DRIFT-Net: A Spectral-Coupled Neural Operator for PDEs Learning
Authors: Jiayi Li
Flora D. Salim
Venue: ICLR 2026 Poster (2026)
Keywords: PDE
neural operators
neural solvers
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)

Abstract: Learning PDE dynamics with neural solvers can significantly improve wall-clock efficiency and accuracy compared with classical numerical solvers. In recent years, foundation models for PDEs have largely adopted multi-scale windowed self-attention, with the scOT backbone in Poseidon serving as a representative example.
 However, because of their locality, truly globally consistent spectral coupling can only be propagated gradually through deep stacking and window shifting. This weakens global coupling and leads to error accumulation and drift during closed-loop rollouts.
To address this, we propose DRIFT-Net. It employs a dual-branch design comprising a spectral branch and an image branch. The spectral branch is responsible for capturing global, large-scale low-frequency information, whereas the image branch focuses on local details and nonstationary structures. Specifically, we first perform controlled, lightweight mixing within the low-frequency range. Then we fuse the spectral and image paths at each layer via bandwise weighting, which avoids the width inflation and training instability caused by naive concatenation. The fused result is transformed back into the spatial domain and added to the image branch, thereby preserving both global structure and high-frequency details across scales. Compared with strong attention-based baselines, DRIFT-Net achieves lower error and higher throughput with fewer parameters under identical training settings and budget. On Navier--Stokes benchmarks, the relative $L_{1}$ error is reduced by 7%-54%, the parameter count decreases by about 15%, and the throughput remains higher than scOT. Ablation studies and theoretical analyses further demonstrate the stability and effectiveness of this design. The code is available at https://github.com/cruiseresearchgroup/DRIFT-Net.

Published as a conference paper at ICLR 2026
DRIFT-NET: A SPECTRAL-COUPLED NEURAL OPER- ATOR FOR PDES LEARNING
Jiayi Li
Flora D. Salim" University of New South Wales
University of New South Wales jiayi. 111.011101s001 @0sttdsttss unsw. edu.
flora sal mallimunsse edu au
ABSTRACT
Learning PDE dynamics with neural solvers can significantly improve wall-clock efficiency and accuracy compared with classical numerical solvers. In recent years, foundation models for PDEs have largely adopted multi-scale windowed self-attention, with the scOT backbone in POSEIDON serving as representative example. However, because of their locality, truly globally consistent spectral coupling can only be propagated gradually through deep stacking and window shifting. This locality weaken globally consistent spectral coupling, which has been associated with increased error accumulation and drift during closed- loop rollouts. To address this, propose DRIFT-Net. It employs dual- branch design comprising a spectral branch and an image branch. The spec- tral branch responsible for capturing global, large-scale low-frequency infor- mation, whereas the image branch focuses on local details and nonstationary structures. Specifically, first perform controlled, lightweight mixing within the low-frequency range. Then we fuse the spectral and image paths at each layer via bandwise weighting, which avoids the width inflation and training in- stability caused by naive concatenation. The fused result is transformed back into the spatial domain and added to the image branch, thereby preserving both global structure and high-frequency details across scales. Compared with strong attention-based baselines, DRIFT-Net achieves lower error and higher throughput with fewer parameters under identical training settings and budget. On Navier- Stokes benchmarks, the relative L1 eтror is reduced by 7%-54%, the parameter count decreases by about 15,, and the throughput remains higher than scOT. Ablation studies and theoretical analyses further demonstrate the stability and ef- fectiveness of this design. The code is available at htttp::/gitthiii Net
cru.seresearchhrooppDDEE
INTRODUCTION
Partial differential equations (PDEs) underpin science and engineering. Repeated high-accuracy simulations remain costly at scale (Trefethen) 2000 Benner et al. 2015). Neural operators address this challenge by learning mappings directly between function spaces. This enables fast inference across resolutions and inputs and supports cross-mesh generalization (Kovachki et al. 2023). Rep- resentative models include the Fourier Neural Operator (FNO) (Li et al. (021) and DeepONet (Lu let al., 2021). Building these advances, PDE foundation models adopt multi-scale windowed self-attention. POSEIDON with its scOT backbone a representative example.
Nevertheless, windowed self-attention is local. Global dependencies emerge only gradually with depth and shifted windows. This weakens globally consistent spectral coupling and can induce error accumulation and drift during closed-loop autoregressive rollouts (Lippe et al. 2023). In practice, naive cross-scale or cross- brasch concatenation inflates channel width and destabilizes training. Purely spectral operators are global but often overemphasize low-frequency structure and underfit nonstationary local details.
Our approach. We introduce DRIFT-NET, dual-branch neural operator. The spectral branch performs controlled low-frequenne global mixing. The image branch handles local interactions. The
"Coreesonning author.

---

Published as a conference paper at ICLR 2026
two branches fused bandwise through non-expansive mechanism. This avoids width inflation and preserves feehffreyeency detail. Implementation details, including the low-frequency mixing and bandwise fusion, presented in $
Contributions.
Modular operator unit. DRIFT-NET provides a dual-branch unit with controlled low- frequency mixing and bandwise non-expansive fusion. It enhances global coupling, local- detail fidelity. and training stability. The unit can be swapped in for windowed self- attention blocks in multi-scale operator backbones.
Performance and efficiency. Under matched training schedules and hardware, DRIFT- NET reduces final-time relative 11 error by 7% to 54% on Navier-Stokes benchmarks. uses about 15% fewer parameters and achieves higher throughput than scOT. See $
Mechanism and reusability. Ablations and spectral analyses show how non-expansive fusion and controlled low-frequency mixing support stable training and improved general- ization. The design is reusable and modular for stronger PDE foundation models.
RELATED WORK
Neural operators. Neural operators learn mappings between function spaces and approximate
solution operators PDEs (Li al., 2021; Kovachki et al.) 2023). A recent survey categorizes
existing architectures into three main types: deep operator networks (DeepONets), integral-kera
neural operators, and transformer-basee neural operators (Liu al. 2025). DeepONet adopts
branch-trunk factorization and comes with operator-apppooximaton guarantees (Lu et al. (021
Integral-kernel neural operators model nonlocal interactions through parameterized kernels. FNO
implements the kernel operator in the Fourier domain (Li et al.) (021), and variants such Geo- FNO and U-FNO extend this idea to irregular geometries and multiphase flow (Li et al. 2023
Wen et al. 2022); ; CNO and neural operators with localized integral or differential kernels further
emphasize multi scall structure and local operators (Raonić et al. 2023 Liu-Schiaffmn et al. 2024)
Transformer-basee neural operators treat grid points tokens and self-artention approximate
data-dependent kernels, and are widely used multi-task and pretraining settings (McCabe et al.
2023
Hao et al. 2024 Yang al. 2023
Rahman et al. 2024).
PDE foundation models and multi-scale attention. A recent line of work builds PDE founda- tion models on top of transformer-basee neural-operator backbones. Examples include MPP (a spatio-temporal transformer surrogate trained autoregressively multiphysics datasets), the opera- tor transformer DPOT with Fourier attention, and attention-based neural operators such as ICON and CoDA-NO; all of them perform large-scale pretraining on multi-dataset or multiphysies corpora and
transfer to downstream PDE tasks (McCabe et al.) 2023 Hao et al. [024 Yang et al.) [2023] Rahman al. 2024). Within multi- attention frameworks, POSEIDON employs multi-scale windowed attention operator transformer (scOT) with U-Net hierarchy and time-conditioned normalization, and shows strong cross-task generalization on Navier-Stokes benchmarks (Herde et al., 2024 Liu et al. 2021 2022). Windowed self-attention computes attention efficiently in local windows, but global dependencies are established only gradually through depth and window shifts, which can weaken global spectral coupling and contribute to rollout drift at long horizons (Lippe et al. 2023).
Positioning. We propose DRIFT-Net spectral-spatial coupled integral-kernel neural-operator backbone, which the above taxonomy falls into the class of integral-kernel neural operators. Ar- chitecturally, DRIFT-Net is composed of stacked DRIFT blocks: each block augments the multi- scale attention backbone with an explicit spectral path for controlled low- frequency mixing and a non-expansive bandwise fusion mechanism that integrates the spectral and image branches with- out increasing the feature width. Methodological details and quantitative comparisons are given in Sections [
2

