UrbanGraph: Physics-Informed Spatio-Temporal Dynamic Heterogeneous Graphs for Urban Microclimate Prediction
Authors: Weilin Xin
Chenyu Huang
Peilin Li
Jing Zhong
Jiawei Yao
Venue: ICLR 2026 Poster (2026)
Keywords: Spatio-Temporal Graph
Heterogeneous Graph
Dynamic Graph
Physics-Informed ML
Urban Microclimate
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)

Abstract: With rapid urbanization, predicting urban microclimates has become critical, as it affects building energy demand and public health risks. However, existing generative and homogeneous graph approaches fall short in capturing physical consistency, spatial dependencies, and temporal variability. \revise{To address this, we introduce UrbanGraph, a framework founded on a novel structure-based inductive bias. Unlike implicit graph learning, UrbanGraph transforms physical first principles into a dynamic causal topology, explicitly encoding time-varying causalities (e.g., shading and convection) directly into the graph structure to ensure physical consistency and data efficiency. Results show that UrbanGraph achieves state-of-the-art performance across all baselines. Specifically, the use of explicit causal pruning significantly reduces the model's floating-point operations (FLOPs) by 73.8\% and increases training speed by 21\% compared to implicit graphs. Our contribution includes the first high-resolution benchmark for spatio-temporal microclimate modeling, and a generalizable explicit topological encoding paradigm applicable to urban spatio-temporal dynamics governed by known physical equations.

Published as a conference paper at ICLR 2026
URBANGRAPH: PHYSICS-INFORMED TEMPORAL DYNAMIC HETEROGENEOUS FOR URBAN MICROCLIMATE PREDICTION
SPATIO- GRAPHS
Weilin Xin--t
Chenyu Huang
Peilin Li
Jing Zhong' Jiawei Yao
National University of Singapore
Tongji University
Tsinghua University
ABSTRACT
With rapid urbanization, predicting urban microclimates has become critical, as it affects building energy demand and public health risks. However, existing gen- erative and homogeneous graph approaches fall short in capturing physical con- sistency, spatial dependencies, and temporal variability. To address this, we in- troduce UrbanGraph, framework founded novel structure- inductive bias. Unlike implicit graph learning, UrbanGraph transforms physical first princi- ples into dynamic causal topology, explicitly encoding time-varying causalities (e.g., shading and convection) directly into the graph structure to ensure physical consistency and data efficiency. Results show that UrbanGraph achieves state-of- the-art performance across all baselines. Specifically, the use of explicit causal pruning significantly reduces the model's floating- poiiii operations (FLOPs) by 73.8% and increases training speed by 21% compared to implicit graphs. Our contribution includes the first high-resolution benchmark for spatio-temporal mi- croclimate modeling, and generalizable explicit topological encoding paradigm applicable to urban spatio-temporal dynamics governed by known physical equa- tions.
INTRODUCTION
Urban microclimate prediction is crucial for urban sustainability and public health (Grant et al. 2025 He et al. 2024). This task represents a broad class of apatio-temporal urban physical field prediction problems, such as urban wind field simulation and pollutant dispersion forecasting. The core challenge of these problems is that the physical state any point in urban space is determined by the collective interactions among numerous and diverse urban entities (c.g.. buildings, vegeta- tion) through vime-narying physical processes such as radiation and convection (Coutts al. [013]] de
et al. 2015, Irmak et al., 2017: Abd Elraouf et al.) 2022). While high-fidelity ahysics-based numerical simulations, such as Computational Fluid Dynamics (CFD), are the stan- dard approach for solving such problems, their immense computational overhead makes them in- feasible for lcrge,scale, time-series prediction tasks. Therefore, exploring computationally efficient data-dríven methods to strike a balance between prediction accuracy and efficiency has become an essential research direction.
Although data-driven methods are promising, they still face challenges in accurately modeling the underlying physical processes. While urban data is spatially discretized, physical interactions are often non-local (e.g., shadows skipping intermediate spaces) and anisotropic (e.g.. directional wind flow). Grid- based models (CNNs) struggle to capture these long-range irregular dependencies with- excessive (Carter al. 20166] Kemppinen al. 2024). Graph Neural Networks (GNNs) offer a more natural framework for modeling the spatial dependencies among urban entities. How- ever, existing GNN-based approaches often lack physical consistency. They typically employ uniform message-passien passggggggnigggggge mechanism that cannot distinguish between different physical processes, such vegetation evapotranspiration and building shading (Zhao al. (20TT). Furthermore, these methods struggle to model temporal variability. They mostly rely on fixed graph structure, which incapable of representing how physical processes evolve in real-time in response to changing en- vironmental conditions. Consequently, there is pressing need in the field for a unified framework capable of explicitly modeling multiple physical processes and their temporal evolution.
"Corresponding author. Equal contribution.

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Published as a conference paper at ICLR 2026
+ Vigittion prepetaapee 21 Selling Cradieg - Dorveduu Celarce repeation a Winatooy
io Sen
Climate
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Burding
LoveCover
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1x2
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Figure I: Overview of the UrbanGraph framework, (a) Spatio- Temporal Pipeline: The model trans- forms rasterized urban features and dynamic weather conditions into high-resolutien microclimate heatmaps via GNN learning. (b) Physics-Informe Topology Construction: Physical laws (e.g,, shading, diffusion) serve hard structural constraints to dynamically prune non-causal edges from the candidate set, constructing a sparse and physically consistent graph topology.
Addressing this gap necessitates a fundamental shift in how we model urhan dynamics. The core challenge lies in designing structure- based inductive bias capable of encoding multiple, inde- pendent, and time-varying physical processes. (i) Standard graph topologies struggle to abstract continuous physical fields (e.g., radiative transfer and fluid dynamics) into a discrete representa- tion without losing critical causal information. (ii) Furthermore, processing such complex graph sequences requires neural architecture that can disentangle the diverse physical interactions. The model must not only handle the dual dynamics of both node features and graph topology but also differentiate between distinct physical operators (e.g.. shading vs. convection), striking a balance between physical interpretability and computational efficiency(Heo et al.).
To address these challenges, we propose UrbanGraph (see Figure [ a framework founded on novel structure-based inductive bias for spatio-temporal modeling. Unlike standard approaches that rely on implicit latent graph learning, UrbanGraph transforms physical first principles into a dy- namic causal topology. By explicitly encoding time-varying causalities Suclitthes-uhhhh solar shading and anisotropic wind convection convection-directly into the graph structure, we impose a hard structural con- straint that forces the model's receptive field to align with the actual physical domain of influence. This explicit causal encoding effectively reduces the hypothesis space, preventing the model from learning spurious correlations from noise. Subsequently, where the heterogeneous pressage-passing mechanism functions as a physical operator approxima- tor, assigning dedicated learnable parameters disentangle distinct physical processes(Schiichknnn (Schlichtkrull et al. 2017).
design spatio-temporal graph network
To summarize, we make the following contributions:
We propose a structure-based inductive bias via dynamic topological reconfiguration. By explicitly encoding time-varying physical processes into the topology of dynamic het- erogeneous graph, this method offers novel pathway for injecting time-evolving causal knowledge into graph learning hard constraint.
We develop dynamic heterogencous graph neural network architecture that efficiently learns from complex graph sequences. Through a specialized heterogeneous message- passing mechanism, the model achieves physical operator decoupling, allowing for precise modeling of distinct environmental interactions. Interactions.ooopeeeeett Comprehensive experiments demonstrate that the architecture achieves state-of-the-ar performance in both prediction accuracy and computational efficiency. Compared to four categories of baselines, it improves accuracy by up to 10.8% (in R²) and efficiency by 17.0% (in FLOPs).
We provide a new, well-validated perspective for modeling urban systems. Results quanti- tatively demonstrate that the heterogeneous and dynamic mechanisms are key to the perfor- mance improvement, contributing gains of 3.5% and 7,1% respectively. Furthermore, the architecture's results multiple target variables show strong generalization capabilities.
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2 RELATED WORK
Classical Microclimate Prediction Methods. Classical methods for urban microclimate prediction can be broadly categorized into two types. The first consists of physics-based simulation models,
such as CFD and ENVI-met (Toparlar et al. 2017 Tsoka et al. 2018 Liu al. 2021 Barros Moreira de Carvalho & Bueno da Silva 2024). These methods offer high physical fidelity but suffer from immense computational overhead, making them impractical for large-scale, long-term time-series prediction tasks. The second category comprises data-driven approaches, including tra- ditional machine learning (Arulmozhi et al. [02]]] et al. 2023) and grid-based deep lcarning models like CNNs (Kumar et al. [202]] Kastner & Dogan 2023 Fujiwara et al.] 2024). While these
methods are computationally efficient, the former struggle to capture complex spatial dependencies, and the latter are constrained by the Euclidean data assumption, making them unable to process the inherently non-structural geometry of urban environments. While generic GNNs (Kipf' & Welling, 2016 Xu et al. 2019; Zhou et al., 2020) offer a framework for spatial dependencies, they lack the inductive bias to abstract continuous fields. UrbanGraph addresses this by explicitly bridging the gap between continuous field dynamics and discrete graph topology.
Physics-Informed Methods. The physics-informed approach incorporates fundamental knowledge into the learning process (Karniadakis et al.) [02T]. This integration is achieved primarily through three bias types. The learning bias uses soft constraints (e.g., PDE residuals in the loss function) but incurs significant training overhead (Shao al.] [023]] Taghizadeh et al.) (025). The observational
biay leverages physics to modify input features (e.g.. by extracting high-level physical indicators) (Pan et al. 2025). A third type is the inductive bias, which imposes hard constraints via network modules graph structures to simulate physical processes (Xue; Qu et al. 2023] Gao et al. 2024).
However, this traditional hard-constraint approach often sacrifices model flexibility. UrbanGraph addresses this challenge by adopting a novel, efficient form of the inductive bias. By imposing physics as a dynamic structural constraint via graph topology, UrbanGraph ensures consistency and interpretability without sacrificing necessary flexibility or incurring the PDE solver overhead associated with the learning bias.
