical Dynamic TC datasets (PDTC) we constructed\" which I read as you (partially) constructing a new dataset? If not, please clarify and adjust the main text.", "limitations": "N/A", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "# Strength\n\n- clear presentation of work with carefully crafted figures, well motivated intro\n- clean and conistent introduction of math symbols\n- straightforward sections well interconnected including links to corresponding appendices\n\n# Weakness\n\n- abstract language of a very complex pipeline may loose some applied ML scientists on reading, suggestion: add specific example with illustration in appendix and add a high-level description in layman's terms to main manuscript\n- as acknowledged in Question 7, the model performance experiments do not ship with error bars", "was_revised": true, "final_justification": "The authors did adequately respond to my concerns, cf. my corresponding comment. My decision to accept the work stays.", "rebuttal": "First of all, we are pleased to see that the reviewers have recognized the clarity of our presentation. We sincerely appreciate all the valuable suggestions, which have greatly helped us to improve the paper. The reviewer’s comments are shown below in italicized font, followed by our responses in regular font. We hope that our responses address the concerns raised and meet with your approval.\n\n**Comment 1**: *abstract language of a very complex pipeline may loose some applied ML scientists on reading, suggestion: add specific example with illustration in appendix and add a high-level description in layman's terms to main manuscript.*\n\n**Response 1**: Thank you for your valuable suggestion. Indeed, tropical cyclone (TC) estimation refers to regressing multiple TC attributes, such as maximum wind speed, pressure, and wind radii, from satellite-based multi-modal data. To better motivate our method and highlight the underlying challenges, Appendix A of the manuscript provides a detailed overview of the different types of distribution shifts present in TC estimation. In response to your suggestion, we will include a specific example with an illustration figure in the revised appendix to better demonstrate the full pipeline in an intuitive and step-by-step manner. Since figures cannot be shown in the rebuttal box, we do not present them here.\n\n**Comment 2**: *as acknowledged in Question 7, the model performance experiments do not ship with error bars.*\n\n**Response 2**: Thank you for your valuable suggestion. We agree that including error bars is important to reflect the model's stability and reliability. We have now supplemented Table 1 in the manuscript with performance metrics including the mean absolute error (MAE), root mean squared error (RMSE), and standard deviation (STD) across multiple runs. The updated results are shown below:\n\n| Method       | Wind MAE | Wind RMSE | Wind STD | Pressure MAE | Pressure RMSE | Pressure STD | Inner-Core MAE | Inner-Core RMSE | Inner-Core STD | Outer-Core MAE | Outer-Core RMSE | Outer-Core STD |\n|--------------|----------|-----------|----------|---------------|----------------|---------------|------------------|-------------------|----------------|------------------|-------------------|----------------|\n| ADT          | 11.20    | 14.20     | –        | 8.00          | 10.20          | –             | –                | –                 | –              | –                | –                 | –              |\n| MTCWA        | –        | –         | –        | –             | –              | –             | 11.70            | 18.20             | –              | 26.40            | 33.00             | –              |\n| STIA         | 10.70    | 14.41     | 9.67     | –             | –              | –             | –                | –                 | –              | –                | –                 | –              |\n| NS           | –        | –         | –        | –             | –              | –             | 10.50            | 15.51             | 11.44          | 26.35            | 36.12             | 24.71          |\n| TC-MTLNet    | 13.82    | 18.06     | 11.62    | 12.00         | 15.46          | 9.79          | –                | –                 | –              | 31.49            | 42.83             | 29.14          |\n| DeepTCNet    | 8.84     | 11.76     | 7.76     | 8.13          | 10.42          | 5.31          | 8.09             | 13.71             | 11.25          | 25.86            | 33.49             | 21.29          |\n| **IDOL**     | **5.84 ± 0.09** | **7.51 ± 0.13** | **4.72 ± 0.12** | **5.75 ± 0.04**     | **7.12 ± 0.05**       | **4.2 ± 0.07**      | **6.21 ± 0.11**         | **12.05 ± 0.2**         | **10.33 ± 0.19**      | **17.17 ± 0.35**         | **23.45 ± 0.44**         | **15.96 ± 0.49**      |\n\n**Note**: Wind, Inner-Core, and Outer-Core refer to estimation tasks of Wind Speed (m/s), Inner-Core Size (nmi), and Outer-Core Size (nmi) errors, respectively.