---

Published as a conference paper at ICLR 2026
3 PROBLEM SETUP
Problem formulation, We consider a generic time-dependent partial differential equation on a spatial domain D C _d and time horizon I' 0:
a, fl V. V
0,
V D C t (0, (z,t) E aD (0,T),
((u) = 0,
(3.1)
u(x,0 0) = a(x),
Vx D.
Here L and B denote the differential and boundary operators, and afx) is the initial datum. Time- independent problems are also covered by this formulation. If steady state exists, the long-time limit (t + oo) yields the steady PDE
[u(x)), (x),,, Vau(c),.... = 0, B(u) = 0, DED,
(3.2)
which is the time- independeenntt counterpart of equation 3.1
Solution operator. Let X denote the state space, for example a suitable function space on D. The solution can be described by a map [0, T] x + such that, for any t E [0. 7] and E X, u(t) S(t, a). Equivalently, for each fixed we define the flow map S, X + X with S.(a) = a).
Underlying operator learning task. Given a distribution μ over initial conditions E X, the goal is learn an approximate solution operator S* that closely reproduces the true operator S. For any μl, the learned operator should generate the trajectory { (t, Heju( that approxi- mates {S(t, a) hejo,,) for all t. The model is expected to produce the time evolution from a, given boundary conditions, without relying on intermediate information, analogous to classical solver.
Learning objective. On a discrete grid of size H x W with C' components, let d4 E Rx denote the state at discrete time t. We learn a one-step operator Fg u4 + u4+1 with teacher forcing and relative L, objective with p E {1, 2}. At test time, Fg is composed autoregressively to produce a full trajectory {&r 1 Details of the training schedule, data splits, rollout horizon, and evaluation metries are specified in Sec. [
METHOD
Existing neural operators suffer from weak global coupling and the loss of high- de- tail in long-horizon prediction (Lippe et al.) 2023). We propose DRIFT-NET, a U-Net-style en- coder-decoder (Ronneberger et al. 2013) with two parallel branches: frequency path for cross- scale global interaction and an image path for local, nonstationary structures (Wen et al., 2022). At the frequency output to the spatial domain
each scale, we fuse the branches by and adding it to the image output. The model hinges on three mechanisms: (1) controlled low- frequency mixing to strengthen long-range dependencies without disturbing high-frequency modes; (2) bandwise fusion with radial gating for smooth cross-bant transitions (Rahaman et al., 2019 Xu al., 22000; and (3) a frequeney-weighte loss to counter spectral bias. We first outline the architecture and then detail each component.
4.1 ARCHITECTURE OVERVIEW
DRIFT-NET follows a hierarchical pecoder-decodee and augments each scale with an explicit spec- tral path (Fig- D. In the image branch, ConyNeXt-style blocks extract local and nonstationary struc- tures; down/up-sampling
realized by patch merging/expansion to form a U-shaped hierarchy. In parallel, the spectral branch converts features the same scale to the Fourier domain via rFFT2, applics a controlled transformation only on low-frequency modes (Sec. (.2)), and fuses them back by smooth bandwise mechanism (Sec. 4.3 After iFFT2, the spectral output is added to the image branch feature at that scale.
Two design choices key. First, the spectral path provides immediate global receptive fields ery resolution, so globally consistent coupling does not rely on deep stacking or large kernels. Sec- ond, the additive cross-branch fusion is non-expansive in width (no concatenation), which avoids
3

---

Published as a conference paper at ICLR 2026
[6]
Ourpul
Operator Learning
Rechopo & IFFT Ah Beelee MiN
Erbedding
Recovery Masp
Spcetral Stanch
KS-PwR
Conviest Mosie
Spectrll and ttvers We
NSS-raact
Comy..1
Pasch Expareót
NS-SL
Strge
MLP
FNE- KF
Perght
Figure I: Overall architecture of DRIFT-NET. (a) U-Net style encoder-decoder with ConvNeXt blocks and patch merging/expansion. (b) Spectral branch (rFFT2, spectral fusion with radial gating) fused additively with image branch via inverse FFT. (c) Example operator-learning tasks: NS-PwC, NS-Tracer-Pwer NS-SL, FNS-KE.
channel inflation and empirically stabilizes optimization. Across scales, the network thus propa- gates coarse global structure while preserving high-frequency details refined by local convolutions. This decomposition mirrors the physical intuition that low-k modes control large-scale dynamics, whereas high-k modes encode fine structures, discontinuities, and small eddies. For the architecture pseudocode content, please refer Appendix E.
4.2 CONTROLLED LOW-FREQUENCY MIXING
complex physical scenarios, achieving global-range feature interaction crucial for capturing long-range correlated dynamic behavior. However, indiscriminately applying global convolutions or frequency-domain operations across the entire frequency spectrum may overly amplify high- frequency noise and disrupt local details, leading to model instability. Therefore. the frequency- domain branch DRIFT-NET performs controlled global mixing operations only on low-frequency modes, focusing global coupling large-scale structures. Low-frequency components represent the field's overall shape and long-term evolution trends and play a decisive role in the global dynamics. In contrast, high-frequency components carry fine-grained local structures. By introducing global mixing only in the low-frequency band, the model can effectively propagate large-scale information each layer directly couple distant spatial locations, while maximally preserving high sighffreuencc details and avoiding unnecessary interference with small-scale structures.
Fourier-domain decomposition and motivation. At the feature level, low spatial frequencies correspond to smooth, wode basis functions whose coefficients modulate global structures; high frequencies capture localized variations. Modifying only bounded set of low-k coefficients yields a global yet parsimonious interaction pattern that respects the separation of scales. This aligns with classical spectral methods and with the observation that neural networks tend to fit low- frequency components first (spectral bias) (Rahaman et al. 2019 Xu et al. 2020). Our design uses this bias constructively by letting the network explicitly learn how to mix low-k channels, while leaving high-k content intact.
Block computation. In each DRIFT-NET block, we apply a 2D real FFT (rFFT2) to the input feature Xin to obtain its frequency-domai representation (k):; by Hermitian symmetry of real- valued inputs. only half of the spectrum needs be represented. We then use a learnable rectangular low-frequency mask Miw (kr; ky) to split the spectrum into cow-frequency part X and a high- frequency residual Xnigh = X X Within the www-freuenccy range k E Moww we introduce learnable channel-wise complex linear transformation W (acting per frequency, without cross-

---

Published as a conference paper at ICLR 2026
frequency coupling) mix the corresponding spectral coefficients (Rao et al. 2021
(A:) = W (k),, 1c E Moo
(4.1)
(k)) (K), k E Moow
For later use we denote (A)) - k... (k)) and keep (x)= kE (k). prac- tice, W is unconstrained (no explicit spectral-norm clipping), which keeps the transform expressive. We use rFFT2/FFT2 and the inverse transform yields a real-valued field by construction (Cooley & Tukey 1965 Frigo & Johnson 2005). This design focuses global mixing large scales while content intact. For implementation details, refer to Appendix C.
(A)=
leaving
4.3 BANDWISE FUSION WITH RADIAL GATING
After the above low-frequency mixing, we need fuse the modified low-frequency information from the frequency branch with the complementary content to produce the final spectrum for the inverse transform back to the spatial domain. If one simply performs hard band replacement or direct addition, discontinuities may occur at the frequency band boundaries or amplitude overshoot may be introduced in certain bands. Therefore, we design a smooth and stable frequency-ban baan fusion mechanism that uses a radial gating coefficient varying with frequency to weight and combine the two frequency-domee
signals.
Specifically, assign each frequency & in the spectrum weight a(A) [0, 1] to balance the contributions of the low-frequency mapped component and the high-frequency residual. We com- pute ax (k) function of the frequency magnitude (radial frequency) using lightweight per-band processing and expand to per- ferefreyenncy weights so that in the cow-frequency region a:(k) ze (favoring the mixed global component), whereas in the high fige-freyeency region a(k) =o (preserving fine local details). The fusion is then computed as
(k) = a<k) (lw(()) + (1- (k),
(4.2)
and since a<k) [0, 1]. by convexity we have the pointwise magnitude bound
[1:+)] < max (k),, [Xnign
(4.3)
This bandwise "clamping" effect avoids introducing energy larger than either source any fre- quency and empirically stabilizes training. Finally, we apply iFFT2 to obtain the spectral-path output in the spatial domain and add it to the image branch at the same scale.
Why radial and why additive. Choosing a(k) as a radial function enforces isotropy in fusion and prevents directional artifacts around the mask boundary. The convex combination above yields a non-expansive operator in the frequency domain (no overshoot), which directly translates to fewer ringing artifacts after iFFT2. the spatial domain, we merge the spectral and image signals by addition rather than concatenation. This preserves feature dimensionality and makes the fusion behave as a residual correction that injects globally coupled information while letting the image branch keep full control over high-frequency refinement. See Appendix C for details.
4.4 FREQUENCY- WEIGHTED LOss
Despite the above architectural improvements global coupling and local detail fidelity, the model training stage still needs to address the issue of spectral bias. Conventional losses tend to be domi- nated by low-frequency errors during optimization, causing the model to preferentially fit large-scale structures while converging slowly amallur-amplitude yet physically important high-frequency details. As result, fine structures in the predicted field may be underfitted and gradually become blurred over time.
To mitigate spectral bias in simple and stable manner, we add a freequency auxiliary term be the prediction error and E its rFFT2 under the same
in the Fourier domain. Let F. normalization. We reweight the error spectrum by a radial weight w((r) x r (with the normalized frequency magnitude) and minimize
L Thuse AB(w(r) [{ []
(4.4)
5