Heterogeneous Graph Methods. In the context of urban physical field prediction, Graph Neu- ral Networks typically simplify the complex urban system into a homogeneous graph (Yu et al.) 2024 Zheng & Lu 2024). However, this simplification limits the model's fidelity and interpretabil- ity. Heterogeneous graphs, which consist of multiple types of nodes and edges, can represent the rich semantic relationships in complex systems (Schlichtkrull et al., 2017 Zhang et al. 2019 Zhao et al. 2021). By designing type-aware message- paaagggg mechanisms, Heterogeneous Graph Neu- ral Networks (HGNNs) have achieved success various tasks, such as quantifying road network homogeneity (Xue et al.) 2022), perceiving urban spatial heterogeneity (Xiao et al.) 2023). learn- ing urban region representations (Kim & Yoon| 2025), predicting the interactive behaviors of traffic participants (Li al. 202I), and uncovering the dynamics of building carbon emissions (Yap al.) 2025). We bridge this gap by leveraging heterogeneity for physical operator decoupling, assigning distinct learnable operators fundamentally different environmental interactions.
Dynamic Graph Methods. In applications for urban physical field prediction, Graph Neural Net- works often rely
static graph topology to represent the spatial relationships between entities (Mandal & Thakur [023] Shao et al., 2024 Xu et al. 2024). However, this assumption conflicts with physical reality, as the scope and intensity of physical processes (e.g.. building shading) are determined in real-time by external environmental factors (e.g., solar position). Dynamic Graph Neural Networks (DGNNs) provide a more realistic framework for this problem (Skarding et al. 2020 Zheng et al., 2024). DGNNs have become a mainstream and effective approach for handling other urban tasks with time-varying interactions, particularly in traffic forecasting, demonstrating their potential in the field of urban computing (Zhao et al. 20200] Xie et al. 2020) Bui et al.) 2022). In these mainstream applications, the evolution of the graph is typically treated as a data-driven, observational phenomenon (Li et al.] 2019b; Jin et al. 2020). In physical field prediction tasks, however, the graph topology (c.g., shading relationships) is explicitly reconfigured at each timestep by exogenous physical first principles. Consequently, propose a First-Principe Driveen approach that utilizes dynamic topological reconfiguration as a causal pruning mechanism to explicitly model time-varying interactions.
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3 PRELIMINARY
Target Variables. The Universal Thermal Climate Index (UTCI) (Jendritzky et al,, 2012) and the Physiological Equivalent Temperature (PET) (Matzarakis al. 1999) represent the isothermal air temperature that would elicit the same physiological stress response. Air Temperature (AT) is the most direct measure of atmospheric heat. Mean Radiant Temperature (MRT) quantifies the radiative heat exchange between the human body and its surrounding surfaces, such as sunlit pavements or shaded building facades. Wind Speed (WS) primarily affects convective heat loss and the efficiency of evaporative cooling from the skin surface. Relative Humidity (RH) determines the efficiency of the body's 's primary cooling mechanism: sweat evaporation.
ENVI-met model. The data in this paper were generated using the ENVI-met model. ENVI- met is high-resolution, three-dimensional, non-hydrostatic numerical model widely recognized for simulating surface-plant-oo interactions within complex urban structures. The model captures the feedback mechanisms among different urban elements by coupling an atmospheric model with de- tailed soil and vegetation models. This enables accurately simulate how solid boundaries ('hard' boundaries), such as building walls, and porous obstructions ('soft' boundaries), such as vegetation canopies, alter local airflow, temperature, and humidity. The fundamental equations governing these processes are detailed in Appendix A
Problem Formulation. We model the urban environment by discretizing Geographic Information System (GIS) data into grid cells, where each cell is treated as a node v E V. The state of the environment represented by a sequence of dynamic heterogeneous graphs {Ge], where the graph at timestep t is defined as Gú = E, IR). Here, V is the static set of nodes, R is the static set of relation types (e.g.. 'covered by shadow from cell'), and & the set of edges that varies with time. The static node feature matrix X IN | explicitly encodes pixel-wise GIS properties: Building Height, Tree Height and Land Cover Type. Additionally, u, represents the dynamic global context, comprising meteorological foreing data: Solar Radiation, Solar Position, Ambient Temperature, Humidity, Wind Speed, and Wind Direction.
For any one of the six target variables, denoted by given a sequence of historical graph ob- servations of length Thist, [G.) (t and the corresponding sequence of context vectors (u -1 the model aims to learn specialized mapping function (+) to predict the values of this specific variable for the next T prod timesteps:
(k) Moo+1 -.. (k) T }= =(())
= ( Thet1 {we] ttto That1 X)
where ((4)) R is the predicted vector for the target variable a futuree timestep T.
Relational graph convolutional networks. RGCNs are an extension of GCNs, initially developed for tasks such link prediction and entity classification. They are specifically designed handle multi-relational graph data. The core idea is to learn distinct feature transformations for different types of relationships between nodes. The forward -pss update of single RGCN layer is defined as:
h (1+1) =
w (1) w n
JENJEN; Cir
where (0)) E (dd is the hidden state of node in the I-th layer, and d() is the dimensionality of the representation at this layer. N; denotes the set neighbors of node o; under relation r E IR. w is a learnable, relation-specife weight matrix that allows the model to distinguish between different types relations, and ( is the weight matrix for the self-connection. o represents an element- wise activation function (e.g., PReLU), and ai, is problem-specife, normalization constant that can either be learned or preset (e.g.. C,, = N.).
4 METHOD
Our proposed UrbanGraph framework consists two core components: a physics-informed graph representation and spatio-temporal dynamic relational graph network. To rigorously evaluate the
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effectiveness of our approach, first generated a large-scale fidelity physical simulations, the detailed generation process and parameter configurations which described in Appendix [B.]] Second, to address the challenge that urban systems exhibit high heterogeneity in both spatial and temporal dimensions, we detail our physics-informed graph repre- sentation in Section [41] which is designed to efficiently capture the underlying physical interactions among different urban elements. Finally, in Section 4.2 we introduce the UrbanGraph architecture, which explicitly leverages the varevngyying relationships between urban elements perform node prediction tasks.
dataset through high-
Vegetation Evapotranspiration
Shading
Convective Diffusion
Semantic Similarity
Internal
Contiguity
Tree
Building
Builing
Wind Direction
0.9
Building
Top-K
Tree
Redius of Influence
Scope of Influence
0.8
D.1
Figure 2: An illustrative overview of the five edge types used in our graph representation. Dynamic edges derived from physical processes like shadowing and wind, while static edges are based on spatial proximity, feature similarity, and object integrity.
4.1 DRYSICS-INFORMEE GRAPH REPRESENTATION
For the graph any given timestep Ge E, R), its edge set & is reconstructed based on the environmental conditions of the current hour. This process is designed to explicitly capture the physical mechanisms that govern the spatial distribution of microclimate factors. The edge set & encodes five distinct types of relationships, which are categorized into two main classes: static and dynamic. Figure 2 provides visual illustration of the construction mechanisms for these five edge types.
Physics-Informer Dynamic Edges. To explicitly model time-varying physical processes, intro- duce three types of dynamic edges whose connections are updated hourly:
SHADING. This edge type encodes directional radiative obstruction. By establishing links based on geometric line-of-sight, we strictly enforce the dependency of the shadowed region on the occlud- ing object. directed edge of type 'shadow" is established from a shading object node e; (building or tree) with height hobj to ground node v; if their Euclidean distance d(u,, ; Uy) less than equal to the shadow length Lshadow,t, and the angular deviation falls within a predefined shadow angle width Asshadow- The shadow properties calculated as follows:
Lshadoowt hooj/ (On(Oeter.))
(3)
Pshadow, ! (Pazimuth, 180 )
(4)
where Oeter,t is the solar elevation angle at timestep t, Pazimuth,t is the solar azimuth angle, and Pshadowwt is the principal direction of the shadow projection.
VEGETATION EVAPOTRANSPIRATIO. This edge type models localized bio-physical interac- tions, serving as a delen-dependent spatial filter. Specifically, a directed edge established from tree node v; any other node vy if their Fuclidean distance d(v;, vty) does not exceed dynamic
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radius of influence, Ractiesty. This radius is calculated based on the global horizontal radiation T:Wh//²²) for the current hour, where Riase: is presettable base radius:
Rectivity, Rhose clip(44/1000, 0.5, 1.2)
(5)
CONVECTIVE DIFFUSION. To encode fluid dynamic anisotropy. this edge redefines topologi- cal proximity using a wind-modulated 'effective distance' metric (Eq. 7 approximating the ad- vection process a discrete graph. The condition for creating this edge is that their "effective distance' d ( Ry), must be less than or equal to a base local radius, Riocal- This effective dis- tance is adjusted by modulation factor, Owindd, which accounts for the wind speed Uwind, and wind direction alignment A0wind:
Owind, 1.0 + Awind cos(D))) (Wwind,t Umax)
(6)
(ess 0z) d(ri, wz)/ awind, Riocat
where Amind is the wind effect intensity coefficient, determining the extent to which wind speed and direction stretch or compress the 'effective connection distance" .Umaz represents the maximum wind speed observed in the study scenario, ensuring the numerical stability of the model. These threshold parameters serve as preset physical upper bounds derived from established urban physies literature, ensuring the graph topology remains within a valid physical domain while allowing the network to learn specific interaction strengths. Detailed parameter configurations for constructing all edge types are provided in Appendix [
Static Semantic Topology. To complement the dynamic physical edges and provide structural redundancy against heuristic imperfections, we introduce two static edge types that capture non- local dependencies and local continuity:
SEMANTIC SIMILARITY EDGES. To capture non-local functional interactions, we construct di- rected edges from each node to its l nearest neighbors in the normalized static feature space. This mechanism allows the GNN to aggregate information from spatially distant but physically similar entities (e.g., similar materials), serving as a backup information pathway.
INTERNAL CONTIGUITY EDGES. To model intra-object energy transfer (thermal inertia) within large continuous bodies, 'internal nodes' establish connections with their eight immediate neigh- bors (Moore neighborhood). This ensures local physical consistency within building clusters or vegetation patches.
4.2 URBANGRAPII ARCHITECTURE
To align neural computation with the encoded structural priors, we designed a dynamic and hetero- geneous architecture for UrbanGraph. As illustrated in Figure 3 the overall architecture comprises four core components: Feature Encoders, a Spatial Graph Encoder, a Spatio-Temporal Evolution Module, and Prediction Head.
Feature Encoders and Spatial Graph Encoder. At timestep f, MLP-encoded global environmen- tal (u(mee) and temporal (ufime) features are broadcast and concatenated with spatial node repre- sentations BRGGN extracted by a three-layer RGCN. This fusion enables the subsequent LSTM to contextualize global forcing within local topologies. Crucially, the RGCN functions as a physical operator approximator: by assigning dedicated weight matrices W,, (Eq, to specific relations (e.g., shading vs. convection), it disentangles complex dynamics into distinct physical sub-processes, structurally mitigating the over-smoothing issues typical of homogeneous GNNs.