\n\n**In summary, compared with traditional methods (i.e., ADT and MTCWA) and previous state-of-the-art approaches (e.g., DeepTCNet), the proposed IDOL demonstrates superior capability in handling distribution shifts, achieving both the best and most stable estimation performance.**\n\n**Comment 3**: *About available code.*\n\n**Response 3**: As indicated in Question 5 of the checklist, the code is already publicly available at the location we cited, with the correct suffix \"IODL-A370\". It is possible that the cited text was wrapped in the manuscript and therefore cannot be accessed correctly. Furthermore, we plan to release the code on GitHub under the MIT license in the near future to ensure broader accessibility.\n\n**Comment 4**: *Does your approach compare to predicting TCs from state-of-the-art weather foundation models such as Google's GenCast, IBM's PrithviWxC, or Microsoft's Aurora?*\n\n**Response 4**: Thank you for the valuable review. The proposed IDOL is originally designed for tropical cyclone (TC) estimation. To further demonstrate its transferability and effectiveness under distribution shifts, we adopt TC-Diffuser, the current state-of-the-art (SOTA) model for end-to-end multi-task TC forecasting, as the backbone in a transfer setting. The corresponding results are presented in Table 6 of Appendix C.2 in our manuscript, which demonstrate IDOL’s strong ability to handle distribution shifts, a challenge that is also inevitable in TC forecasting.\n\nSecond, regarding TC forecasting, foundation weather models such as Google's GenCast do not adopt an end-to-end architecture for multi-task TC forecasting. Instead, they forecast TC trajectory and intensity by identifying the cyclone center based on Mean Sea Level Pressure (MSLP) in the predicted atmospheric fields from ERA5 datasets. Due to the massive scale of ERA5 datasets, which require substantial time for downloading and processing, we were unable to conduct direct performance comparisons with the mentioned foundation models on the same TC test cases within the limited rebuttal period.\n\nNevertheless, to further compare the performance of our approach and the foundation weather model, we have supplemented the performance of another publicly available weather foundation model, Pangu (as reported in paper [1]), on comparable TC forecasting tasks, as shown in the following table:\n\n| Model                   | Metric | Traj. 6h | Traj. 12h | Traj. 18h | Traj. 24h | Press. 6h | Press. 12h | Press. 18h | Press. 24h | Wind. 6h | Wind. 12h | Wind. 18h | Wind. 24h |\n|-------------------------|--------|----------|-----------|-----------|-----------|------------|-------------|-------------|-------------|-----------|------------|------------|------------|\n| Pangu                   | MAE    | 42.80    | 44.75     | 50.85     | **65.68**     | 16.00      | 16.50       | 16.70       | 16.90       | –         | –          | –          | –          |\n| TC-Diffuser             | MAE    | 19.39    | 20.83     | 41.82     | 77.41     | 1.24       | 0.84        | 1.85        | 2.81        | 0.75      | 0.43       | 0.93       | 1.38       |\n| **TC-Diffuser w/ IDOL** | MAE    | **18.70**| **19.50** | **40.80** | 74.20 | **1.21**   | **0.81**     | **1.66**     | **2.47**     | **0.73**  | **0.37**    | **0.91**    | **1.31**    |\n\n**Note**: Traj, Press, and Wind refer to forecasting tasks of Trajectory (km), Pressure (hPa), and Wind Speed (m/s) errors, respectively. Additional supplementary experiments comparing our approach with weather foundation models will be included in the revised manuscript.\n\n**In summary, our IDOL is efficient in handling distribution shifts, thus achieving better forecasting performance than the foundation model Pangu.**\n- [1] Zhang, Shiqi, et al. \"TC-Diffuser: Bi-Condition Multi-Modal Diffusion for Tropical Cyclone Forecasting.\" Proceedings of the AAAI Conference on Artificial Intelligence. Vol. 39. No. 1. 2025.\n\n**Comment 5**: *Eq. (2): additional details on $g$ and $\\mathcal{O}_\\text{id}$ in supplementary material, please.*\n\n**Response 5**: In Eq. (2), the function $g$ refers to the proposed estimation heads based on the Correlation-Aware Attention mechanism, while $\\mathcal{O}_\\text{id}$ denotes the modules designed to model task identity tokens by leveraging internal invariant physical correlations to regulate feature distributions.\n\nSpecifically, $\\mathcal{O}_\\text{id}$ comprises the proposed Task Dependency Flow Learning and Correlation-Aware Information Bridge. Additional details will be provided in the supplementary material in future revisions.\n\n**Comment 6**: *In l246-l247 you state: \"the Physical Dynamic TC datasets (PDTC) we constructed\" which I read as you (partially) constructing a new dataset? If not, please clarify and adjust the main text.*\n\n**Response 6**: Yes, the Physical Dynamic TC Datasets (PDTC) is constructed by us. Detailed information and construction procedures of this dataset are provided in Appendix C.1 of the manuscript.