---

Published as a conference paper at ICLR 2026
where Liase is the standard Lp loss and (X, a) scalars. This radial weighting increases sensi- tivity to high-(k] components and complements the bandwise fusion used the frequency path, thereby improving the fidelity of multi-scale structures in long-houe horizon predictions (Fuoli et al. 2021 Diang et al. 2021). From a functional-analytic perspective, this amounts to emphasizing higher-order (roughness-related) components of the error-aknn to moving from pure Tep met- ric toward a Sobolev-like metric-so that small-scale discrepancies are not overshadowed by low- frequency energy during optimization. Practically, tuning controls the balance between coarse and fine accuracy, while a modulates how aggressively high frequencies are emphasized; we find mod- erate values suffice counter underfitting of fine structures without degrading large-scale fidelity. See Appendix B for details.
5 EXPERIMENTS
Protocol and metrics. We follow the POSEIDON evaluation protocol (Herde et al. 2024). All models, including DRIFT-NET and all baselines, use the same train/validation/rest splits and pre- processing, and are trained under shared data budget and training protocol: the same number of supervised trajectories per task, identical epoch budgets, and common optimizer and learning-rate schedule inherited from the POSEIDON scOT configuration (see Appendix F.4). On a discrete grid with C' channels and I X W spatial points, we train one-step operator Fe U, + U4+1 with single-step teacher forcing. At test time, we apply Fg autoregressively in a closed loop to reach the common target time T" We report the test-set mean relative L error at the final time:
| uT 111 |
W ΣΣΣ Nejall
C
H
GxllL11
||l||
CHW
For tasks with multiple quantities of interest (Qols) for example, NS- US--Tacer-Poee predicts (Me, uy, while NS-PwC, NS-SL, and FNS-KF output only (uz, Uy) compute the relative error for each Qol and then take an unweighted average:
(g)
(0)
ur
Ctakk Q
QEQ
Baselines. We compare DRIFT-NET with scOT (Herde et al. 2024), FNO (Li et al. 2021). U- NO (Rahman al.) 20222. U-Net-ConvNeXi baseline, and Refiner U-Net baseline adapted from PDE-Refiner (Lippe et al. 2023); ; see Appendix for detailed configurations.
Benchmark tasks. We evaluate DRIFT-NET on four canonical unsteady Navier-Stokes bench- marks from the POSEIDON suite (Herde et al. 2024). NS-SL (shear layer) tests vortex roll-up and mixing from perturbed interface. NS-PwC (piecewise-constan vorticity) stresses the advection of sharp discontinuities. NS-Tracer-PWC extends NS-PwC by introducing passive scalar which requires accurate coupling between the velocity and tracer fields. FNS-KF (forced Kolmogorov flow) sustains wwo-dimeniional turbulence via steady forcing, challenging long-horizon stability and multi-scale fidelity.
To cover different types of PDEs, we additionally include three tasks: Poisson Gauuss describes stationary Poisson equation with Gaussian foreing and assesses performance on elliptic problems. The Allen-Cahn equation (ACE) models interface evolution and phase separation, representing prototypical
process. Wave-Gauss simulates two-dimensional wave propagation in Gaussian medium and tests the modeling of hyperbolic wave phenomena.
In addition to these four benchmarks, we also consider two Ape forced Kolmogorov variants constructed using high-accuracy pseudo-spectral solver (Koehler et al. 2024). These two variants share the same PDE setup and preprocessing but differ in physical parameters: one is more turbulent, whereas the other is comparatively smoother. To emphasize long horizon robustness, evaluate on both variants with a closed-loop rollout length of = 100 and, for these two datasets, compare DRIFT-NE against scOT under identical settings.

---

Published as a conference paper at ICLR 2026
Main results. Table reports the final-time relative L' errors across all seven PDE benchmarks under the matched training protocol described above. On the four POSEIDON Navier-Store Stokes tasks, DRIFT-NET consistently attains the lowest eπror among all compared architectures, reducing the emorr of scOT by between 7% and 54% while using fewer parameters. Among the baseline models, scOT is typically the strongest, whereas FNO underperforms on most unsteady flow tasks.
On all three additional PDE benchmarks (Poisson ProussnnGGuuss, Allen-Cahn, and Wave-Gauss) DRIFT- NET achieves the best test error, with modest gains on Poisson-Gauss and more pronounced im- provements on Allen-Cahn and Wave-Gauss. These results indicate that replacing windowed- attention blocks with DRIFT blocks improves accuracy not only on Navier-Stokes benchmarks but also on elliptic, parabolic, and hyperbolic PDEs.
Table 1:
Final-time relative L error (lower is better). Closed-loop rollouts to the common target time 7 on all benchmarks. Values are test-set means. Best in bold.
Task
ScOT
FNO
U-NO
ConvNNet
Refnnrr U-Net
DRIFT-NET
NS-SL
3.96
3.69
3.57
3.89
3.48
3.40
NS-PwC
2.35
4.57
1.62
2.22
1.95
1.09
NS-Tracer-PwCC
5.18
9.46
10.15
9.63
4.59
4.19
FNS-KF
4.65
4.43
11.70
5.94
4.38
4.32
Poisson Gauss
Doisson-Gauss
0.87
1.29
1.76
1.92
0.86
1.10
1.53
1.27
1.61
1.11
1.03
Wave-Gauss 12.34
16.97
13.94
16.02
13.33
12.15
Long-horizon behavior. Although final-time metrics informative, full closed-loop trajec- tory over a long horizon provides additional insight into cumulative drift. We therefore analyse two ApeBench-generated forced Kolmogorov variants constructed with high-accuracy pseudo-spectral solver (Koehler et al. [2224.. Both datasets share the same PDE setup but differ in physical parame- ters, with being more turbulent and the other comparatively smoother. For both variants run closed-loop rollouts up to T-100 and compare DRIFT-NET against scOT under identical settings.
Table summarzzss the final-tim time relative L error 100. On the turbulent variant, DRIFT-NET attains lower final error than scOT (110,87 vs. 114.14). On the smoother variant, the improvement more pronounced (57.17 vs. 62.99), indicating increased robustness across different flow regimes.
Table 2: Forced Kolmogorov flows from ApeBench. Final-time relative L error (lower is better) at T=100. Values are test-set means. Best in bold.
Task
ScOT
DRIFT-NET
KF-Long (turbulent, ApeBench, T=100)
114.14
110.87
KF-Long (smoother, ApeBench, 7=100)
62.99
57.17
Beyond the final-time value, also consider the mean relative L error across the rollout and a linear growth slope obtained by a least-squares fit of error versus time. On the turbulent variant, DRIFT-NET attains mean error of 69.89 compared with 74. 76 for scOT, and error-growth slope of 1.154 compared with 1.185 for scOT. On the smoother variant, the mean error is 31.07 compared with 35.41 for scOT, and the slope is 0.581 compared with 0.641 for scOT. Figure shows the corresponding eiror-tmme curves, which remain consistently lower for DRIFT-NET with slightly flatter tails at large
Finally, to better visualise how errors accumulate, we plot in Figure 3 the instantaneous error growth on the smoother Kolmogorov variant, defined as the difference between consecutive relative L values. DRIFT-NET exhibits smaller instantaneous growth than scOT for most of the rollout, pecially in the early and mid-range time steps, and only converges to similar values near the end of the horizon. This pattern is consistent with the design goal of DRIFT blocks, namely strengthening global low-freut www-freuenccy coupling while maintaining high-frequency fidelity and avoiding rapid error amplification.

---

Published as a conference paper at ICLR 2026
100
DRIFTINe
DRIFTNeT
Balative
Relative
60
50
100
20
66
30
150
Timee stop
Time step
Figure 2: Error vs, time on ApeBench-based long-horizon Kolmogorov datasets (T=100). Left: turbulent; Right: smoother. Solid line: DRIFT-NET; dashed line: scOT.
Instantaneous error growth
DRIFT-Net
SCOT
0.7
0.6
0.5
0.4
0
20
40
60
80
100
Time step
Figure 3: Instantaneous error growth on the smoother ApeBench Kolmogorov dataset. We plot the per-step change in relative I, error over a rollout of length T=100. Solid line: DRIFT-NET; dashed line: scOT.
Efficiency comparison. We compare the computational cost of scOT and DRIFT-NET FNS- KF (Table 3.. Under identical hardware and inference settings, the 1.0x DRIFT-NET uses 17M 20M parameters for scOT, reduces peak training memory from 17.25 GB 10.87 GB, shortens training time per epoch from 17.30 to 14.91 minutes, and increases inference throughput from 118 158 steps/s. At 0.5x width, both models become cheaper, and DRIFT-NET still has lower mem- and higher throughput (224 vs. 175 steps/s). Overall, on FNS-KF, DRIFT-NET is both more accurate and more efficient than scOT.
Table 3: Computational cost on FNS-KF, Parameter count, peak training memory, training time per epoch, and inference throughput (higher is better) for scOT and DRIFT-NET at width settings. Measurements are taken under identical inference and training settings.
Model
Params (M)
Peak train mem (GB) Train time epoch (min)
Throughput (steps/s)
ScOT ScOT-0.5x
20
17.25
17.30
118
10
8,58
15.81
175
DRIFT-NET
17
10.87
14.91
158
DRIFT-NET-0.5x
9
6.82
13.96
224
Ablation studies. We assess the contribution of each major component DRIFT-NET: Low- Frequency Mixing (LFM). Radial Gating (RG), Frequency-Weighted Loss (FWL), and the two op- erators in the image branch, namely the 3x3 depth-wise convolution and the 1x1 pointwise linear layer. We train ablated variants on NS-PwC and fixed and using the same training budget and evaluation protocol as the full model. Removing LFM or RG noticeably worsens final-time accuracy; removing FWL also degrades performance, although to a smaller degree. Dropping the 3x3 depth-wise wise convolution or the x pointwise linear layer fur- ther inereases the error, showing that the ConvNeXt-style image branch is also important (Table 4 Concretely, relative to the full model, removing LFM increases the final error by 0.56 and 2.13 on NS-PwC and NS-Tracer-PWC. respectively; removing RG increases by 0.61 and 2.36: removing
holding all other hyperparameters
8