Opatio-Tempora Evolution Module. This module responsible for fusing the spatial and global dynamic features and uses Long Short-Term Memory (LSTM) network to model their temporal evolution. We specifically select LSTM over Attention mechanisms to align with the Markovian na- ture of physical transport processes (e.g., heat diffusion), where the future state evolves continuously from the immediate past. Furthermore, unlike coupled spatio-temporal operators (e.g.. LRGCN), architecture decouples spatial interaction from temporal evolution. By resolving the dynamic topology explicitly within the RGCN module, we provide the LSTM with a representation, thereby reducing optimization complexity.

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h12
Prediction
LSTM Layer
LSTM Layer
LSTM Layer
Head
MLP Fuslon Layer
MLP Fusion
Fuslon Layer
Layer
MLP Layer
Layer
RGCN Block
RGCN Block
RGCN Block
RGCN Block
Relationships
R5
Warming.up
Tw1
XW 2h
RGCN Layer
IW My
tanh
fz
Waaz
O
C2
WWss 2h,
Values
h4
Self-lop
RGCN Block
LSTM Layor
Figure 3: Architecture of UrbanGraph. (a) End-to-End Framework: Processes historical data, weather, and dynamic graphs. The top-left grids denote global and cyclically encoded time fea- tures. At each step, RGCN blocks extract spatial features, fused via MI.P before I.STM temporal propagation. (b) RGCN Block: Aggregates multi-relational neighbor messages (R1 R5) with node self-features. (c) LSTM Layer: Captures temporal dependencies.
At each prediction timestep I (from 4 to preed), we concatenate the spatial representation of a node, RGCN with the global environmental embedding, etnu, and the temporal embedding, etime The resulting concatenated vector passed through fusion MLP generate the input feature for the LSTM layer, LSTM This is expressed as:
LSTM B,t
fueion RGCN + e @ e timel)
(8)
The sequence of fused features is then fed into an LSTM layer to model the temporal dynamics. To provide the model with an effective initial state, an MI. projects the spatial features from the initial graph, h RGCN to form the initial hidden state hg- The initial cell state Co is initialized as a zero vector. This expressed as:
ho MLP (utt
RGCN)
Prediction Head. Finally, a separate MLP decodes the last hidden state of the LSTM, LSTM into p.Tpred" a multi-step prediction vector, y.. This generates the predictions for all T Treed future timesteps at once. This is expressed as:
LSTM ÿ. = 10.,..... Ppreal MLP -LPPeed (,,
W.Tyred
(10)
EXPERIMENTS
Dataset. Experiments utilize a high-fidelity ENVI-met dataset where the environment discretized into a 3D grid (4m horizontal, 3m vertical) derived from sighpprecision vector and land cover data (Appendix B.I). While primarily evaluating UTCI, we predict all six variables to demonstrate the architecture s scalability. Temporal graphs follow principles in Section 4.1 The 396 urban blocks

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Published as a conference paper at ICLR 2026
split into Training (70%), Validation (20%), and Testing (10%). Crucially, the test set comprises spatially distinct, unseen blocks to strictly evaluate generalization to new configurations.
Baseline Models. We benchmark UrbanGraph against four state-of-the-art categories: 1) Grid- based Methods (CGAN-LSTM (Isola et al. 2017). Pix2Pix+PINN) to assess graph necessity. where the latter utilizes soft physics-loss, constraints; 2) Static Spatio-Temporal GNNs (GCN/GINE- LSTM, STGGN (Yu et al. 2018). ASTGCN (Guo et al. 2019)) to validate dynamic topology against fixed structures; 3) Generative Graph Models (GGAN-LSTMM GAE-LSTM) compare with latent structure learning; and 4) Dynamic Graph Models (LRGCN (Li et al. 2019a)) to demonstrate the efficiency of our explicit causal encoding over implicit recurrent learning.
Evaluation Metrics. We evaluate predictive performance using Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), and Coefficient of Determination (R²). Computational efficiency is assessed via floating-pon point operations (FLOPs), training time, and inference speed. Models are trained using Adam with Mean Squared Error (MSE) loss augmented by a KL divergence term for GAE and binary cross-entropy for CGAN. Training employs RonPlaaa scheduling and early stopping for robustness.
Model Settings. In the main comparative analysis, our proposed spatio-temporal heterogeneous model configured with learning rate of 0.001, batch size of 8, a hidden dimension of 128 for all layers, a 3-layer RGCN encoder, and a I-layer LSTM. It uses multi-head prediction architecture, and all models are run for 3 independent trials. For the subsequent ablation studies and sensitivity model with hyperparameters optimized by Optuna (Akiba et al. (019),, featuring a hidden dimension of 384 and a single prediction head. More detailed hyperparameter settings are available in Appendix D All experiments were conducted single NVIDIA L4 GPU.
analyses,
RESULT
We evaluate UrbanGraph by strictly benchmarking it against baselines in Section 6.1 and conducting
core ablation studies in Section 6.2 Extended analyses, including additional ablations, hyperparam- eter sensitivity, and computational efficiency, are detailed in Appendix E
6.1
MODEL PERFORMANCE
Dryy Rult: Temp ("))
Tiee Height
Ground Truth (10:00)
Ground Trufh (15 (15:00)
Ground Truth (16:00)
Grruudd Trufh (18:00)
3:
42.5
32-
40.0g
31
37.5
15.0
32.5
Relative Humddty(%)
Land Cover
Prediction (10.00)
Predicton (13:30)
Predidtion (18:00)
Prediction (18:00)
80
40.0
70
37.5
25.0
32.5
60
Wind Speed (mls)
Duiding lleight
Error (10:00)
Erro (15:00)
Errr 118 00)
Error (18:03)
Height ums
23 14 17 -our
Figure 4: Input data configuration and prediction visualization. (a) Dynamic Global Features: Time- varying meteorological forcing (e.g., Wind Speed, Temperature, Relative Humidity). (b) Static GIS Features: Node-level spatial attributes including Building Height, Tree Height, and Land Cover ID. (c) Prediction Results: Visual comparison between Ground Truth, Model Prediction, and Absolute Eror maps.
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By integrating dynamic meteorological forcing with static GIS features, UrbanGraph achieves high- fidelity microclimate prediction across complex urban environments. As shown in Figure 4 visual comparisons confirm that the model accurately captures fine fine-grained thermal gradients, exhibiting strong spatial consistency with ground truth and minimal prediction error. To further substantiate these visual findings, we provide extended qualitative visualizations in Appendix [ which offer additional intuitive evidence of the model's 's ability to capture complex spatial distributions.
T UrbanGraph achieves state-of-the-un performance (highest Rt2 0.8542). Compared to the strongest dynamic graph baseline LRGCN (R²² = 0.8422), UrbanGraph improves accuracy while reducing FLOPs by 73.8% (9.13 10 vs. 3.49 10 10 and training time by 21% (24.5s vs. 31.1s,, validating the efficiency of explicit causal pruning over implicit recurrence. Furthermore, surpassing PiX2Px+PPINN (0.8320) confirms that hard structural constraints offer better physical consistency than soft loss constraints, finding corroborated by ablation studies in Appendix
Table I: Performance and efficiency comparison of different model architectures on the test set.
Category
Model
Flops
Test
Time Cost
Aug
Arg RMSE
Avg
Training (epoclvs)
Inferencels
Grid- based
CGAN-LSTM Px2PIx-PINN
1.10 10
0.7712 4. 0080
1.3450 +. .1175
0.9630 +: 0611
15:3252
1.0099
1.5588 +. 1951
10
1.1485
0.866 +
17:5020
1.3031 .0253
GUN-LSTM
8:28 x 10"
0.8347 + 0009
1.1327 + .443
0.8544 + 00308
28.5321
2,8358
2.8699 + .4516
Static
GINE-LSTM
8.50 102
0,9087 + 0226
1,2045 4 0294
0,9000 + 0190
32.3169
1.4643
3.1731 4 2225
STGNNs
STGON
4.18 10"
0.7880 + 0060
1,2908 + 02287
0.967U + 02443
5.3547
0222
0.2928
0041
ASTGCN
2.06 10
0,8317 + 0048
1,1401 + .234
0.8579 + 0120
25.4908
0.0438
1,2503 + 0284
Generative
GAE-LSTM
10
0,8191
1
0.7968 1:
3,2079
3,6022
4501
Graph
GGANN-LTM
9.44 x 10"
0.8415 + 0004
1.0881 + .406
0.8214 + 0318
42 A678 3.1687
2,6488 + 4073
Dynamic
RGCN GRU
x.12 10"
0,8483 1 0035
1.0682 1. 0080
0,8020 1. 0293
8086
1,3612
2,1640 1. 2133
Gruph
LRGCN
RGCN- Transforree
3.49 x 10
5.09 x
0.8465 1: 0065
0.8422 + 0061
1.0791 +. 0253
1.0880
4: .0521
0.8100 4: 0166
0.8096 1: 01188
31 00.000088000 0.1877
37.6163
= 8825
3,0550 +: .0348
3,3345 +. .1882
URBANGRAPH
9.13 10"
0.85-42 d: 0004
1.0535
d: 0333
0.7664
02:0
24.4823 0.9825
2,6914 4: .1404
The convergence curve (Figure 5 confirms the stability of the model's training process. More- over, the hour-by-hour error analysis (Figure shows that our method consistently maintains the lowest RMSE throughout the entire 12-hour prediction horizon. It demonstrates strong robustness against error accumulation, particularly during afternoon hours (e.g.. 14:00 and 17:00) when climate fluctuations are more pronounced.
Real-world generalization requires dynamic edge rules that can withstand observational noise. We verified this robustness through extensive multi-scale validation (Appendix [B.2.]]. The model achieved high accuracy in both micro-scale calibration on the NUS campus (r > 0.73) and city- scale deployment across Singapore (r = 0.842). This successful generalization confirms that our parameterization strategy remains effective across heterogeneous urban morphologies.
To rigorously evaluate the model's generalization across distinct physical domains, we constructed the UWF3D dataset, which records high-resolution vector fields governed by Navier-Stokes equa- tions. UrbanGraph demonstrates exceptional adaptability to this new physics, achieving high accu- racy (R² > 0.88 for the u-component) and significantly outperforming the Grid-GCN baseline. This successful transition from scalar thermal diffusion to complex vector flow dynamics confirms the ro- bustness of our explicit topological encoding framework in capturing diverse physical mechanisms. Detailed setup and results are provided in Appendix G
6.2 ABLATION ANALYSIS
Table 2: Ablation studies for key mechanisms.