\n\n**Comment 7**: *About paper formatting and language.*\n\n**Response 7**: Thank you for your valuable suggestions. We will carefully revise and improve the manuscript based on your comments to further enhance its clarity."}, {"review_id": "Jar1xvmuqu", "reviewer": "Reviewer_gmF3", "summary": "The goal of this paper is to explore prior physical knowledge for improving out of distribution generalization in problems of tropical cyclone estimation. The key contribution is merging physics with machine learning to handle distribution shifts. Evaluation is done on diverse datasets.", "questions": "- Can you show more dynamic use cases in your experiments? In other words, can you simulate for highly changing distribution shifts?\n- Can the proposed approach handle domain shifts?\n- What happens if the model priors are erroneous and/or approximate?\n- How does this approach compare to other invariant representation learning techniques?", "limitations": "Limitations are properly discussed", "rating": 4, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n+ The use of physical priors to improve out-of-distribution (OOD) generalization is timely and important.\n+ The focus on a specific tropical cyclone use case properly grounds the research.\n+ The experimental results are promising.\n\nWeaknesses:\n- It is not clear what happens to the performance is the prior models are approximate or not fully accurate.\n- For the cases of tropical cyclones, it is not clear how often OOD issues must be handled. The scenario does not see overly dynamic.", "was_revised": true, "final_justification": "The authors did a good job in the revision, I think this paper could be accepted if there is room", "rebuttal": "We are pleased that the reviewer recognized the effectiveness of our prior incorporation strategy and the promising experimental results. Moreover, we sincerely appreciate the valuable suggestions regarding experimental demonstrations, which have greatly helped us to revise and improve our paper. The reviewers' comments are shown below in italicized font, and our responses are presented in regular font. We hope that these answers will meet with your approval.\n\n**Comment 1**: *(weakness) It is not clear what happens to the performance if the prior models are approximate or not fully accurate.*  & *(question) What happens if the model priors are erroneous and/or approximate?*\n\n**Response 1**: Thank you for the insightful comment. In our approach, we propose the Prior-aware Approximator (PriorAPP) to incorporate the Holland model as prior knowledge. Since Holland is a classical statistical model in tropical cyclone (TC) research, it is well known that it is not fully accurate. As shown in the first two rows of Table 2 in the manuscript, the task-specific identities ($\\mathbf{id}_\\mathtt{sp}$) are derived based on the Holland model. Therefore, the second row of Table 2 in the manuscript reflects the model’s estimation performance when the prior is not fully accurate. The superior performance of the model with Holland demonstrates both the effectiveness of incorporating physical priors and the robustness of our method to approximate priors.\n\nAs shown in the following table, to further validate the contribution of the prior model and the robustness of our design, we conducted additional experiments under intentionally perturbed prior conditions. Specifically, in the \"*w/ Noisy Prior*\" setting, we inject additional task correlations into the Holland model that are not physically validated in previous research, such as introducing an artificial dependency between inner-core size and outer-core size.\n\n| Method       | Wind MAE | Wind RMSE | Wind STD | Pressure MAE | Pressure RMSE | Pressure STD | Inner-Core MAE | Inner-Core RMSE | Inner-Core STD | Outer-Core MAE | Outer-Core RMSE | Outer-Core STD |\n|--------------|----------|-----------|----------|---------------|----------------|---------------|------------------|-------------------|----------------|------------------|-------------------|----------------|\n| VGG-LSTM           |   10.13 |    13.25 |    8.54 |      7.79 |      10.13 |      6.47 |     8.32 |    13.87 |   11.09 |    28.58 |    37.65 |   24.52 |\n| w/ Prior |    **7.24**|     **9.13** |    **5.55** |      **6.60** |       **8.27** |      **4.97** |     **7.37** |    **13.24** |   **10.99** |    **24.91** |    **33.28** |   **22.07** |\n| *w/ Noisy Prior*   |    *8.54*|     *11.33* |    *7.44* |      *7.58* |       *9.88* |      *6.34* |     *8.1* |    *13.95* |   *11.36*|    *25.84* |    *33.84* |   *21.84* |\n\n**Note**: Wind, Inner-Core, and Outer-Core refer to estimation tasks of Wind Speed (m/s), Inner-Core Size (nmi), and Outer-Core Size (nmi) errors, respectively.\n\n**These results clearly indicate that the model maintains stable and robust performance even under perturbed prior conditions. This suggests that the proposed Prior-aware Approximator, combined with the nonlinear representation power of deep networks, can effectively adapt to approximate and erroneous priors. These supplementary experimental results will be added to the appendix in the revised version.