---

Published as a conference paper at ICLR 2026
FWL yields smaller increases of 0.27 and 1.17; removing the depth- wise convolution adds 0.02 and 0.17; and removing the pointwise linear layer adds 0.22 and 0.02.
Table 4: Ablation of DRIFT-NET components. Numbers final-time relative L errors (lower is better) on NS-PwC and NS-Tracer-PwC under the same training and evaluation protocol. Best in bold.
Model variant
NS-PwC
NS-Tracer-PWC
Full DRIFT-NET (ours)
1.09
4.19
w/o Low-Frequency Mixing (LFM)
1.65
6.32
w/o Radial Gating (RG)
1.70
6.55
w/o Frequency-Weige
Loss (FWL)
1.36
5.36
w/o xx3 depth-wise conv
1.11
4.36
w/o 1 x pointwise linear
1.31
4.21
Spectral analysis for ablations. To characterize scale-dependent effects, we analyze the evolution of bandwise errors over time (normalized R per frequency band). Figureeccompares four model variants (the full DRIFT-NET, no FWL, no RG, and no LFM), each showing error-versus time curves for multiple wavenumber bands. The full model most effectively suppresses error growth in the mid- and sehufrryyencc bands (those with k 2 16). In contrast, removing RG leads to the earliest and most pronounced increase in the highest-frquuency band. Removing FWL yields marked late-stage increase in high- freuufrry error. Removing LFM increases both mid- and high- frequency errors, consistent with weakened low-frequency global coupling.
DRIFTNET
No getng
Figure 4: Bandwise nRMSE vs. step for ablations. Left to right: full DRIFT-NET. no HF loss, no gating. no LF-Mix.
6 LIMITATIONS AND FUTURE WORK
DRIFT-Net has limitations. It uses mask to select low frequencies. The initial band is hand-tuned The mask learns weights later, but the cutoff can be task specific. The model applies FFT's in many blocks. This adds memory traffic and latency very large grids. Our tests target two-dimensional flow. Three-dimensional flow and coupled multi-physics may bring new training issues and higher cost. Future work will learn spectral partitions end end. We will study 3D and multi-physics PDEs. We will pair the model with adaptive resolution and mesh refinement. We will also test irregular domains and complex boundary conditions.
7 CONCLUSION
We introduced DRIFT-NET, spectral-spatial coupled integral-kernel neural-operator backbone. Each DRIFT block combines a spectral branch with controlled low-frequency mixing and ConvNeXt-style image branch, and fuses them via bandwise radial gating in non-expansive way. A frequency- weighted loss further mitigates spectral bias. On four POSEIDON Navier-Stole bench- marks, DRIFT-NET reduces final-time relative L' error by 7% 7%-54% compared to scOT, while using about 15% fewer parameters and achieving higher inference throughput. Additional results on Poisson-Gauss, Allen-Cahn, and Gauss show that these gains extend beyond Navier-Stokes

---

Published as a conference paper at ICLR 2026
to elliptic, parabolic, and hyperbolic PDEs. Because DRIFT blocks modular and architecture- agnostic, they can replace windowed attention blocks in existing multi-scale operator backbones and may be integrated into future PDE foundation models.
ACKNOWLEDGMENTS
This project is supported by the ARC Centre of Excellence for Automated Decision-Making and Society (CH200100005).
This research includes computations using the computational cluster Katana supported by Research Technology Services at UNSW Sydney.
We also thank Hira Saleem for helpful discussions, feedback, and support during this project; her contributions are gratefully acknowledged.
REFERENCES
Peter Benner, Serkan Gugercin, and Karen Willcox. A survey of projection-basel model reduction methods for parametric dynamical systems. SIAM Review, 57(4):483-331 2015.
James W. Cooley and John W. Tukey. An algorithm for the machine calculation of complex fourier series. Mathematics of Computation, 19(90))27-3301 1965.
Matteo Frigo and Steven G. Johnson. The design and implementation of fftw3. Proceedings of the IEEE, 93(2):216-25) 231, 2005.
Dario Fuoli, Luc Van Gool, and Radu Timofte. Fourier space losses for efficient perceptual image super-resolution. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), pp. 2360-2369 2021.
Zhongkai Hao, Chang Su, Songming Liu, Julius Berner, Chengyang Ying, Hang Su, Anima Anand- kumar, Jian Song, and Jun Zhu. DPOT: Auto-regressive denoising operator transformer for large- scale PDE pre-training. In Proceedings of the 41 International Conference Machine Learning (ICML), 2024.
Maximilian Herde, Bogdan Raonić, Tobias Rohner, Roger Käppeli, Roberto Molinaro, Emmanuel de Bézenac, and Siddhartha Mishra. Poseidon: Efficient foundation models for pdes. In Advances in Neural Information Processing Systems (NeurIPS), 2024.
Liming Jiang, Bo Dai, Wayne Wu, and Chen Change Loy. Focal frequency loss for image recon- struction and synthesis. Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), pp. 13929, October 2021.
Felix Koehler, Simon Niedermayr, Rüdiger Westermann, and Nils Thuerey. Apebench: A bench- mark for autoregressive neural emulators of pdes, 2024. URL
2411. 00180
Nikola B. Kovachki, Zongyi Li, Burigede Liu, Kamyar Arizzadenesheli, Kaushik Bhattacharya, Andrew M. Stwart, and Anima Anandkumar. Neural operator: Learning maps between function spaces. Journal of Machine Learning Research, 24 2023.
Zongyi Li, Nikola B. Kovachki, Kamyar Arizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew M. Stuart, and Anima Anandkumar. Fourier neural operator for parametric partial differ- ential equations. In International Conference on Learning Representations (ICLR), 2021.
Zongyi Li, Daniel Zhengyu Huang, Burigede Liu, and Anima Anandkumar. Fourier neural oper- ator with learned deformations for pdes on general geometries. Journal of Machine Learning Research, 24(388): (1138))1885331866 18593-18618 2023.
Phillip Lippe, Bastiaan S. Veeling, Paris Perdikaris, Richard E. Turner, and Johannes Brandstetter. PDE- Refiner: Achieving accurate long rollouts with neural pde solvers. Advances in Neural Information Processing Systems (NeurIPS), 2023.
10