Heterogeneous Graph Mechanism. To validate the importance of modeling diverse physical interactions with distinct relation types, we compare our full model (Base), which uses a heterogeneous graph (RGCN), against a variant that simplifies the graph to be homogeneous (GCN). The results.
(a) Heterogencous.
(b) Dynamic.
Model
MSE
Model
Base
0.8629
1.0976
Base
0.8629
1.0976
Homo
0.8336
1.4275
Static
0,8057
166678
shown in Table 2a] reveal a significant performance degradation when heterogeneity is removed, with the R2 score dropping from 0.8629 0.8347. The performance drop highlights causal entangle-
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b
0.90
0.85
0.86
0.80
0.80
0.75
0.75
0.70
0.70
& 0.65
Model
0.80
0.60
1GGANLSTM BURBANGHAPH
*GONLSTM GGALLTTM
0.55
Test Confidence Test Mean R?
GINELSTM #RGONGRU
#CGANLSTM
0.50
50
150
200
250
300
Epoch
Time
Figure 5: Model performance analysis. (a) Test set R convergence curves for the UrbanGraph model. Shaded areas represent the confidence interval. (b) Hour-by-hour R² comparison between UrbanGraph and baselines on the test set, with error bars indicating standard deviation.
ment in homogeneous graphs where single parameter set fits distinct physical laws. Heterogeneity resolves this by enabling physical operator decoupling.
Dynamic Graph Mechanism. To validate the effectiveness of the dynamic graph mechanism, we compare our model with a variant that uses a static graph (i.e., the same graph structure is shared across all timesteps). As shown in Table 26 disabling the dynamic mechanism leads to significant performance drop in the model (Static), with the score decreasing from 0.8629 to 0.8057. The gain validates vime-igrying causal pruning: unlike static graphs, the dynamic mechanism actively removes physically irrelevant connections (c.g., shifting shadows), thereby reducing optimization difficulty.
Further ablation studies analyzing other key components- such as the contribution of individual edge types, various prediction head architectures, feature fusion strategies, and the effects of explicit edge features-are detailed in Appendix E
7 CONCLUSION
In this paper, proposed UrbanGraph, a physics-informedt dynamic graph framework for microcli- mate prediction. Achieving state-of-the-art accuracy (R² = 0.8542), UrbanGraph outperforms the strongest baseline (LRGCN) with 73.8% reduction in FLOPs and 21% faster training. This result validates the superior efficiency of explicit causal pruning over implicit recurrence.
Furthermore, the UMC4/12 dataset, which we constructed and released, resolution benchmark in this field and will help accelerate the development and fair comparison of new algorithms the future. In summary, UrbanGraph demonstrates the potential of structural pri- ors in bridging the gap between numerical simulation and deep learning. Beyond microclimate pre- diction, our work offers generalizable explicit topological encoding paradigm for dynamics governed by known physical equations.
the first high-
Limitation and Future Work. Our work explicitly encodes predefined physical processes (i.e., prior knowledge) into the graph topology. While this has shown performance advantages, it may oversimplify real physical processes, as might overlook latent relationships present the data that we have not yet modeled and model flcxibility, a critical future direction to develop a Hybrid Topology framework. By augmenting the fixed physical graph with sparse, learnable Residual Graph, future models could uncover unmodeled interaction patterns from data residuals. This approach effectively balances the robustness of engineering rules with the flexibility required to identify new physical mechanisms.
unknown. To address this trade-off between physical consistency
REPRODUCIBILITY STATEMENT
To ensure reproducibility, our code and the UMC4/12 dataset are publicly available at https: 7/gi //github. thub. cww/w///////ooo/oooo wwwi-nnnuuuuee m
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ACKNOWLEDGMENTS
The authors acknowledge the use of large language model for assistance with language editing and improving the clarity of this manuscript.
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Jiawei Xue, Nan Jiang, Senwei Liang, Qiyuan Pang, Takahiro Yabe, Satish V. Ukkusuri, and Jianzhu Ma. Quantifying the spatial homogeneity of urban road networks via graph neural networks. Nature Machine Intelligence, (33:246-257, March 2022. ISSN 2522- 5839. doi: 10. 011884442256-22-00444222 URL http:ttps:/ s42256- 0208660022004488
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A KEY PHYSICAL EQUATIONS IN ENVI-MET
This appendix outlines the key physical equations within the ENVI-met model (Bruse & Fleer 1998) used to generate the dataset for this study.
A.1 MEAN AIR FLOW
The model describes three-dimensional turbulence by solving the non-hydrostatic, incompressible Navier-Stokes equations. The fundamental equations for the mean wind velocity components u,v.w
are as follows:
Du
0pl
pPu
u
+ Km
+ +f(0 - Ug) - -Sa
(11)
0t
dr:
dx
0x²
Ou
dr
0pl
1820'
un
+ Km
- f(u - -Ug) Sa
(12)
0t
dy
(xx?
ow
Ow
Öp'
@
8(2)
+ th Dz.
+ Km
Sw
(13)
Ot
Oz
Ox²
(2)
where p'is the local pressure perturbation,6 the potential temperature, Kn is the turbulent diffu- sivity for momentum, f is the Coriolis parameter, and Su(s) are the momentum source/sink terms induced by elements such as vegetation.
A.2 TEMPERATURE AND HUMIDITY
The distribution of potential temperature 0 and specific humidity g in the atmosphere is described by the advection-diffusion equations, which include internal source/sink terms:
00
00
800
" Oz.
Kn
Qh
(14)
0t
0x
0g us Ds.
0g
0
Kn
Q₂
(15)
Im?
where anand K, are the turbulent exchange coefficients for heat and moisture, respectively, Qn and Q2 are the source/sink terms that couple the heat and moisture exchange processes the surface and with vegetation.
A.3 RADIATIVE FLUXES
The model solves the energy balance for surfaces and walls by calculating the shortwave radi- ation, Rew.net. and the net longwave radiation,Ruu. The shortwave radiation flux at any point, Row (z), consists of direct and diffuse radiation, and accounts for the shading effects of buildings and vegetation:
R swr R2) + sww (2)
R (1 (2) Re as
(16)
where the Rd terms represent the incoming radiation the top of the model, and the a coefficients are reduction factors ranging from 0 to I that quantify the effects of direct radiation amnr diffuse radiation sm and the sky view factor owf-
For the complete set of model equations, parameterization schemes, and numerical solution meth- ods, please refer the original publication.
B HIGH-RESOLUTION SPATIO-TEMPORAL DATASET FOR MICROCLIMATE AND THERMAL COMFORT
B.1 DATASET GENERATION
We constructed the UMC4/12 dataset based on public geospatial data and the ENVI-met model. We selected a typical extreme heat day as the basis for our simulations, using the standard metcoro- logical year data (EPW) from Singapore Changi Airport. To ensure morphological diversity in the
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dataset, employed stratified sampling strategy to select 11 representative km² sites across Sin- gapore. The stratification was based on key urban morphology metrics, and the sample pool covers wide range of urban typologies, from ultra-hit high-density commercial districts to mature residen- tial areas with large parks (see Appendix Table AT). The metrics include Average Building Height (Avg.BH), Green Space Ratio (GSR), and Building Coverage Ratio (BCR).
Table A1: Distribution of morphological and material properties for the 11 selected kkm² sites in Singapore.
Data Index
(vg.BH(m)
GSR
BCR
Pavement%
Smashed Brick %
Loamy Soil%
Deep Water %
13.36
0.021
0.078
0.520
0.095
0.367
0.019
2
19.76
0.055
0.155
0.734
0.062
0.023
3
12.86
0.255
0.219
0.487
0.000
0.471
0.043
23.97
0.184
0.217
0.630
0.043
0.316
0.010
5
10.11
0.116
0.235
0.643
0.026
0.302
0.029
12.01
0.429
0.126
0.260
0.020
0.718
0.002
28.14
0.165
0.242
0.671
0.023
0.286
0.020
8
13.86
0.209
0.338
0.733
0.036
0.220
0.011
9
33.73
0.198
0.108
0.297
0.050
0.554
0.098
10
19.81
0.105
0.109
0.291
0.023
0.222
0.464
16.06
0.444
0.128
0.211
0.062
0.654
0.072
We built the 3D model input files for the ENVI-met simulations by integrating multiple public geospatial data sources. Specifically, resampled and performed 3D voxelization
data with varying precisions: building footprints were extracted from vector- based OpenStreetMap data (Hak- lay & Weber 2008), while the land cover classification (Gaw et al. 2019) and canopy height maps ('Tolan et al.) (024)) utilized Im high resolution. This process generated ENVI-met input files (.NNX) with a uniform horizontal resolution of 4 meters and vertical resolution of 3 meters. To ensure high fidelity, we assigned realistic material properties to different surfaces and building boundaries, and specified corresponding tree species vegetation of varying heights. The detailed material assignments and parameters are provided in Appendix Table A2 and A3 The simulation period covered the hours from 08:00 to 19:00, when urban heat effects are most significant.
Table A2: Class definitions mapping land cover types to surface materials for ENVI-met simulation.
Type
Material
Class
Buildings
Pavement
1
Impervious surfaces
Pavement
1
Non- Non-vtgettted pervious surfaces
Terre battue
2
Vegetation with limited human management (w/ Tree Canopy)
Loamy Soil
3
Vegetation with limited human management (w/o Tree Canopy)
Loamy Soil
3
Vegetation with structure dominated by human management (w/ Canopy) Vegetation with structure dominated by human management (w/o Canopy) Freshwater swamp forest
Loamy Soil
3
Loamy Soil
3
Unsealed Soil
4
Freshwater marsh
Unsealed Soil
4
Mangrove
Deep Water
5
Water courses
Deep Water
5
Water bodies
Deep Water
Marine
Deep Water
5
Figure Al provides a visualization of the primary input data layers- tree height, land cover type, and building height-for two representative sites, illustrating the morphological diversity within the UMC4/12 dataset.
Following the ENVI-met simulation, we generated high-resolution spatio-temporee data for the six target variables. Figure A2 illustrates the simulation output for one of the urban blocks, displaying the evolution of all six variables over the course of the day.