**\n\n**Comment 2**: *For the cases of tropical cyclones, it is not clear how often OOD issues must be handled. The scenario does not see overly dynamic.*\n\n**Response 2**: Thank you for the insightful comment. To assess the extent of distributional shifts in tropical cyclone (TC) estimation, we analyzed the label distributions across all TCs in the training and test sets. Specifically, we compute the Jensen-Shannon Divergence (JSD) between each test TC’s label distribution and that of the training set. A higher JSD indicates a more significant distribution shift. Based on median statistics, we empirically set a threshold of 0.39 to define out-of-distribution (OOD) cases. Our results show that 44% of test samples exceed this threshold, confirming that OOD issues represent a significant challenge in tropical cyclone estimation that warrants further attention and dedicated handling.\n\nMoreover, from a meteorological perspective, the development of tropical cyclone (TC) attributes is inherently dynamic and nonlinear. Their evolution is influenced by internal processes such as eyewall replacement cycles, convective bursts, and variations in structural features like intensity distribution and inner-core compactness [1]. These dynamic behaviors introduce significant variability in TC structure and intensity evolution. As a result, no training set can fully capture the entire spectrum of possible TC states, highlighting the necessity of building models with strong generalization ability under distribution shifts. This is precisely the motivation behind our proposed identity distribution-oriented learning framework.\n- [1] Rojas, B., Didlake, A., & Zhang, J. (2024). Asymmetries During Eyewall Replacement Cycles of Hurricane Ivan (2004). Monthly Weather Review.\n\n**Comment 3**: *Can you show more dynamic use cases in your experiments? In other words, can you simulate for highly changing distribution shifts?*\n\n**Response 3**: Yes, we can show more dynamic use cases in our experiments. However, due to the inability to attach pictures in the rebuttal box, these cannot be displayed here. Nevertheless, as demonstrated in Figure 5 of the main text and Figures 11 to 13 in Appendix C.2, the presented cases already exhibit significant distribution shifts, effectively showing IDOL's capability to handle distribution shifts. Specifically, Figure 5(a) in the main text, Figure 11(a) and Figure 12 in Appendix C.2 highlight sample pairs with distinct TC shape organizations, e.g., a blurred center versus a clear eye shape, which indicates significant input data distribution shifts. Additionally, Figure 5(b) in the main text, Figure 11(b) and Figure 13 in Appendix C.2 illustrate notable label distribution shifts, reflected in entirely different distribution patterns.\n\n**Comment 4**: *Can the proposed approach handle domain shifts?*\n\n**Response 4**: Yes, we believe the proposed approach can handle domain shifts for the following reasons:\n\nFirstly, researches on domain shifts often employ domain-invariant feature learning, using visualizations of stable feature distributions across different domains to demonstrate their methods' effectiveness [2, 3]. This suggests that domain shifts can be partially reflected through feature distribution shifts. Our approach leverages prior knowledge to constrain feature distributions with physical invariance, aligning the goal of modeling invariant task identities with extracting domain-invariant features. The key distinction of our IDOL lies in integrating physical priors into distribution constraints, which we argue enhances generalization learning capability.\n\nSecondly, in invariant learning, features from different domains should be close to each other, which means they will have similar variances. Given that tropical cyclones across different years exhibit unique developmental traits and variable environments, temporal domain shifts are evident. If our model extracts physically invariant identity tokens across these time domains, their statistical variance should remain consistent. As shown in Figure 4(b) of the manuscript, our physical identity tokens display smaller variance across time domains compared to DeepTCNet features, highlighting greater robustness to domain shifts. This improvement supports that incorporating prior physics enables the model to better understand the internal TC dynamics and generalize to unseen, variable environments.\n- [2] Chen, Yang, et al. \"Achieving domain generalization for underwater object detection by domain mixup and contrastive learning.\" Neurocomputing 528 (2023): 20-34.\n- [3] Chen, Haojie, et al. \"Self-supervised domain feature mining for underwater domain generalization object detection.