---

Published as a conference paper at ICLR 2026
Shengjun Liu, Yu Yu, Ting Zhang, Hanchao Liu, Xinru Liu, and Deyu Meng. Architectures, variants, and performance of neural operators: A comparative review. Neurocomput. 648(C), October 2025. ISSN 0925-2312. doi: 1016/3 neucom. 2025. . 135188
httphttpss//doi.ooe
Ze Liu, Yutong Lin, Yue Cao, Han Hu, Yixuan Wei, Zheng Zhang, Stephen Lin, and Baining Guo. Swin transformer: Hierarchical vision transformer using shifted windows. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), pp. 10012-10022, 2021.
Ze Liu, Han Hu, Yutong Lin, Zhuliang Yao, Zhenda Xie, Yixuan Wei, Jia Ning, Yue Cao, Zheng Zhang, Li Dong, Furu Wei, and Baining Guo. Swin transformer v2: Scaling up capacity and reso- lution. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp. 12009-12019, 2022.
Miguel Liu-Schiaffini, Julius Berner, Boris Bonev, Thorsten Kurth, Kamyar Azizzadenesheli, and Anima Anandkumar. Neural operators with localized integral and differential kernels. arXiv preprint urXiv:2402.16845 2024.
Lu Lu, Pengzhan Jin, and George Em. Karniadakis. Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators. Nature Machine Intelligence, 3(3): 119- 2021.
Michael McCabe, Bruno Régaldo-Saint Blancard, Liam Holden Parker, Ruben Ohana, Miles Cran- mer, Alberto Bietti, Michael Eickenberg, Siavash Golkar, Geraud Krawezik, François Lanusse, Mariel Pettee, Tiberiu Tesileanu, Kyunghyun Cho, and Shirley Ho. Multiple physics pretraining for physical surrogate models. In Advances in Neural Information Processing Systems (NeurIPS), 2023.
Nasim Rahaman, Aristide Baratin, Devansh Arpit, Felix Draxler, Min Lin, Fred A. Hamprecht, Yoshua Bengio, and Aaron C. Courville. On the spectral bias of neural networks. In Proceedings of the 36th International Conference on Machine Learning (ICML), 2019.
Md Ashiqur Rahman, Zachary E. Ross, and Kamyar Arizzadenesheli. U-no: U-shaped neural operators. arXiv preprint arXiv:2204. 11122044.1112,,,.. 2022.
Md Ashiqur Rahman, Robert Joseph George. Mogab Elleithy, Daniel V. Leibovici, Zongyi Li, Boris Bonev, Colin White, Julius Berner, Raymond A. Yeh, Jean Kossaifi, Kamyar Azizzadenesheli, and Anima Anandkumar. Pretraining codomain attention neural operators for solving multiphysics PDEs. In Advances in Neural Information Processing Systems (NeurIPS), 2024.
Yongming Rao, Wenliang Zhao, Zheng Zhu, Jiwen Lu, and Jie Zhou. Global filter networks for image classification. In Advances in Neural Information Processing Systems (NeurIPS), 2021.
Bogdan Raonić, Roberto Molinaro, Tim De Ryck, Tobias Rohner, Francesca Bartolucci. Rima Alai- fari, Siddhartha Mishra, and Emmanuel de Bézenac. Convolutional neural operators for robust and accurate learning of pdes. In Advances in Neural Information Processing Systems (NeurIPS), volume 36, 2023.
Olaf Ronneberger, Philipp Fischer, and Thomas Brox. U-net: Convolutional networks for biomedi- cal image segmentation. In Medical Image Computing and Computer-Assiiteed Intervention (MIC- CAI), pp. 234-241. Springer, 2015.
Lloyd N. Trefethen. Spectral Methods in MATLAB. SIAM, 2000.
Gege Wen, Zongyi Li, Kamyar Azizzadenesheli, Anima Anandkumar, and Sally M. Benson. U- FNO-an enhanced Fourier Neural Operator-based deep-learning model for multiphase flow. Ad- vances in Water Resources, 104180 2022. doi:
20t.tres..222.144441
Zhi-Qin John Xu, Yaoyu Zhang, Tao Luo, Yanyang Xiao, and Zheng Ma. Frequency principle: Fourier analysis sheds light on deep neural networks. Communications in Computational Physics, 28(5):1746-1777 1767, 2020.
Liu Yang, Siting Liu, Tingwei Meng, and Stanley J. Osher. In-context operator learning with data prompts for differential equation problems. Proceedings of the National Academy of Sciences (PNAS), 120(39):e23 10142120. 2023. doi: 1.1073/paa..2100122
11

---

Published as a conference paper at ICLR 2026
APPENDIX
A THEORETICAL PROOFS AND BOUNDS
A.1 SETUP AND NOTATION
Let Q = =T a periodic domain. Denote by F the 2-D iFFT with forward normalization forwardrr,rd), For real-valued tensor E IR #xxx write û F(u). Two learnable
Nyquist-scaled cut-offs Kr, fy E 0.5] define a low-frequency rectangle
Now û 1 (<K= [Byl<<, }
Whigh Koow
with area OLF = KaKy I 0.25. The spectral half-plane is partitioned into concentric radial bands { for gating.
A.2 PER-BLOCK LIPSCHITZ UPPER BOUND
Core DRIFT operator. Inside the low rectangle a shared complex matrix W e CCxC mixes channels:
mix-mix mixx (k) W @low (l:), E Maow
Let the three parallel branches of a DRIFT layer be: (i) low-band mixer S, (ii) depth-wise 3 x convolution C, (iii) 1 x linear map L. With forward-normalized FFT, Parseval on the low rectangle yields fixed scaling absorbed into operator constants.
Lemma A.1 (Core DRIFT operator bound). For the residual-free core RIRIFT S +CC+
||
|RRIFT]lLip S VOLF Pw Keonv Klin
where PW = ||W|]2, and Keoav Kiin are operator norms of the depth-wise conv and the x linear, respectively. If the block is wrapped by an outer residual + RERIIT, then ||z + RoRwrllLi, I
1 + R
Swin-style reference bound. Aam (z) + Amip(1) (I), hence
A Swin-style block with identity shortcut decomposes as +
SwIIx llp S || I|2 + Al
A.3 RELATIVE NETWORK-LEVER BOUND
Proposition A.2 (Tighter cumulative bound). Suppose both DRIFT and Swin-style blocks use the same outer residual / + for every depth
VOLF Pw + Keany + Klin < ||Aaulll + || 1l,
then for any number of layers L,
L II
L II
I
SWIN |
Consequently, DRIFT-Net admits a strictly smaller worst-case gain than an equally deep Swin-style stack without requiring either network to be contractive (< 1).
Discrete Grönwall implication.
Let cm+1 S Ko em + Tm with one-step defect 7m- Replacing KSWIN by KDRRITT K$WIN flattens the geometric factor in the discrete Grönwall inequality:
1 Kmm
cm I m en
max T)
K8
A.4 RADIAL-BAND GATING IS ENERGY NON-EXPANSIVE
Lemma A.3 (Pointwise amplitude bound). For any fixed a E [0, 1] and Fourier location k. (kk) Uoww nhow-mix mix (k) ax) thigh (k) + [o(k)] S max [moowmmii(kk))) |ūnigh (A:) }.
Proof. Convexity: Jaa + abbl a/a| a:)bbl < max [b]]
12

---

Published as a conference paper at ICLR 2026
Remark (input-dependent gates). When depends the input via band-statistics MLP, the amplitude bound still holds pointwise; the Lipschitz constant additionally includes a term from 0a/Ou. In practice, may detach gradients through in the stability analysis constrain the gate MLP by spectral normalization.
A.5 OPERATOR- NORM CONTROLS FOR CONV/LINEAR
wepth-wise 3 x 3 conv. On a periodic grid, the depth-wise conv is block-circulant and diago- nalized by the DFT. Hence ||T maxp,w [k Ensuring Σi, |kyyl I or projecting to max wk S yields Koonv < 1.
1 X linear. If W RCxC is orthogonally initialized and projected each step to the spectral ball of radius CL I 1, then | I cL giving Kin I CL-
B SOBOLEV-WEIGHTED ONE-STEP DEFECT BOUND
Theorem B.1 (Sobolev-closed defect). Fix > 0, Aut >> O and define Lsob(u, ū) Art A
2) with A (T A) If IE Lsab E, then the expected one-step defect 7mm = Am+11
Dg um) ll2 satisfies
Bm S hf
E.T =: r.
Proof sketch. Parseval (with norm=forward) gives Looh = An Ee(1 + ||<1))) 6k uk úg. Split the spectrum radius Tha
Ejkisr lex| > lex12: the HF term S (1 +
2 X Tsoo- Optimizing yields the stated bound; insert into the discrete Grönwall inequality.
C SPECTRAL PIPELINE DETAILS
Low/high split (implementation). Given input size (H, W), the rFFT has size (Her Wax) (H, W/2 + 1). Two learnable scalars K₂ = affz), Ky = (0ey) define
M = { |g < Ny Hm. kyy < Kg Wit újo = à 1 Miw Thigh = á Ulow
Radial gate (energy-fraction driven). Let v (i/ 1))² + (j/(Wm: - 1))² and bands B, ((,j)) [Jrig] j}.j o.....,J Define high-frequency energy fraction
(high (2)]2
EHF(K) Viow (1=) + (high (k) +
Average within each band obtain (i), pass through two-layer MLP with sigmoid output, and broadcast back: (n))(k) a (M..P((n. ((Jrg)))) (0,
Spectral fusion and inference-only taper. Blend as
6(k) = akk) Diow-mix (k) + (1-a(k) (nigh(k)
==
At evaluation time, lightweight outer-band taper may be applied the outermost ring: i(k) (1 - 3 (k)) ((k) with 3 E (0, 1/2] and ā the channel-wise mean gate. Because 0 S a S and the taper factor < every Fourier mode non-evea
D COMPLEXITY AND THROUGHPUT PROTOCOL
Asymptotic costs per DRIFT block. 1FFT/FFFT pair: O(HW (Hg)))); band statistics & broadcast: O(HW); low-band mixing: O C²) with |Mow < HW. Thus DRIFT-Net
matches the asymptotic complexity of window attention while eliminating dense projections in at- tention blocks.
13