To expand the dataset while efficiently managing computational resources, we systematically parti- tioned the original I km2 simulation results into 250m 250m blocks with 50-meter overlapping
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Table A3: Material properties used in the ENVI-met model configuration.
Material
2g Roughness Length
Albedo
Emissivity
Pavement
0.010
0.3
0.9
Terre battue
0.010
0.4
0.9
Loamy Soil
0.015
0.0
0.9
Unsealed Soil
0,015
0.2
0.9
Deep Water
0,010
0.0
0.9
Tree Height
Land Cover
Building Height
Land Cover
Building Height
Calppay U
bus uaru maak ow)
Figure A1: Visualization of the input data for ten sample sites from the UMC4/12 dataset. For every site, three data layers are visualized: (left in the triplet) Tree Height, (middle) Land Cover Type, and (right) Building Height.
area. This resulted in final dataset containing 396 unique urban blocks. Each block is discretized into 2,500 nodes. For each block, we provide a time series covering a 12-hour interval for 6 key mi- croclimate and thermal comfort variables. Overall, the UMC4/12 dataset offers approximately 11.9 million high-quality spatio-temporal data points for each target variable, enabling the systematic evaluation of spatio-temporal prediction models in complex urban environments.
B.2 REAL-WORLD VALIDATION STRATEGY
To ensure that our physics-informel informed framework generalizes to real-world scenarios, we implemented a two-tier validation process covering both micro-scale fidelity and city-scale consistency.
B.2.1 MICRO-SCALE CALIBRATION WITH FIELD MEASUREMENTS
We conducted rigorous validation of the ENVI-met model based the campus of the National University Singapore (NUS).
network deployed
open rooftop (Reference Point) was selected to provide the driving meteorological inputs. We compared simulation results with measured data from five distributed sensor stations covering diverse morphologies.
As shown in Figure A3 sensor
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09:00
11:00
13:00
15:00
17:00
68
60
PN
UTC
Figure A2: Visualization of the spatio-temporal simulation output for single urban block. Each row corresponds to a different target variable: AT, WS, RH, MRT, PET, and UTCI. Each column represents a specific hour, showing the dynamic evolution of the microclimate from morning (09:00) to evening (19:00).
APEITO
Measurement Locations
100
190 1MM1
50m radius
Temp
g 36 F
Building
Street pavement
Water
80
Measurement boundary
th 8 13 x
Tere
200
1.000
yo (00 WS-Chut 8
200
200
88
26
1:22
WSS-00 CHE
9.32.
2020044
300
600
nun
Reference Point
60
Time
Time
Time
Figure A3: ENVI-met model validation. (a) Map of the validation area and sensor locations on the NUS campus. (b) Comparison of simulated vs. measured diurnal cycles for Temperature, Relative Humidity, and Wind Speed, showing strong agreement (r > 0.73).
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The plots in Figure A3p show the hourly variations of key variables: air temperature, relative hu- midity, and gust wind speed. The results indicate high agreement with measured values (Pearson's correlation coefficient that our simulation setup reliably reproduces key microclimate dynamics in complex urban environ- ments, providing solid physical basis for subsequent data-driven modeling.
0.73, p 0.01), accurately capturing diurnal trends. This confirms
B.2.2 CITY-SCALE CROSS- VALIDATION
To further assess the model's dynamic response capability in the temporal dimension and its gener- alization at the city scale, we introduced the HiGTS dataset (Jian al. 2024), which provides global hourly UTCI at 0.1% x 0.1% resolution.
a
Predicted Linwersel Therml Climate: IndovUUTC))
b
180
130"W
180* 10'N
Overall Performanoe oa (Binned by 0 2'C)
9C
N 38
MAE 1.488"C 1.896'
Agprosatoo Mode Predicted UTTO
46'4"
35
Houryy Gnd Comparison
1:1 Perfect Fit Line
34
0
Singapore
32
45'5
30
28
00'9
136"W
90'E
105'E
28
30
32
34
-30YC
50'C
Reference UTCI from HIGTS("C)
Figure A4: Sityl generalization validation against the HiGTS dataset. The scatter plot com- pares UrbanGraph predictions with HiGTS reference hourly UTCI for Singapore. The results demonstrate a strong correlation (r = 0.842) and low bias, confirming the model's robustness in generalizing real-world urban environments.
We deployed the trained UrbanGraph model to predict the hourly UTCI for the entire Singapore island May 3rd, 2023, and compared the aggregated results with the HiGTS reference values.
As shown the scatter plot in Figure A4 the two datasets show a strong correlation (r = 0.842), with slight systematic underestimation (Bias -0.6670 0.667"C), C). The hourly analysis reveals that pre- diction bias primarily originates from trend discrepancies between the simulation inputs and the reference dataset specific moments (e.g.. abrupt weather changes) rather than flaws in the model itself. This validates that UrbanGraph can effectively generalize to real-world urban data beyond the training distribution.
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C PARAMETER SETTINGS FOR PHYSICS-INFORMER GRAPH REPRESENTATION
This appendix details the key parameters used in the construction of the dynamic heterogeneous graph, as introduced Section 4.1 and provides the rationale for their settings.
C.I PARAMETER RATIONALE
Number of Nearest Neighbors (k). The value is chosen to balance informational richness with computational overhead. Allowing each node to connect to its eight most similar neighbors (con- sistent with the size of a Moore neighborhood) effectively captures non-local semantic information while avoiding the noise that could be introduced by connecting too many distant nodes. As demon- strated in the sensitivity analysis in Section E.2 this value represents the optimal trade-off' between model performance and efficiency.
Maximum Shadow Extent (Rohadon). These upper limits are set to prevent unrealistically long shadows, which can occur at low solar elevation angles, from creating computational redundancy in the graph representation. The maximum shadow extent for buildings (15 grids, or 60m) is larger than that for trees (5 grids, or 20m), which is consistent with their typical differences in height and obstruction capacity an urban environment.
Shadow Angle Width (A@shodow). This parameter expands the theoretical line-like shadow into an area of influence. This accounts for the apparent motion of the sun over an hour and the penumbra effect caused by diffuse light, making the shadow model more physically realistic.
Base Radius of Influence for Vegetation (Rease). The base radius of influence for vegetation is set to 5 grids (20m), based on the typical effective range of local cooling effects from single or small patches of green space reported in existing microclimate research (Kim al.) 2024).
Wind Effect Coefficient (Awind)) As a modulation coefficient, a value of 0.3 is a relatively con- servative choice. It allows the wind field to significantly guide the anisotropy of connections without completely dominating the graph structure, thus preserving the influence of other physical processes.
Maximum Reference Wind Speed (Umaz). This value is used to normalize the actual wind speed. A value of 8.0 m/s was chosen as the reference upper limit as it represents the maximum wind speed historically observed in Singapore.
The boundary parameters for these edges are structural constraints, with their values set by referenc-
ing classical urban climatology studies (Ziter et al. 2019: Dare 2005 Ng 2009 Lin al. 2023) This setting is necessary for explicit physical embedding, as it translates domain knowledge (c.g., the effective decay distance of vegetation cooling) into reliable physical upper bounds for most typ- ical urban environments. Within these bounds, the actual interaction strength is adaptively learned by the network. The robustness of this setup is empirically validated by its successful generaliza- tion to the UWF3D dataset (Appendix G) where these physical bounds yielded high accuracy completely different physical task.
D MODEL IMPLEMENTATION DETAILS AND HYPERPARAMETERS
To ensure fairness, transparency, and reproducibility in our experimental comparisons, this appendix details the implementation specifics and key hyperparameter configurations for our proposed Urban- Graph model and all baseline models.
D.1 BASELINE MODELS AND HYPERPARAMETER SETTINGS
The following table summarizes the key hyperparameters for UrbanGraph and all baseline models used in the different experimental phases. In our comparative experiments, strive ensure a fair comparison by maintaining a similar model scale (i.e., hidden dimension size), such that performance differences primarily originate from the model architectures themselves.
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Table A4: Parameters for Dynamic Heterogeneous Adjacency Construction.
Parameter
Value
Description
Semantic Similarity Links
k
8
The number of neighbors for semantic similarity links.
le-6
small constant to avoid division by zero during feature normalization.
Shadow Links
Rehadow
15
Maximum extent building shadows (in number of grids).
5
Maximum extent of tree shadows (in number of grids).
Dehaadow
25.0
The effective angular width for shadow calculations.
Vegetation Activity Links
Roase
5
The base maximum radius of influence for vegetation activity (in number of grids).
Local Wind Field Links
Awind
0.3
Coefficient that modulates the impact of wind direction on the connection range.
Umar
8.0 m/s
Used to normalize wind speed for calculating the wind modulation factor.
Table A5: Key hyperparameters for the proposed model and all baseline models.
Model
Hidden Dim
Spatial Encoder
Temporal Encoder
Key Hyperparamettess
UrbanGrapp (Ours)
128/384*
RGCN(3)
LSTM(1)
1r=0, 001, batch
optimizer-AAci
weight_deccy==e-55
GCN-LSTM
128
GCN(3)
LSTM(L)
same
GINE-LSTM
128
GINE(3)
LSTM(L)
same
RGCN-GRU
128
RGCN(3)
GRU(L)
RGCN-Transformer
128
RGCN(3)
Transformer
d.model-128, nhead-4,
num.encooer_leyerre22
CGAN-LSTM
128
U-Net
LSTM(1)
1r.G-0. 1r.B-0.0002,
betal-0.5, 1ambda_I1-100
GAB-LSTM GGAN-LSTM
128
GAE(3)
LSTM())
Satent.dim=122 1
128
GGAN
LSTM(L)
Satent_dinn111 1e_9-0.0001,
D=0.0004 betal=0.5
NNot: The hiddlen dimension of UrhonGraph is 128 in the main model comparison phuse. For the ablotion and sensitivity analysis phuses,, it is set based on the results of Optana optimization.
D.2 IMPLEMENTATION DETAILS FOR
BASELINES
To compare our graph-based approach with traditional grid-based methods, we adapted the data input for certain baseline models.
Data Rasterization. For the CGAN-LSTM model, we convert the graph data at each timestep into a 50x50 grid image. Each node in the graph is mapped a pixel in the image, where the pixel value represents key physical feature of the node (e.g., air temperature). The spatial relationships between nodes are implicitly represented by the adjacency of pixels on the 2D plane.