\" Expert Systems with Applications 265 (2025): 126023. \n\n**Comment 5**: *How does this approach compare to other invariant representation learning techniques?*\n\n**Response 5**: In Table 1 of the manuscript, we have already compared the proposed IDOL with other invariant representation learning methods, including classic approaches (e.g., IRM, V-Rex) and recent state-of-the-art (SOTA) methods (e.g., SADE, DirMixE). The results indicate that IDOL outperforms these general invariant learning methods, likely due to the integration of domain-specific knowledge. Moving forward, we plan to include additional invariant representation learning methods in the comparison to enhance the comprehensiveness of the experiments."}, {"review_id": "l89UmM5DWJ", "reviewer": "Reviewer_3jY9", "summary": "The paper presents Identity Distribution-Oriented Physical Invariant Learning framework (IDOL), which is a learning method that addresses different types of distribution shifts for tropical cyclone multi-task estimation.  The framework is diverse enough to handle label and semantic shifts.  The method utilizes proven data-centric approaches and presents comprehensive evaluation.", "questions": "-Is there a way to show visually the split between invariant and variant components?\n-These phenomena change with changing atmospheric and other dynamics. Is there an efficient way to infuse new external variables?\n-How can this framework work in an unsupervised way?", "limitations": "Yes.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths:\n-The architecture is well thought and addresses invariant and variant features.\n-The application of the framework has real-world implications.\n-Comprehensive evaluation shows improvements over existing methods.\n\nWeaknesses:\n-The trade-offs between slight performance over the new architecture are not explained.\n-It is unclear how much ground truth labels (which may not be available) are required for addressing domain shifts.\n-The paper can be strengthened with some considerations on simplification of the architecture to reduce the deployment since this has real word implications.", "was_revised": false, "final_justification": "", "rebuttal": "We are pleased that the reviewer recognized the well-designed architecture and comprehensive evaluations of our work. We also sincerely appreciate the constructive comments on the contribution demonstration, which have been highly valuable in helping us improve the manuscript. The reviewers' comments are shown below in italicized font, and our responses are presented in regular font. We hope that these answers will meet with your approval.\n   \n**Comment 1**: *The trade-offs between slight performance over the new architecture are not explained. -It is unclear how much ground truth labels (which may not be available) are required for addressing domain shifts. -The paper can be strengthened with some considerations on simplification of the architecture to reduce the deployment since this has real word implications.*\n\n**Response 1**: Thank you for the valuable comments. As demonstrated in Table 1 of the main text and Table 4 in Appendix C.2, our proposed method achieves the best estimation performance without increasing model parameters or inference time. Since all multi-attribute labels for tropical cyclones are publicly available, our approach is implemented within a supervised learning framework. By jointly considering the short inference time and low computational complexity of stacked convolutions, IDOL achieves the balance between prediction accuracy and computational efficiency, making it readily deployable in real-world applications.\n\nMoreover, to better understand the model complexity, we analyze the parameter size of the proposed identity modeling modules and the feature extraction backbone (two VGG13 networks) in IDOL. The parameter size of them are 9.78M and 266.11M, respectively. This indicates that the identity distribution-oriented learning module itself is lightweight. To further investigate the trade-off between accuracy and efficiency, we replaced the VGG13 backbone with a significantly simpler CNN architecture and retrained the model on the same dataset. The comparative results are presented below:\n| Model           | Parameter Size (Million) | Inference Time (s)  | Wind MAE | Wind RMSE | Wind STD | Press MAE | Press RMSE | Press STD | Inner-Core MAE | Inner-Core RMSE | Inner-Core STD | Outer-Core MAE | Outer-Core RMSE | Outer-Core STD |\n|-----------------------------|---------|---------|---------|-----------|---------|----------|------------|-----------|----------|------------|----------|----------|------------|----------|\n| DeepTCNet    | 270.42  | 4.88  | 8.84     | 11.76     | 7.76     | 8.13          | 10.42          | 5.31          | 8.09             | 13.71             | 11.25          | 25.86            | 33.49             | 21.29          |\n| ***VGG w/ IDOL***     | *275.89*   | *3.18*    | ***5.93*** | ***7.60*** | ***4.75*** | ***5.77*** | ***7.15***  | ***4.23*** | *6.24* | *12.06*     | *10.31* | *17.06* | ***23.26*** | ***15.80*** |\n| *CNN w/ IDOL*       | ***12.88***     | ***2.52***   | *6.32*     | *8.27*      | *5.34*    | *6.08*     | *7.62*       | *4.59*     |  ***6.00***     | ***10.75*** |  ***8.92***     |  ***16.79***     | *23.66*     | *16.67*     |\n\n**Note**: Wind, Press, Inner-Core, and Outer-Core refer to the estimation tasks of wind speed (m/s), pressure (hpa), inner-core size (nmi), and outer-core size (nmi), respectively.