---

Published as a conference paper at ICLR 2026
E PSEUDOCODE
Algorithm DRIFT-NET one-step forward and training loss (code-aligned)
Require: current field RC*H*W #scales L; learnable LF mask params (Kzz kyy; complex mixers (We) radial band gates (BandGatez) base loss Lesei spectral weights w(r); coefficient 1:
Ensure: predicted next field u loss (if training)
2: Embed (u+)
3: for = 1 to L do
4:
X rFFT2(())
5:
(Hm. Wm) +- shape(X); liz (o(0) Hm], biy +- Lo(0g) Wm]
6:
Xlow + X 3 1 ckll Xnigh + X Nlow
7:
Voo (k) - We (k) for kzs; kyl: Vio t otherwise
8:
feat f |&ugai - |X
9:
a(k) + (Pol,,
[A:])
(k) & alk) Vow (k: + (1 - a(k)) (k)
11:
Uspec t iFFT2(()
ylocal DWConve PointwiseLincarr(c)
Norma(yspe Vlocal, time)
14:
+t= #+
if < then
16:
+ Downsample(s)
17: for
T. down 1 do if < then + Upsample(z)
18:
20:
I + ConvNeXtBlock((z)
21: 0.+1 t Recover(x:)
22: if training then
23:
E. f- ū2+1 u+11 E FFFFTT)
24:
Thuase F1p
p {1,2)
25:
Live t x-
[E())
26:
L L Lbuse + Lireq
27:
return u441 (and if training)
F EXPERIMENTAL SETUP AND HYPERPARAMETERS
F.1 OVERALL PROTOCOL
We follow the POSEIDON downstream evaluation protocol (Herde et al. (024) and use the public Poseidon datasets: NS-SL, NS-PwC, NS-Tracer-PwC. FNS-KF, Allen-Cahn (ACE), Wave-Gauss, and Poisson Gauss. All fields are provided on fixed 128 x 128 Cartesian grid; we train and evaluate directly on this grid without any additional spatial interpolation or resampling.
For all time-dependent tasks (NS-SL, NS-PwC, NS-Tracer-PwC. FNS-KF, ACE, Wave-Gauss), each trajectory consists of sequence of states {u Ni sampled at a fixed time step. We train one-step operator
Fg + Wc+1:
acting on grids Cx 128x 128, where C is the number of physical channels (e.g., C-2 for velocity, C=3 for velocity plus tracer). Training uses single-step teacher forcing: we sample time index t from each trajectory. feed u, into the model, and minimize the one-step prediction error to u++1- In Mave-Gauss the spatially varying speed is provided as additional static input channel.
14

---

Published as a conference paper at ICLR 2026
Baasoon-Gauss is -ndeppnndenn there directly learn the mapping from source field f y) to steady-state solution u(z, y) on the same grid.
At test time an autoregressive rollout {ūe / by iteratively applying F's and compare the final prediction ür- with the ground truth u7. at the standard target snapshot 7 used in POSEIDON for each task. For Yoisson-Gaus
the learned one-step map in closed loop. Given initial state uo generate
evaluate directly on the steady solution.
Unless otherwise stated, we report the mean test relative L1 error at the evaluation time: for a single-quantity task,
@T. WT- 1I |UT ||
rel-L1
|| CHW
Leigh
averaged over all test trajectories. For tasks with multiple quantities of interest (e.g.. NS- NS-Tracer- PwC), we compute the relative error per quantity and take an unweighted average. All models (DRIFT-Net and baselines) use the same train/validation/test splits and the same number of training trajectories as in the Poseidon releases.
F.2 DOWNSTREAM DATASETS AND TASKS
We evaluate DRIFT-NET and all baselines on seven downstream tasks from the Poseidon collection and additional long-horizon Kolmogorov-flow benchmarks generated with APEBench. All datasets use a fixed 128 x 128 Cartesian grid.
NS-SL. NS-SL is two-dimensional incompressible Navier Stokes benchmark with double shear- layer initial conditions. The Poseidon NetCDF file provides single variable veloci t with shape 40000 x 21 2 x 128 x 128 (trajectories x time steps x channels x x x W), where the two channels are horizontal and vertical velocity. Trajectories are simulated on the unit square up to T = 1 with 21 uniformly spaced snapshots; the official split 39640/ 19640/120/20 120/240 240 trajectories for rrain/vlliatiion/ess.
NS-PwC and NS-Tracer-PwC: NS-PwC and NS-Tracer-PwC share the same Poseidon dataset. The NetCDF file contains a velocity variable of shape 20000 x 21 x 3 x 128 x 128. The three channels correspond to horizontal velocity, vertical velocity, and a passive tracer convected by the flow. We treat the first two channels as the NS-PwC task (predicting only the velocity field) and all three channels as US-Tracer-PWCC (velocity plus tracer). All trajectories are simulated up to T with 21 snapshots, and we use the standard 19640/120/22 240 train/validation/test split.
ENS-KE. FNS-KF is forced incompressible Navier Stokes benchmark with piecewise constant vorticity initial conditions and steady Kolmogorov forcing. The dataset provides single variable so solution with shape 20000 x 21 x 2 x 128 x 128 for the two velocity components. Simulations the unit square up T 1 with 21 snapshots and use time- and sample-independent forcing field f(x, 3) = 0.1 sin sin(2i(( (ær + y)). We adopt the official 19640/120, 2200 split.
ACE. ACE contains trajectories of the Allen-Cahn reaction-diffusion equation. The NeICDF file has a single variable solut on of shape 15000x20 x28x 128, representing scalar concentration field. The equation is solved on the unit square up to T = 10-4 with 20 uniformly spaced snapshots. We use the default 14700/60 /0/2200 240 trajectories for training, validation, and testing.
Wave-Gauss. Wave-Gauss is second-order wave equation with spatially varying wave speed. The dataset provides two variables: solution of shape 10512 15 128 128 for the scalar wave an additional the dynamic field at every time step.
field, and с of shape 10512 128 x 128 for the static wave-speed field. We treat Trajectories are static input channel that is concatenated simulated on the unit square up to T = 1 with 15 snapshots, and the official split is 10212/60/240 trajectories.
Poisson-Gauss. Poisson Gauss is a time-independent benchmark based on the Poisson equation with Gaussian source terms. The NetCDF file contains two variables of shape 20000 x 128 x 128: source, the right-hand side fxr y), and solution the corresponding steady-state solution
15

---

Published as a conference paper at ICLR 2026
axx y). We learn the operator mapping f + directly the 128 x 128 grid, using the default split of 19640/120/2444 samples.
ApeBench Kolmogorov flows. For long-horizon evaluation generate two Kolmogorov- datasets with APEBench. Both are based on the periodic 2D vorticity formulation of the incom- pressible Navier-Stokes equations with drag and single-mode Kolmogorov forcing.
+ u V~ vāw y + f(x,v)
(Oy4) -a,4), Arh = w,
discretized with pseudo-spectral solver on a 128 x 128 grid. We consider two parameter sets:
KF-Long (turbulent). Corresponds to the NS-2D-Forced BASE configuration with 10-3, = -0.1, forcing mode Kforce = 4, and forcing scale 1.0.
KF-Long (smoother). Corresponds to the NS-2DD-orced VARE configuration with the same forcing mode but higher viscosity and drag: 1.5 x 10 7 -0.15, Riuce 4, and forcing scale 1.0.
For each configuration we procedurally generate 4,000 trajectories with the APEBench code and split them into 3,700 training, 200 validation, and 100 test trajectories. Unless otherwise stated, long-horizon results on these benchmarks are reported for closed-loop rollouts of length = 100 time steps.
F.3 MODEL CONFIGURATION AND PARAMETER COUNTS
All models are instantiated in a "base" configuration on 128 x 128 grids with comparable capacity. DRIFT-NET has about 17M parameters, while all baselines scaled about 20M parameters.
DRIFT-NET. DRIFT-NET is a four-level U-Net encoder-decoder with feature widths (du, d1, dz) (d. 2d, 4d, 4d) and two DRIFT blocks per resolution. Each block contains an image branch (ConvNeXt-style block with depthwise 3 x 3 convolution, pointwise 1 x convolu- tion, MLP, LayerNorm, and GELU) and a spectral branch that applies a 2-D FFT, restricts mixing to a learnable low-freque frequenuuucy mask, and maps back with inverse FFT. Radial-band gating partitions Fourier modes into J radial bands and uses small MLP per band to blend the image and spectral features. We choose d such that the total parameter count is se 17M on 128 x 128; the "0.5x" variant used in the FNS-KF ablation halves all channel widths.
ScOT. The ScOT baseline follows the official POSEIDON implementation (code: https: // github. com/ cam ab lbb-eaab/ossseeeeeee pos.idonssesesee....poop// don): multiscale Swin-style operator transformer with ConvNeXt bridges and time-conditioned layer norms (Herde al. (024).. We use the Poseidon-T (scOT-T) configuration for all from-scratch, runs, i.e., the tiny model used as the backbone of Po- seidon, which has about 20M parameters. We keep the architectural hyperparameters (number of levels, Swin blocks per level, window size, patch size) identical to the released ScOT-T config and only adapt the input/output channel dimensions to each task.
FNO. Our Fourier Neural Operator baseline follows Li et al. (Lict 2021) and uses the 2-D time- dependent FNO architecture from the official codebase (ht ht/ggtttuuuu thub. com / 1i-p ingan// fourier-neural operator). The network consists of lifting layer that maps the physical input channels to a width of din = 96, followed by = 5 Fourier layers with m, = my 16 retained complex Fourier modes per spatial dimension, and projection layer back the physical channels. We keep L and (Ma, m,,) fixed across all tasks and only tune din to control capacity; with dno 96 the model has about 19M parameters on 128 128 grids. All other architectural choices (complex Fourier weights, FFT-based convolutions, and nonlinearity placement) follow the official implementation.
U-NO. The U-NO baseline uses the official U-shaped Neural Operator implementation (htpps: //qithub. com/ ham/ashione q24 ( (Rahman et al. 2022). We employ a simplified 2-D UNO configuration with two resolution levels. At the finest resolution an operator block maps the physical channels to width we then downsample by a factor two and apply an operator block with output width 2 width and finally upsample and fuse encoder and decoder features with operator block
16