Model Implementation. We employ classic U-Net the generator for the CGAN and Patch- GAN as the discriminator. The model's task to generate the prediction image for the next timestep based on sequence of historical images. During training, combine an L1 loss (with weight \ε1) with an adversarial loss. The feature sequence extracted by the U-Net encoder then fed into an LSTM module for temporal modeling.
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E DETAILED ANALYSIS OF MAIN EXPERIMENTS
E.1 DETAILED ABLATION STUDIES
We conduct series of ablation studies systematically evaluate the contributions the key com- ponents within the UrbanGraph framework.
Physics Injection Strategy. To rigorously isolate the impact of different physics-injection
paradigms, we conducted controlled experiment. We compared three variants sharing the iden- tical backbone architecture (GCN+LSTM)) and hyperparameter settings (e.g., hidden dimensions, learning rate). The only difference lies in the mechanism of physics injection: 1) Baseline: A standard data-driven model without any physical constraints. Soft Constraint: The baseline aug- mented with PDE-based loss functions (PINN approach). 3) Hard Constraint (Ours): The proposed UrbanGraph that encodes physics directly into the graph topology.
Table A6: Quantitative comparison different physics injection strategies.
Strategy
Flops
Test
Time Cost
R
RMSE
Avg MAE
Training (epocivis
Inference/s
Baseline (Data-driven)
8.28% x 10"
0.7846 + 0039
1.29118
.088
0.9963 + 0248
11 11.9636 0.0046
1.0002 = 0082
Soft Constrains (PINN)
28 10"
0.7876 + 1.302
12.0993
0123
Hard Constraint (Ours)
9.13 x 10P
0.8542 1 0044 1.0535 + 0338
0.7866 + 0250
24,4233 0. 9328
2.6914 = 1144
As shown in Table A6 the "Soft Constraint' yields negligible improvement (AR2 R +0.0030) over the baseline. In contrast, the 'Hard Constraint" achieves substantial performance leap (AR? +0.0696). Although constructing the dynamic topology incurs a computational cost (in- creasing training time from 12s to 24.5s), the return investment is significant: The hard structural constraint delivers over 23 times the accuracy gain of the soft loss constraint.
Temporal Modeling. To validate the contribution of the SempoolTemporal Evolution Module (LSTM), we compare the full opatio-Temports model against variant where the LSTM module removed. This variant performs independent predictions for each hour, thereby eliminating tempo- ral dependencies. As shown in Figure in the Appendix, the results demonstrate the effectiveness of temporal modeling. Our model's predictive accuracy (R²) surpasses that of the variant across all prediction hours. Furthermore, Our model exhibits lower variance across multiple independent trials, indicating enhanced model stability.
0.8
0.6
RR Score
0.4
0.2
Single model
Time Series model
0.0
1
2
3
4
5
6
8
9
10
11
12
Figure A5: Hour-by-hour R² score comparison for the temporal modeling ablation study. The 'Time Series model' (our full UrbanGraph model) is compared against the 'Single hour model' variant without the LSTM modulc). The results demonstrate that explicitly modeling temporal dependen- cies leads to superior performance across the entire 12-hour prediction horizon. Error bars represent the standard deviation from multiple independent trials.
Fusion Mechanism. We compare three different strategies for fusing the spatial node representa- tions with the global dynamic features: Concatenation Fusion, Multiplicative Fusion, and Attention
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Fusion. As shown in Table A7 the simple concatenation strategy achieves the best performance across all evaluation metrics. This approach not only achieves the highest accuracy but also has the lowest computational load (FLOPs) and the fastest training and inference speeds.
Table A7: Comparison of different fusion strategies for combining spatial and global features. Best results are in bold.
Test
Time Cost
Strategy
Flops
Avg
Avg RMSE
Training (epoch/s)
Inference/s
Attention
9.42 x 109
0.8491 + .0052
1.0675 + .0254
27.5568 + 1.0310
3.1741 + +1151
Multiplicative
9.30 109
0.8515 .0020
1.0623 + .0317
25.9573 1.4409
2.8543 .2100
Concatenation
9.13 109
0.8542 .0044
1.0535 + .0388
24.4823 0.9323
2.6914 = .1404
Prediction Head Architecture. We evaluate two strategies for multi-step prediction: a Single-Head architecture, which uses single shared prediction head generate predictions for all 12 hours at once from the final hidden state of the LSTM; and Multi-Head architecture, which employs a separate prediction head for each future timestep. The results in Table show show that the single-head strategy performs better in terms of both predictive accuracy and computational efficiency (FLOPs). For relatively short prediction horizon, the single-head architecture can more effectively leverage the final hidden state, which encodes information from the entire sequence, for joint prediction, thereby avoiding cumulative errors.
Table A8: Comparison between Single-Head and Multi-Head prediction architectures on the test set.
Test
Time Cost
Strategy
Flops
Avg R²
Avg RMSE
Training (epoch/s)
Inference/s
Multi-Head
9.21 10"
0.8542 + .0044
1.0535 + .0338
24.4823 + 0.9323
2.6914 1404
Single-Head
9.13 x 10
0.8603 + .0008
1.0190 + .0421
21.5903 1 3.1143
2.4785 + 5019
Warming-up Mechanism. We introduce warming-up mechanism that initializes the LSTM's hidden state using the spatial features from the initial graph. This aims to provide temporal prediction task with a starting point that rich in physical priors. As shown in Table A9 removing this mecha- nism and using random initialization instead (the NP1 model) leads to noticeable decline in performance, with the R² score dropping from 0.8629 to 0.8510.
Table A9: Effectiveness of the
Warming-up up Mechanism.
Model
MSE
Base
0.8629
1.0976
NP1
0.8510
1.1526
Node Feature Augmentation. We compare the effects of using different node features input. As shown in Table A10a the model using aggregated neighbor features (Base) achieves the best per- formance. The model without any spatial information enhancement (M3) performs worse than the Base model. However, performance degrades when using only static topological features (such as degree centrality) or when combining them with aggregated neighbor features. This result suggests that introducing additional topological features in our task may add redundant information or noise, thereby impairing the model's predictive accuracy.
Input Feature Ablation. To verify the necessity of each input feature, we conduct a systematic ablation on the static node features u statie the temporal encoding features utime, and the global climate features u As shown in Table A10b) the baseline model (Base) that includes all three feature types performs the best. Removing any single feature type leads to performance drop. Notably, the model using only static node features (F1) shows the most significant degradation, with its R score dropping from 0,8629 to 0.7179.
Edge Types. To evaluate the specific contribution of each of the five proposed physics-informed and semantic edge types, we conduct an ablation study by systematically removing one edge type at time. As shown in Table All the base model, which includes all five edge types, achieves the best performance. Removing any single edge type results in a decline in the model's predic- tive accuracy, demonstrating that both the physics-informed and semantic edges provide valuable
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Table A10: Ablation studies for feature augmentation and input feature types.
(a) Data Augmentation.
(b) Input Features.
Model
Neighbor
Structure
R²
MSE
Model
R-
MSE
MI
0.8347
1.2798
M2
0.8462
1.2181
F2
0.8529
1.1423
0.8507
0.8519
1.1495
Base
0.8629
1,99766
Base
0.8629
1,0976
inductive biases for the model. Notably, removing the Local Wind and Shadow edges leads to the most significant performance degradation, which underscores the importance of explicitly modeling time-varying physical processes. Furthermore, the performance drop caused by removing Similar- ity edges confirms the necessity of capturing non-local spatial interactions in urban microclimate prediction.
Table All: Ablation study on different edge types. The checkmark (v) indicates that the corre- sponding edge type is included in the model.
Mudel
Tree activity
Similarity
Shadow
Local Wind
Internal
MSE
0.8504
1.1534
E2
0.8531
1.1568
E3
0.8238
1.4960
1.4341
E5
0.8425
1,2403
Base
0,8629
1.0976
E.2 SENSITIVITY AND COMPUTATION PERFORMANCE EVALUATION
Sensitivity to the Number of Neighbors (k). To investigate the model's sensitivity the number of neighbors, k, used in constructing the Semantic Similarity Edges, we conducted tests with different values of As shown in Figure[A6j. the model's performance (R?) improves as increases, reaching peak at k=8 before exhibiting minor fluctuations. Considering that larger k increases graph density and computational cost, we select the 'elbow point' of the performance curve, k=8, as the optimal configuration. The model is not highly sensitive to the choice of k within a certain range, demonstrating good robustness.
Sensitivity to Training Data Volume. To evaluate the model's data efficiency and generalization capability, we performed sensitivity test on the amount training data. We reserved a fixed 10% test set and incrementally increased the training set size using fractions of the remaining data, starting from 2%. As illustrated Figure A6p, the results reveal a significant positive correlation between model performance and data volume, with all accuracy metrics improving substantially as the amount of data increases. However, the model also exhibits a clear diminishing returns effect: the majority the performance gain occurs before the training data volume reaches 40-60%, after which the performance curve begins to plateau. Performance tends to saturate when approximately 90% of the available training data is used.
Computational Performance Evaluation. To assess the model's computational overhead in ur- ban scenarios of varying complexity, we analyzed the relationship between the graph's structural properties (i.e., the number of nodes and edges) and computational costs (inference time and peak GPU memory usage). The analysis (Figure A7).d) indicates that both inference time and memory consumption show positive correlation with the number of edges in the graph (with Ra values of 0.5976 and 0.4627, respectively). An interesting finding is that computational cost is negatively correlated with the number of non-building nodes (Figure A.c.). This suggests that the number of non-building nodes can serve as an inverse indicator scenario's 's structural complexity: scenes with open spaces (e.g.. parks) typically have sparser graph structures and therefore more computationally efficient. Furthermore, the linear relationship between cost and graph complexity suggests the feasibility of applying the model to larger areas.
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0.85
0.860
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1.3
0.864
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R 0.97
0.70
0.852
1.1
0.65
12 16
40
100
K
Sampel (%)
Figure A6: Sensitivity analysis the model. (a) Model performance (R2 and RMSE) on the test set versus the number of neighbors, k, for constructing similarity edges. The performance peaks at k=8. (b) Model performance as function of the percentage of training data used. Performance gains show diminishing returns and begin to saturate approximately 90% of the data.
a
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5.8 5.8
5.0
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Num of Non-Bulding Nodes
Num of Non-Buiddng Nodes
Num of Average Edges (10")
Num of Average Edgas (10")
Figure A7: Computational performance analysis. inference time peak GPU memory and the average number of non-building nodes per window. (b) show the positive linear correlation between computational costs and the average number of edges per window.