\n\n**In summary, as shown in the table, replacing the backbone with a lightweight CNN architecture has slight impact on the performance on overall estimation performance. This demonstrates that the proposed identity distribution-oriented physical-invariant learning framework is not only effective and lightweight, but also robust to changes in the feature extraction backbone, making it highly adaptable and scalable for practical deployment.**\n\n**Comment 2**: *Is there a way to show visually the split between invariant and variant components?*\n\n**Response 2**: Yes, it is possible to visualize the separation between invariant and variant components by first applying dimensionality reduction on them and then using kernel density estimation (KDE) to show visually their distributions across different time domains. However, as the rebuttal box does not support figure attachments, we do not present the result here, which will be added in the revised appendix. \n\nAdditionally, as shown in Figure 4(b) of the manuscript, we provide an intuitive illustration of the invariant and variant components across different temporal domains. In the context of invariant learning, features from different domains should remain close in distribution, which implies similar statistical variances across domains. Taking the components shown in Figure 4(b) as an example, the task-shared identity ($PID_{sh}$) and task-specific identities ($PID_v$, $PID_p$, $PID_{ri}$, and $PID_{ro}$) consistently exhibit low variance across time domains, and are therefore regarded as invariant components. In contrast, the features extracted by the baseline DeepTCNet demonstrate fluctuating variance across different temporal domains, which are regarded as variant components.\n\n**Comment 3**: *These phenomena change with changing atmospheric and other dynamics. Is there an efficient way to infuse new external variables?*\n\n**Response 3**: Yes, there is an efficient way to incorporate new external variables. Since the proposed Correlation-Aware Information Bridge consists of graph convolutions and learnable parameters of a mixed Gaussian distribution, we can effectively infuse new external environmental variables by increasing the number of nodes in the knowledge graph. This enables the model to better learn representations of input data and their latent correlations with output tasks, while applying these effects to constrain feature distributions.\n\n**Comment 4**: *How can this framework work in an unsupervised way?*\n\n**Response 4**: Thank you for your insightful question. We believe our framework can be extended to an unsupervised setting in future work. One potential direction is to perform clustering on the TC convection structures to extract inherent patterns without label supervision. Another promising approach is to leverage contrastive learning between satellite images and descriptive text to align multi-modal features in an unsupervised manner. These adaptations would allow the model to learn meaningful representations without relying on explicit labels."}, {"review_id": "erPkbK856h", "reviewer": "Reviewer_SbdX", "summary": "This work tackles distribution shifts (covariate, label, concept shifts) in tropical cyclone multi-task estimation by proposing IDOL, a physics-guided framework that imposes identity-oriented constraints on feature distributions. Leveraging the Holland wind field model and dark knowledge correlations, IDOL decomposes task dependencies into physical chains (e.g., wind speed → core sizes) via task-specific tokens and bridges input-output distributions via task-shared tokens. Extensive experiments  conducted on multiple datasets and tasks demonstrate the outperformance of the proposed IDOL.", "questions": "1. The task operates under a multi-task learning framework. The network structure involves shared and task-specific components. How do changes in the ratio of shared-to-task-specific components (e.g., the degree of parameter sharing) affect model size and performance metrics?\"\n2. Physical priors (Holland model) are central to IDOL but lack ablation on their necessity.", "limitations": "yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1. Novel Physics-Guided Framework. Proposes IDOL to address simultaneous distribution shifts (covariate/label/concept shifts) in TC estimation using physics-informed identity tokens. This bridges a critical gap between invariant learning and meteorological priors.  \n2. Technical Sophistication: Elegantly integrates the Holland wind field model (§4.1) and dark knowledge correlations (§4.2) to decompose task dependencies and constrain feature distributions.  \n3. Rigorous Experimental Validation.\n\nWeaknesses\n1. Lacks formal proofs for invariance guarantees.", "was_revised": false, "final_justification": "", "rebuttal": "We are pleased that the reviewer recognized the novelty of our physics-guided framework and the rigor of our experimental validation. We also sincerely appreciate the constructive feedback regarding the experimental demonstrations, which have been instrumental in improving the quality of our manuscript. The reviewers' comments are shown below in italicized font, and our responses are presented in regular font. We hope that these answers will meet with your approval.\n\n**Comment 1**: *The task operates under a multi-task learning framework. The network structure involves shared and task-specific components. How do changes in the ratio of shared-to-task-specific components (e.g., the degree of parameter sharing) affect model size and performance metrics?\"*\n\n**Response 1**: Thank you for your valuable comments. In our work, to address various distribution shifts, we propose IDOL, which characterizes the distribution of feature embeddings to model both task-shared and task-specific invariant identity tokens. **Unlike previous multi-task learning frameworks that typically separate shared and specific components from backbone features, our approach adopts physical priors to regulate the distributions of the features to learn physical invariance. Specifically, the original feature distributions are guided by physical priors and are then separately transformed into task-shared and task-specific identity tokens.** \n\nHowever, to explore how different degrees of parameter sharing affect model size and multi-task performance, we conducted supplementary experiments by varying the parameter ratios between task-shared and task-specific identity tokens. Specifically, we define the ratio based on the dimensional size of the corresponding identity token, with configurations including 1:1, 1:2, 1:3, 2:1, and 3:1. For example, a ratio of 1:2 means that the task-shared identity token has half the dimensionality of the task-specific identity token. The results are presented below.\n\n| Model           | Model Size (MB) | Wind MAE | Wind RMSE | Wind STD | Pressure MAE | Pressure RMSE | Pressure STD | Inner-Core MAE | Inner-Core RMSE | Inner-Core STD | Outer-Core MAE | Outer-Core RMSE | Outer-Core STD |\n|-----------------------------|------------------|---------|-----------|---------|----------|------------|-----------|----------|------------|----------|----------|------------|----------|\n| **IDOL (1:1)**              | **1124.31**          | 5.93 | 7.60 | **4.75** | **5.77** | **7.15**  | 4.23 | **6.24** | **12.06**     | **10.31** | **17.06** | **23.26** | **15.80** |\n| 1:2             | 1124.35          | **5.75**     | **7.46**      | 4.76    | 5.78     | 7.17       | 4.25     | 6.36     | 12.24 | 10.45     | 17.95     | 24.74     | 17.02     |\n| 1:3             | 1124.39          | 6.10     | 7.85      | 4.95    | 5.95     | 7.36       | 4.33     | 6.30     | 12.07 | 10.29     | 18.11     | 24.52     | 16.53     |\n| 2:1             | 1124.35          | 5.91 | 7.58      | 4.75    | 5.9     | 7.33       | 4.35 | 6.32     | 12.03     | 10.24     | 17.94     | 24.52     | 16.72     |\n| 3:1             | 1124.38          | 5.93 | 7.69      | 4.89    | 5.79     | 7.14       | **4.17** | 6.13     | 11.81     | 10.09     | 18.79     | 25.34     | 17.00     |\n\n**Note**: Wind, Inner-Core, and Outer-Core refer to the estimation tasks of wind speed (m/s), inner-core size (nmi), and outer-core size (nmi), respectively.\n\n**In summary, as shown in the table, under the given model design and experimental settings, varying the parameter ratio between task-shared and task-specific identity tokens has slight impact on model size and overall estimation performance. This is mainly because the proposed identity tokens, even with lightweight configurations, are sufficient to impose physical constraints on the feature distributions, thereby guiding the model to effectively capture the intrinsic characteristics required for multi-task learning.**\n\nIncreasing the dimensionality of a specific identity token primarily enables more fine-grained representation learning, which may lead to slight variations in task-wise performance, but does not result in significant overall performance gains. This further confirms the effectiveness and efficiency of the proposed identity token design in ensuring consistent and robust multi-task learning.\n\n**Comment 2**: *Physical priors (Holland model) are central to IDOL but lack ablation on their necessity.