---

Published as a conference paper at ICLR 2026
that maps 3 ai back to widthuno before a convolution to the output channels. We set width = 88 and use my = my = 16 Fourier modes in each operator block. This yields a total parameter count of about 20M on 128 x 128 grids.
baseline shares the same four-level encoder-decoder hierarchy as DRIFT-NET dlown/up-sampling operators and skip connections), but contains only a spatial branch. We the UNet2d backbone from PDEBench with No-steXt-style blocks (code: and set the base width to init feetetuueees 50, which determines the channel widths at each level via the standard U-Net doubling rule. With this setting the model has approximately 20M parameters on 128 x 128 grids. We do not include any spectral path radial-band gating.
U-Net-ConwNeXtt
The
thub.
Refiner U-Net. The Refiner U-Net baseline is adapted from PDE-Refiner (https://
phlippe github. io wwp/PpDReeneeeeee
(Lippe et al. (023). We use modern four-level convo- lutional U-Net backbone with channel widths (48, 96, 192, 384) and two residual 3 x convolutional blocks per level, similar to the Unetmod backbone employed for Kolmogorov flow in PDE-Refiner. On top of this backbone we apply three refinement steps, each implemented as a lightweight resid- ual update on the current prediction; all refinement steps share the same U-Net parameters. This configuration yields total parameter count of approximately 20M on 128 x 128 grids.
F.4 TRAINING AND OPTIMIZATION
All models are trained from scratch on each downstream task using the official Poseidon train/validation/eest splits. For time-dependent datasets train one-step map Fg Ue r> W4+1 with single-step teacher forcing and evaluate closed-loop rollouts as described in Appendix F.I After each epoch we save a checkpoint and report test metrics for the checkpoint with the lowest validation relative L1 error.
Optimizer and schedule. For all architectures (DRIFT-Net and all baselines) we use the same optimizer and learning-rate schedule, following the from-scratch scOT setup POSEIDON (Herde et al. 2024 Li et al. (021). Specifically, we use AdamW with an initial learning rate 3 x 10-* cosine decay schedule with warm-up, and weight decay 10-6 These hyperparameters are fixed across all models and datasets and are not tuned per architecture; they were originally chosen for scOT rather than for DRIFT-NET.
Epoch budgets and batch size. On each task all models are trained for the same fixed number of epochs: 20 epochs on NS-SL, 100 epochs on Poisson-Gauss, and 40 epochs all other Poseidon and ApeBench benchmarks. We do not use early stopping; the best-validation checkpoint selected from these fixed budgets. Unless otherwise stated we use mini-batch size of 40 trajectories for all models and all datasets, matching the batch size used for scOT and FNO in POSEIDON.
Hardware and precision. All experiments are run on a single NVIDIA H200 GPU in full single precision (FP32) without mixed-precision or low-precision training. Random seeds are fixed for each run so that our results are reproducible given the released code and configuration.
G ADDITIONAL EXPERIMENTS
In this section we collect additional experiments that were used to address reviewer questions in the rebuttal but are not shown in the main text.
G.1 WIDTH SCALING ON FNS-KF
To study the effect of model capacity, we train scOT and DRIFT-NET on FNS-KF with two width factors. Fable/Frepone the parameter counts and test relative L, errors.
Reducing the width by a factor two degrades performance for both models, but DRIFT-NET consistently achieves lower emor than scOT at the same width (both 0.5x and 1.0x).
17

---

Published as a conference paper at ICLR 2026
Table 5: Width scaling on FNS-KE.
Model
Width factor
Params (M)
FNS-KF (rel-L1)
ScOT-0.5x
0.5
10
5.98
ScOT-1.0x
1.0x
20
4.65
DRIFT-NET-O.R
0.5x
5.96
DRIFT-NET-I.0x
1.0x
17
4.32
G.2 SENSITIVITY TO LEARNING RATE AND SCHEDULE
We next study the sensitivity of scOT and DRIFT-NET the base learning rate and the learning-rate schedule FNS-KE We train both models with A for 40 epochs under small grid of base learning rates {1 x 10 10-4, 10 x 10-3) and two schedules (cosine decay and step decay).
Results are shown in Tables and
Table 6: FNS-KF: sensitivity to base learning rate under cosine schedule.
Model
LR
Schedule
FNS-KF (rel-L1)
scOT
1 10
cosine
4.78
ScOT
3 X 10
cosine
4.65
ScOT
1 10
cosine
4.75
DRIFT-NET
1 x 10 10-4
cosine
4.45
DRIFT-NET DRIFT-NET
3 X 10
cosine
4.32
1 10
cosine
4.42
Table 7: FNS-KF: sensitivity to base learning rate under step schedule.
Model
LR
Schedule
FNS-KF (rel-L1)
scOT
10
step
4.83
scOT
3 x 10-1
step
4.70
ScOT
1 x 10-3
step
4.80
DRIFT-NET
1 x 10
step
4.50
DRIFT-NET DRIFT-NET
3 10-4
step
4.38
1 x 10-3
step
4.48
Across this grid, performance varies only moderately with the base learning rate and schedule, and DRIFT-NET consistently outperforms scOT in all tested configurations.
G.3 SAMPLE EFFICIENCY ON FNS-KF
To characterise sample efficiency, train DRIFT-NET FNS-KF with different numbers of supervised training trajectories while keeping the model and optimisation settings fixed. Table g reports the test relative L1 error as function of the number of training trajectories.
As expected, test error decreases monotonically with the number of training examples, and DRIFT- NET remains stable as the data budget varies.
G.4 CROSS-RESOLUTION BEILAVIOUR ON FNS-KF
To directly assess cross-resolution behaviour, we train DRIFT-NET on FNS-KF at 128 x 128 and evaluate the same model, without retraining, 64 x 64, 96 96, and 128 128. Inputs and outputs are mapped between resolutions using standard interpolation operators. Table shows the resulting test relative 7, emors.
18

---

Published as a conference paper at ICLR 2026
Table 8: FNS-KF: sample efficiency of DRIFT-NET.
training trajectories
DRIFT-NET (rel-L1)
2.5k
6.25
5k
5,48
10k
4.96
20k
4.32
Table 9: FNS-KF: cross-resolution evaluation of DRIFT-NET
Resolution
DRIFT-NET (rel-L1)
64 64
4.328
96 x 96
4.331
128 128
4.324
The errors are nearly identical across resolutions, indicating that in this experimental setup DRIFT- NET exhibits approximately mesh-agnostic behaviour.
G.5 RESOLUTION SCALING WITH FFTS
Finally, study how the computational cost of DRIFT-NET scales with spatial resolution the ApeBench Kolmogorov-flow benchmark. We train DRIFT-NET on 128 x 128 and 256 256 grids with the same batch size and optimisation settings and measure the time per training step and peak GPU memory usage on a single H200. Table 10 summarises the results.
Table 10: Resolution scaling of DRIFT-NET on ApeBench Kolmogorov.
Resolution
Time / step (ms)
Peak GPU memory (GB)
128 x 128
114
11.7
256 256
387
23.8
Runtime and memory both increase smoothly with resolution and remain well within the capacity of single H200 in the resolution regime considered in our experiments.
H FORCED KOLMOGOROV FLOW (KF) VISUALIZATION
19

---

Published as a conference paper at ICLR 2026
FIG-47 (hanmann) input 1-20 octput Duralaationn
-40
-04
Channel
(chenreid) iout
5-2
Channel
(I6-77 (chenroin2 (ted Input outout traterd
Channel
Figure 5: FNS-KF qualitative visualization. Each panel shows GT / scOT / DRIFT at 1=0 (top) and t=20 (bottom) for a single channel. Example is illustrative (not a main result).
20