(a) illustrate the negative correlation between
Scalability Test on City-Scale Grids. To verify the feasibility of deploying UrbanGraph large- scale urban grids (as queried regarding 50k-100k nodes), we conducted stress test on large urban region. The region was partitioned into 36 spatial windows, comprising total of approximately 90,000 nodes. The total edge reconstruction time for the entire 13-hour sequence was recorded at 39.56 seconds (using 16 CPU workers). This empirical evidence confirms that the computational cost for city-scale edge reconstruction is negligible compared to physics-based simulations, and the divide-and-conquer strategy effectively ensures scalability.
E.3 EDGE FEATURES AND WEIGHTS
To explore the potential of encoding richer physical information into the graph structure, de- signed and evaluated an explicit scheme for edge attributes and edge weights the early stages of research. As mentioned in the main text, final model did not adopt this design, experimen- tal results showed that introducing this explicit information did not lead to significant performance improvement for the UTCI prediction task. This section details our initial exploratory design.
EDGE ATTRIBUTE VECTOR. In our initial design, each edge eij E & in the graph carried a 5- dimensional attribute vector a;j E R to encode rich spatio-temporal physical information. This vector composed of the following components:
Fuclidean Distance d(v;, uy): The straight-line distance between the nodes.
Relative Displacement (Ar, Ay): The difference in position in the grid coordinate system.
Wind Alignment (cos( (cos(A) )) The cosine of the angle between the edge vector and the current hour's wind direction, used to quantify the convective influence of the wind.
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Edge Type ID: A categorical ID indicating which of the five relationship types the edge belongs to.
E.4
EDGE WEIGHT CALCULATION
To quantify the interaction strength between different nodes, we designed a dynamic scheme for calculating edge weights, Wij- All edge weights start from a base value Whase (set to 1.0) and are dynamically modulated according to the following rule:
Wij = Wbase/ (1 + À d(ve, U5)/ 3 3y
(17)
The specific settings for each modulation factor are as follows:
Distance Decay (A): All edge weights decayed based their Euclidean distance. To better distinguish between non-local and local effects, we set a smaller distance decay fac- tor, Asim (set to 0.005), for semantic similarity edges, while other edges based on physical proximity use larger decay factor, Aphys (set to 0.01).
Physical Process Enhancement (5): Weights are further modulated by dynamic physical processes. For example, a shadow edge determined to be actively casting a shadow in the current hour has its weight multiplied by enhancement factor, Sshadow (set to 1.2).
Source Node Attribute Influence (7): Weights are also influenced by the attributes of the source node. For instance, the weight of a vegetation activity edge is positively affected by the height of its source tree, htrees controlled by the modulation factor "iree (set 0.2).
Although this scheme is theoretically more physically interpretable, our ablation experi- ments showed no improvement in predictive performance when introducing explicit edge at- tributes (E) and edge weights (EW) compared to a simpler model that only uses edge types (results shown in the table A12 This suggests
Table A12: Ablation study explicit edge at-
tributes (E) and edge weights (Ew).
Model
E
Ew
R²
MSE
0.8629
1.0976
EF
0.8530
1.1513
that, for the UrbanGraph architecture and the UTCI prediction task, the model can effectively and implicitly learn the strength of these inter- actions from the dynamic graph topology and node features, without needing explicitly injected edge weights and attributes.
E.5 MULTI-TASK VS. SINGLE-TAS LEARNING
To evaluate whether shared representations could enhance performance, compared the proposed Single-Task Learning (STL) frame- work (where separate model is trained for each variable) against a Multi-Task Learning (MTL) variant, which Graph encoder followed by variable-specific heads. As shown Table A13] STL consis- tently outperforms MTL, with the performance drop being particularly pronounced for vari- ables with distinct physical mechanisms (e.g.. Wind Speed vs. MRT). We attribute this to negative transfer arising from the inherent heterogeneity of the underlying physical processes: fluid dynamics (governing Wind Speed) and radiative trans- fer (governing MRT) require learning distinct and often confficting spatial dependencies. Forcing a shared encoder to capture these diverse physical laws dilutes the specificity of the node embeddings, confirming that independent training ensures each model specializes in the specific physical operator relevant to its target.
Table A13: Performance on target variables.
Target
MIL
UTCI
0.8629 + .696
0.7460 + .0800
shared Urban-
AT
0.5650 = 1324
0.4080 + .1382
WS
0.7500 1 .0178
0.4794 1 .0315
+
RH
0.5159 1 2039
0.4105 1 .2667
1.
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F GENERALIZATION AND VISUALIZATION
PREDICTION RESULTS ON DIFFERENT ARCHITECTURES
To provide qualitative assessment of model's performance, this section presents visual com- parison the spatio-temporal prediction results between UrbanGraph and the four categories of baseline models. Each figure displays the ground truth, the predictions from UrbanGraph and rep- resentative baselines, and their respective prediction error maps (Prediction Ground Truth) for selected test scene different hours of the day. White areas in the maps correspond buildings. which are excluded from the analysis.
Figure A9 compares UrbanGraph with non-graph and homogeneous graph baselines, which repre- sent fundamentally different approaches to spatial modeling. Figure A10 provides comparison against generative graph models and temporal variants, assessing different graph learning strategies and sequence modeling components.
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GroundTruth
UrbanGraph
MRT
Error
GroundTruth
Phys elgg Crevatent se Hirr PD vakue
UrbanGraph
PET
12
Error
20
Figure A8: Qualitative prediction results for thermal comfort indices. This figure visualizes the performance of UrbanGraph on MRT and PET. Similar the previous figure, each block compares the ground truth, model prediction, and the resulting enror map, demonstrating the model's strong performance on composite indices.
F.2 PERFORMANCE ON MULTIPLE TARGETS
The robustness of our physics-informed informed representation and the UrbanGraph architecture is validated by the consistent performance five remaining target variables (Table A13). where all R² scores
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Hour 9:00
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Hour 19:00
Ground
UrbanGraph
Ours
Error
CGANLSTM
Non-Graph
Error
GONLSTM
Error
Homo-Graph
GINELSTM
Error
Figure A9: Visual comparison against Non- Graph (CGAN-LSTM) and Homogeneous Graph (GCN- LSTM, GINE-LSTM) baselines. Compared to the grid-based CGAN-LSTM. UrbanGraph better captures fine- greiggained spatial details. Unlike the homogeneous models that treat all interactions uni- formly, UrbanGraph's 's heterogeneous approach leads to more physically consistent predictions and lower overall error.
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Hour 19:00
Ground
GGANL STM
Error
Generative Graph
GAELSTM
Error
RGONGRU
Temporal Variants
Error
RGCNTrans
Hod 2007
Error
Figure A10: Visual comparison against Generative Graph (GGAN-LSTM, GAE-LSTM) and Tem- poral Variant (RGCN-GRU, CGCN-Transformer baselines. UrbanGraph's physics-informed, de- terministic graph construction (shown in Figure A9 avoids the higher errors seen in generative approaches. Furthermore, its LSTM component proves more effective at capturing long-term de- pendencies compared to the GRU and Transformer variants.
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exceed 0.5 and MRT/PET performance nearly matches UTCL. Qualitative generalization capabilities for these five variables are visualized in Figures A8 A1l
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Figure A1l: Qualitative prediction results for microclimate variables. This figure visualizes the performance of UrbanGraph AT, WS, and RH. For each variable, the top row shows the ground truth, the middle row shows the model's prediction, and the bottom row displays the prediction error map across different hours.
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G GENERALIZATION ON VECTOR FIELDS
G.1 DATASET GENERATION AND PHYSICAL SETUP
To evaluate the model's generalization on vector fields, we utilized the UWF3D dataset. This dataset consists of high-fidelity CFD simulations generated using the open-source platform OpenFOAM, with the following specific configurations:
Physical Modeling. Unlike the thermal dataset generated by ENVI-met, UWF3D solves the steady- state Reynolds- Averraged Navier-Stokes (RANS) equations coupled with the standard c turbu- lence model. This setup captures complex non-linear fluid dynamics such flow separation, cavity circulation, and wake turbulence.
Geometric Configuration. The simulation domain represents 540m x 540m idealized urban block. Building geometries are randomly generated via parametric design (Rhino/Grasshopper) based on real-world prototypes, ensuring morphological diversity.
Boundary Conditions. The inflow boundary follows a logarithmic wind profile with a reference velocity of 10m/s 10m height. The simulations operate high Reynolds numbers (Re 107 10*), ensuring Reynolds independence consistent with real-world urban aerodynamics.
Mesh and Solver. The computational domain is discretized using an unstructured mesh containing approximately 2 to million grid points per sample. This high spatial resolution allows for precise prediction of the 3D velocity vector field (u, v, w) at each spatial node.
a
100m
540m
Urban wind
Indoor natural ventilation
Pedestrian wind safety
OFAMV
Top
Unstructured
Inlet
Wall
Outlet
Inlet
Symmetry
Outlet
Turbulence
DE
M.
v(Z)
(.
CII
LISE
Monttaring
Building height (m)
(m/s)
(m/s)
w (m/o)
Figure A12: Visual overview of the UWF3D dataset configuration and simulation samples. The figure illustrates the diversity of parametrically generated urban geometries and their corresponding high-fidelity CFD velocity fields. The simulations, solved via RANS equations with the turbulence model, explicitly capture complex acrodynamic phenomena such as flow separation and wake recirculation around varying building morphologies.
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G.2 MODEL SETUP AND COMPARATIVE IMPLEMENTATION
To rigorously validate the framework's ' adaptability, we established benchmark between the pro- posed UrbanGraph and Grid-GCN baseline. Given that this task involves purely fluid dynamics without thermal radiation or biological processes, we adapted the graph construction rules to focus exclusively on the Navier-Stokes mechanisms.
G.2.1 BASELINE: GRID-GCN
The Grid-GCN serves control group representing the standard computer vision approach applied to physical fields.
Graph Construction. It constructs homogeneous lattice graph the 64 x 64 sampling grid. Connectivity is defined strictly by Euclidean proximity using the Von Neumann neighborhood (con- necting only 4 immediate neighbors: up, down, left, right).
Mechanism. Crucially, this topology forces isotropic message passing, where features are aggre- gated uniformly from all spatial directions regardless of the local wind vector. This effectively treats fluid prediction as a generic image smoothing task, ignoring the directional nature of momentum transport.