*\n\n**Response 2**: Thank you for your thoughtful review. To further validate the contribution of the Holland model in modeling task-specific identities, we conducted supplementary experiments in which the priors is replaced with learnable linear layers. The corresponding results, which will be included in the revised manuscript, are presented as follows:\n\n| Method       | Wind MAE | Wind RMSE | Wind STD | Pressure MAE | Pressure RMSE | Pressure STD | Inner-Core MAE | Inner-Core RMSE | Inner-Core STD | Outer-Core MAE | Outer-Core RMSE | Outer-Core STD |\n|--------------|----------|-----------|----------|---------------|----------------|---------------|------------------|-------------------|----------------|------------------|-------------------|----------------|\n| VGG-LSTM (w/o $\\mathbf{id}_\\mathtt{sp}$)      |   10.13 |    13.25 |    8.54 |      7.79 |      10.13 |      6.47 |     8.32 |    13.87 |   11.09 |    28.58 |    37.65 |   24.52 |\n| w/ $\\mathbf{id}_\\mathtt{sp}$ by Holland   |    **7.24** |     **9.13** |    **5.55** |      **6.60** |       **8.27** |      **4.97** |     **7.37** |    **13.24** |   10.99 |    **24.91** |    **33.28** |   **22.07** |\n| w/ $\\mathbf{id}_\\mathtt{sp}$ by Linears    |    8.75 |    11.48 |    7.43 |      7.83 |      10.25 |      6.61 |     7.68 |    13.29 |   10.85 |    25.49 |    33.79 |   22.18 |\n\n**Note**: Wind, Inner-Core, and Outer-Core refer to estimation tasks of Wind Speed (m/s), Inner-Core Size (nmi), and Outer-Core Size (nmi) errors, respectively. $\\mathbf{id}_\\mathtt{sp}$ refers to the proposed task-specific identitiy tokens.\n\n**In summary, the performance of the model with task-specific identities modeled by Holland is better than that of the model with task-specific identities learned by Linear layers. It’s because informing prior can help the model better capture the physical relationships among tasks and the development mechanism of tropical cyclones. Besides, from the table, we can also observe that the model with task-specific identities learned by Linear layers still performs better than the one without task-specific identity modeling, which demonstrates that even without prior knowledge, constraining the feature distribution to model task-specific identities is still effective for mitigating distribution shifts, thus improving the estimation accuracy of tropical cyclones.**\n\n**Comment 3**: *Lacks formal proofs for invariance guarantees.*\n\n**Response 3**: Thank you for the valuable comment, which helps improve the theoretical completeness of our work. At this stage, the proposed IDOL is designed to learn invariant feature distributions in the tropical cyclone (TC) domain from a physical and causal modeling perspective. The learned invariance is empirically validated through comprehensive and rigorous experiments.\n\nWe are actively exploring a more principled theoretical framework to provide formal invariance guarantees. However, the representation of distribution shifts arising from the complex and evolving nature of TCs remains highly abstract and challenging to formulate explicitly. In the future, this limitation may be addressed by further integrating Bayesian Invariant Learning and Physics-Informed Learning, which together can model uncertainty while ensuring physical consistency across diverse environments."}]

Author rebuttal:

Meta-review: This paper introduces IDOL, a physics-guided deep learning framework for tropical cyclone multi-attribute estimation under distribution shifts. The method integrates infrared satellite imagery with physical priors (Holland wind field, dark knowledge correlations) through identity tokens that regulate feature distributions across shared and task-specific components. Experiments on extended Digital TC and a new PDTC dataset demonstrate improved estimation of wind, pressure, and size attributes, and transfer experiments with TC-Diffuser further highlight applicability.

Reviewers converged on the view that the paper is technically solid, novel, and well-motivated, with careful empirical validation and clear positioning in the context of distribution shifts in meteorology. Strengths emphasized include the creative use of physics priors, elegant task dependency modeling, and consistent empirical gains. The main concerns raised were the lack of formal invariance guarantees, questions about the necessity of priors and ablations, and evaluation breadth relative to stronger baselines. The rebuttal was detailed: the authors provided ablations on the role of the Holland model, sensitivity analysis on shared vs task-specific tokens, error bars, and clarified dataset construction. This successfully resolved several reviewer doubts (leading to one upgraded rating), though some reviewers maintained their scores, citing the absence of formal proofs and limited broader validation.

Overall, the consensus after rebuttal and discussion is that the contributions are meaningful, methodologically sound, and supported by substantial evidence. While not flawless, the paper advances physics-informed invariant learning for climate applications, and its ideas are likely to stimulate follow-up work. I recommend acceptance.
Decision: Accept (poster)