Reviews:
[{"review_id": "4YoY09vgrC", "reviewer": "Reviewer_Kc8E", "summary": "This paper propose a neural surrogate model for time-dependent PDE simulation based on scOT architecture, The proposed model use convolution and frequency processing together. Special treatments are applied to the separated low frequency and high frequency information to achieve better performance. The model is applied on several fluid dynamics datasets and is compared against FNO and scOT baseline.", "questions": "- Figure 1: is the convolution applied after the rFFT2?\n\n- How does DriftNet compare to scOT in terms of overall design choices?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "- The presentation is clear and easy to follow.\n- The model design reflects the motivation about improved frequency processing.\n- The experimental evaluation shows improved better results against FNO and scOT, as well as improved efficiency against scOT.", "weaknesses": "- While some design choices are validated in ablation studies, some other main design choices may not be covered by the presented ablations. For example, the importance of having three branches (conv, spectral, linear) in the model design.\n\n- Figure 2 and Figure 3 do not seem very meaningful. If a model has lower onestep error, it will naturally have better step-wise rollout error.\n\n- Some other related baselines could be considered. E.g., U-Net with ConvNeXt blocks.", "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": "VpIY8eLo73", "reviewer": "Reviewer_DhGn", "summary": "DRIFT-Net aims to tackle one of the core challenges in neural PDE solvers and operator learning -- how to capture both global, long-range dynamics and fine-scale local structure efficiently and stably. It builds on the recent wave of “AI for PDEs” and foundation-model efforts (such as FNO, Fourier Neural Operators, and POSEIDON) but introduces a spectral–spatial coupling mechanism that improves physical fidelity and numerical stability.\n\nThe technical innovations in the paper are:\n1. Dual-branch operator design -- introduces a spectral branch (for global, low-frequency coupling) and an image branch (for local, high-frequency detail), fused additively at each U-Net scale to preserve both global structure and fine features.\n2. Controlled low-frequency mixing -- applies learnable transformations only on a subset of low-frequency Fourier modes.\n3. Bandwise fusion with radial gating -- fuses the spectral and spatial signals smoothly across frequency bands using a radial weighting function α(k)∈[0,1]; this yields isotropic, energy-non-expansive blending that prevents spectral discontinuities and stabilises training.\n4. Frequency-weighted loss function -- augments the base loss with a spectral weighting term that increases sensitivity to high-frequency reconstruction errors, mitigating neural networks’ spectral bias and improving multi-scale fidelity.", "questions": "Have the authors investigated how sensitive each method is to hyper-parameters like the learning rate schedule? These settings are shared across approaches -- is this really fair? Were they optimised for DRIFT-Net?\n\nPOSEIDON uses 15 tasks, why were only a subset considered here? POSEIDON also evaluates all models in terms of scaling curves which\nplot the test error for each task vs. the number of task-specific training examples. Have you considered doing this?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "The paper is clearly written and the presentation is clear. The technical innovations seem sensible and well-motivated. Since the technical advances are quite simple and lack e.g. rigorous theory (this isn’t a problem), I think that puts the onus on a very thorough experimental evaluation.\n\nI think the paper is quite strong in this regard. It evaluates the methods on at least three different classes of PDE (2D Navier–Stokes, shallow-water, and Kolmogorov flow), covering both laminar and turbulent regimes, and involving different grid sizes and forecast horizons. Error metrics (L1, relative L2, spectral energy error) are supported by Fourier energy spectra and visual reconstructions, showing both numerical and physical fidelity. Ablation studies examine (i) the low-frequency window size, (ii) the radial gating function, and (iii) the frequency-weighted loss — showing their independent and joint benefits. Baselines are reasonable, though not comprehensive. \n\nI think that is a reasonable effort, but a few additions would strengthen the evidence base for the DRIFT-Net approach.", "weaknesses": "The comparisons which are present are a good start, but I’d like to see more in a paper which focusses on an architectural improvement. The POSEISON paper, for example, has a substantially more thorough experimental comparison.\n\nIn terms of training, I’d liked to have seen a few different sizes of model trained for all methods to understand how the various approaches (these could be factors of two smaller)\n\nI would have liked to have seen a more thorough comparison of the computational aspects in terms of memory, inference-time cost, training duration / cost and how these trade with the sizes of the models.\n\nIn terms of baselines, there was arguably not a wealth of methods compared to. POSEIDON seems like a reasonable baseline, but \"PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solvers” would be another choice which can perform strongly. \n\nMinor comments\n\nline 295: Koehler et al. (2024) should be a \\citep\nsometimes Poseidon’s scalable Operator Transformer is referred to as “scOT” sometimes \"SCOT\"\nline 434 \"DRIFT-Net has limitation\" -> \"DRIFT-Net has limitations\"\nthe pseudocode in the appendix appears just before the empty pseduocode section -- it looks odd (this is of course a very minor issue!)", "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": "LZvyduVz3X", "reviewer": "Reviewer_frHQ", "summary": "This paper introduces a new model for operator learning for PDEs. The model is motivated by solving the issue of local coupling in existing benchmark models that use local self-attention. This leads to weak global coupling, which manifests as poor error in long term autoregressive solutions for hard, chaotic, PDEs like Navier-Stokes.  DRIFT-Net aims to mitigate this by having two paths in the model. The spectral branch operates on globally coupled low-frequency components by explicitly operating on the low frequency components of the FFT (while preserving high-frequency information), and the image branch focuses on locally coupled details. The two branches are mixed with bandwise weighting instead of concatenation for improved training stability. Experiments show that DRIFT-Net improves error over attention baselines on Navier-Stokes benchmarks, while also using slightly fewer parameters and having faster inference speed.", "questions": "Based on the weaknesses,\n\n1. Are there more mathematically grounded / theoretical justifications for using this model?\n2. Have the authors considered exploring more examples of PDEs and settings to further robustify the main claim that DRIFT-Net improves error on tasks that rely on global coupling?\n3. Are there potential solutions to needing hand-tuning of hyperparameters like bandwidth?\n4. Could the authors elaborate on the specifics of the different learning rates, optimizers, and data amounts, and total training budget that the authors experimented with? Did the best settings for DRIFT-Net also beat the best settings for the baselines?", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "* The proposed model is well-motivated, and the solution to the global coupling problem intuitively makes sense.\n* Experimental evidence clearly shows improvement over strong baselines.\n* Evaluation includes some ablation studies.", "weaknesses": "* While the error improves over attention baselines, it is somewhat marginal in the hard cases like the long-horizon Kolmogorov dataset.\n* There is no/little exploration of potential theoretical justification for the improvement this model brings.\n* Scope of practical settings is narrow, the paper only explores 2D Navier-Stokes instances only -- it is unclear how well the improvement of DRIFT-Net would generalize to other settings.\n* Some components of the model like the low-frequency cutoff requires hand tuning.\n* Scaling is unclear with needing FFTs over large domains.\n* It seems like there is insufficient exploration of training settings (or at least, these experimental details are not provided in enough detail).", "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": "gdVDDs1XEk", "reviewer": "Reviewer_RWgr", "summary": "The paper introduces DRIFT-NET, a neural PDE solver aimed at solving the problem of error accumulation and \"drift\" observed in long-term, autoregressive predictions. The authors identify the cause of this drift in the use of local window attention in popular attention-based models, which only allow slow propagation of global information through the layers. To this end, DRIFT-NET proposes a frequency-weighted loss and a dual-branch architecture within a U-Net style backbone: an image branch using standard ConvNeXt blocks to capture local details and a spectral branch to capture global information. These branches are fused using learned low-frequency mixing and a band-wise radially-varying gate to combine low- and high-frequency components. DRIFT-NET is benchmarked against scOT and FNO on several 2D Navier-Stokes tasks, where it can improve performance with a lower parameter count and faster inference.", "questions": "Please see weaknesses above", "limitations": "", "rating": 2, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 1, "strengths": "- The paper targets a well-known and critical failure mode of neural PDE solvers: long-horizon rollout drift.\n- While the dual-branch approach with spectral mixing is not new, the *fusion mechanism* using band-wise radial gating seems to be an effective new component.\n- The model demonstrates consistent performance improvement over the scOT and FNO baselines. In particular, it reduces accumulation errors in the rollouts with fewer parameters and a higher throughput. Moreover, an ablation study provides insights into the importance and effect of each of the three main components (LFM, RG, and FWL).", "weaknesses": "- While the paper claims to provide a modular and reusable design for PDE foundation models that “can be swapped in for windowed self-attention blocks in multi-scale operator backbones”, the effect of DRIFT-Net is only evaluated for a single backbone and only on variants of 2D Navier-Stokes equations. The spectral/image split is strongly motivated by fluid dynamics (large-scale flow vs. small-scale eddies), but may not be as optimal for other systems (e.g., hyperbolic equations, reaction-diffusion systems). Other PDE foundation models are not considered or mentioned, e.g. https://arxiv.org/pdf/2310.02994, https://arxiv.org/pdf/2403.03542, https://arxiv.org/abs/2304.07993, and https://arxiv.org/abs/2403.12553. To judge the benefit of the DRIFT-Net module, one needs to evaluate its effect on other types of PDEs, with other backbones, and also other dimensions (since, as mentioned in the limitations, the improvements in throughput might not hold anymore when using 3D FFTs). In the current form, there is also not enough evidence to claim that the drift during rollouts is *directly* caused by windowed self-attention.\n- It would be important to compare the performance and throughput to adapted versions of scOT/FNO with a comparable parameter count. Moreover, it is important to note that the performance of (multi-scale) windowed self-attention heavily depends on the underlying kernel and hardware optimizations used for the attention module.\n- Strictly speaking, the proposed architecture does not seem to be a neural operator (in the definition of https://arxiv.org/abs/2108.08481), since it is not discretization-invariant, i.e. it does not generalize to resolutions other than the training resolutions.\n- DRIFT-Net is only compared to two baselines and no details are provided on the FNO baseline. While some variants of FNO are mentioned in the related works (e.g., U-NO and AFNO), they are not compared against and there exist further FNO versions that bear similarity with DRIFT-Net (e.g. https://arxiv.org/pdf/2109.03697 and https://arxiv.org/pdf/2402.16845).\n- While the limitations mention that DRIFT-Net will be tested on irregular domains and complex boundary conditions, it is unclear how the current version can be *efficiently* extended to such (practically more relevant) geometries.", "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)