G.2.2 URBANGRAPH
In contrast, UrbanGraph utilizes its heterogeneous graph capabilities encode specific fluid dy- namic operators. We mapped the edge types from the main paper to this aerodynamic context:
Advection Edges. To simulate momentum transport, construct directed edges searching up- stream along the dominant wind vector. This explicitly models the advection process, allowing the network transport flow features from upstream nodes to downstream ones (mimicking the semi- Lagrangian scheme).
Wake Edges. To capture non-local turbulence and pressure drops behind obstacles, construct wake edges that connect building boundary nodes directly to their leeward wake zones. This is topologically analogous to the "Shading" edges in the thermal task (both representing directional obstruction effects), enforcing physical consistency in cavity circulation regions.
G.2.3 PERFORMANCE ANALYSIS
Quantitative results in Table A14show that UrbanGraph achieves an 12 of 0.8886 for the t-component, significantly out- performing the Grid-GCN. The perfor- mance gap highlights a critical physical in- sight: Isotropic aggregation (Grid-GCN) in- evitably over-smooths the vector field, fail- ing to maintain sharp velocity gradients at separation points. Conversely, UrbanGraph's 's anisotropic inductive bias successfully reconstructs complex flow patterns, such as flow separation and wake recirculation, by explicitly routing infor- mation along physically valid flow paths.
Table A14: Performance comparison velocity tor components (R²).
Model
GrddGGNN
0.7827 0.0100
0L6885 + D.0166
0L6858 0.0141
UrbunGrraph
0.0004
34


Reviews:
[{"review_id": "8rr2hCuIOy", "reviewer": "Reviewer_nd8D", "summary": "The paper introduces UrbanGraph, a physics-informed framework to predict urban microclimate. UrbanGraph integrates five physical representations including veg. evapotranspiration, shading, diffusion, similarity and internal continuity and encodes them using a relational GCN. Then, the spatial and temporal contexts are modeled using MLPs and LSTM, along with the physical constraints to predict future urban microclimate. Experiments are conducted using the simulation dataset from ENVI-met, and seven baselines are used to demonstrate the improved effectiveness and efficiency of the proposed model.", "questions": "It will be helpful if the authors can clarify what the technical contributions are for the edge designs in Figure 1.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "S1: High-resolution urban simulations and modeling is an interesting and timely topic for digital twins.\n\nS2: Examples are well prepared and help present the main idea and workflow.\n\nS3: Experiments are conducted using 7 different methods showing improvements.", "weaknesses": "W1: The physics-informed contribution uses different physical representations like shading. This is reasonable but the methodological novelty is not well explained. It seems more to be an application that uses basic physics knowledge to define the graph and the physics is specific to this problem.\n\nW2. The experiments feel like an ablation study. More standalone and recent methods should be included for comparison. It uses only a single dataset or comparison. Using additional datasets can help evaluate the generalizability of the model.\n\nW3: In the appendix, the tree and building layers are the same for the second row in Figure A1. This raises concerns about data correctness.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "BeOAzPHwKh", "reviewer": "Reviewer_jFx8", "summary": "This paper proposes UrbanGraph, a framework for urban microclimate prediction that integrates physics-informed, dynamic, and heterogeneous graph neural networks. The key idea is to explicitly encode time-varying physical processes, such as shading, vegetation evapotranspiration, and convective diffusion, into the topology of a dynamic heterogeneous graph. This graph structure is then processed by a spatio-temporal model combining a Relational Graph Convolutional Network (RGCN) for spatial dependencies and an LSTM for temporal evolution. Moreover, the authors also curate the UMC4/12 dataset, a high-resolution, physics-based simulation benchmark. Empirical experiments demonstrate that UrbanGraph outperforms various strong baselines.", "questions": "1. How expensive is rebuilding 3 physics-driven edge sets every hour for a large city-level grid (say 50k–100k nodes)? Or have you considered or tested any strategies to manage this complexity?\n2. You report on six target variables (UTCI, PET, AT, MRT, WS, RH). Are they trained with a single shared UrbanGraph and separate heads, or trained separately per target (Eq. (1) suggests separate mappings)? If separate, could multitask training further boost R² through shared spatial embeddings?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "1. The problem is well-motivated.\n2. The proposed idea of encoding observational/structural bias directly into the topology, i.e., physics-informed edges rather than physics-informed losses, is principled and technically sound.\n3. The dataset contribution is valuable to the community.\n4. The paper is well written.", "weaknesses": "1. The method is evaluated on a CFD-style simulator (ENVI-met) under several urban configurations. This is fine for an anonymized submission, but the key claim is physics-informed generalization to realistic urban microclimates. Without any real-world/field-sensor validation, it’s hard to tell if the hand-crafted dynamic edge rules are robust to noisy or incomplete inputs. Would it be possible to deploy on real city data (even small-scale)?\n2. The model uses an LSTM as the temporal evolution module. They compare to GRU and Transformer, but the argument for LSTM as the final choice is mostly empirical. Given that the graph itself is dynamic, a temporal attention or cross-time graph operation might better exploit the structured changes in edges.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "h7aam7Q0Be", "reviewer": "Reviewer_dxkG", "summary": "This paper presents UrbanGraph, a physics-informed framework for urban microclimate prediction using dynamic heterogeneous graphs. The authors propose encoding multiple physical processes (shading, vegetation evapotranspiration, convective diffusion) as different edge types in a heterogeneous graph structure, where edges are dynamically reconstructed at each timestep based on environmental conditions. The framework combines Relational Graph Convolutional Networks (RGCN) for spatial feature extraction with LSTM for temporal modeling. The authors evaluate their approach on UMC4/12, a new dataset containing 11.9 million high-resolution spatio-temporal data points generated from ENVI-met simulations across 11 urban sites in Singapore. The results show improvements of up to 10.8% in R² and 17.0% reduction in FLOPs compared to baselines.", "questions": "1 The ablation studies and baseline comparisons effectively demonstrate the superiority of UrbanGraph over simpler models like standard GCNs (proving the value of heterogeneity) and non-graph models like CGANs. However, the paper is missing a comparison against more advanced, integrated spatio-temporal Graph Neural Networks (e.g., STGCN, Graph WaveNet, ASTGCN, or ST-GNNs designed for traffic). These models often feature more sophisticated spatio-temporal fusion mechanisms than the sequential RGCN-then-LSTM approach used here. Could the authors comment on why these state-of-the-art spatio-temporal GNNs were not included as baselines? A discussion (or ideally, a new experimental comparison) would be needed to truly position UrbanGraph's performance within the broader ST-GNN literature, rather than just against its own ablated components.\n2 Some parameters are likely effective for the UMC4/12 dataset, which is based on Singapore's climate. a) How sensitive is the model's accuracy to these specific values? b) If this model were deployed in a city with a vastly different climate and morphology (e.g., a dry, arid climate with sparse vegetation or different wind patterns), would these parameters need to be manually re-tuned? c) Does the model risk failing if the true physical influence (e.g., of wind) differs from the hard-coded heuristic?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1、Well-motivated physics-informed design:\nThe explicit encoding of physical processes into graph topology is intuitive and grounded in urban climate science. The distinction between static edges (semantic similarity, internal contiguity) and dynamic edges (shading, vegetation activity, convective diffusion) appropriately captures both time-invariant spatial relationships and temporally evolving physical phenomena.\n2、Dataset contribution: \nThe UMC4/12 dataset with diverse urban morphologies and high-resolution simulations provides a valuable resource for the research community.\n3、Clear presentation:\nThe paper is generally well-written with good use of figures to illustrate the framework and results.", "weaknesses": "the explicit encoding of physical processes (such as shading, vegetation evapotranspiration, and convective diffusion) into a dynamic, heterogeneous graph topology is a novel and effective method. however, this heavy reliance on predefined rules raises critical questions about the model's flexibility and potential for scientific discovery.  The model is constrained by the five predefined relationship types. As the authors correctly acknowledge in the limitations section, this may oversimplify the real, complex physical interactions.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "ciAR8Cbg3q", "reviewer": "Reviewer_mEEd", "summary": "The authors propose a novel method to generate high resolution forecast of weather variables over cities. The method employs a physics informed graph representation that explicitly maps physical processes.\nThe authors propose to discretize GIS features and then explicitly express the relationship between cells in five different edge types: Vegetation Evapotranspiration, Shading, Convective Diffusion, Semantic Similarity, Internal Contiguity.\nThese different edge types govern how the different cells are connected to each-other.\n\nThe proposed method is trained on and compared to a high resolution numerical model output (ENVI-met), and performs better than several other baseline methods.", "questions": "I am not sure I understand how the final network is constructed, can i get an example of network?\nI would like to see examples of results in the main paper.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "The paper is well written, the advantages of the methods clear and the figures of very high quality. The arguments for the design choices are sound, and make sense in the context of the paper.\nThe five types of edges seem to accurately represent the different processes, and suffice to express the complex relationships between nodes.\nThe model does seem to perform better than a series of baselines both in accuracy and time cost.", "weaknesses": "Although the paper is quite strong, I feel like a few key weaknesses exist:\n- The authors claim that previous methods mostly use fixed graph structures for time series forecasting. Although this might be true, I would argue that their method is also fixed. The graph is a gridded mesh, where the edges weight are varying. Additionally, the advantage of using GNNs is usually to work with non-gridded data. Since the domain is discretized, what is the advantage of using a GNN? Wouldn't a transformer with a weighted attention mask work as well?\n- There is no mention of spatial resolution. Maybe I've missed it, but what is the resolution? The GIS data is discretized, so there is a spatial resolution.\n- I am not sure I understand what the inputs are. Beyond the discretized GIS data, what are the inputs of the model? How are the environmental variables integrated? I also didn't see any mention of embedding the environmental variables. The only mention is the Graph-level global environmental features. Are the environmental features only embedded at the graph level? Is there no per-pixel data?\n- I have only seen a train a validation set mentioned, but not test set.\n- The authors claim to increase the computational efficiency in FLOPS by 17%. But in table 1, GGAN-LSTM performs better in terms of FLOPS. Where does this come from?\n- In table 1, URBANGRAPH is bold for most results, but several models beat it for time cost.\n\n\nMinor weaknesses:\n- Figure 4:\n\t- a) it is very uncommon to show train and validation results. Results are usually shown on the test set.\n\t- a) What is the x axis?\n\t- b) the colors are hard to differenciate\n\t- b) where is URBANGRAPH?\n- Figure 3: I don't understand what the discretized images are (top left)\n- Line 256: \"normalized static feature space.\" which normalized static feature space?\n- Line 379: MAE is not reported", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)