REVIEW 16 cited by
Towards Multi-spatiotemporal-scale Generalized PDE Modeling
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Towards Multi-spatiotemporal-scale Generalized PDE Modeling
read the original abstract
Partial differential equations (PDEs) are central to describing complex physical system simulations. Their expensive solution techniques have led to an increased interest in deep neural network based surrogates. However, the practical utility of training such surrogates is contingent on their ability to model complex multi-scale spatio-temporal phenomena. Various neural network architectures have been proposed to target such phenomena, most notably Fourier Neural Operators (FNOs), which give a natural handle over local & global spatial information via parameterization of different Fourier modes, and U-Nets which treat local and global information via downsampling and upsampling paths. However, generalizing across different equation parameters or time-scales still remains a challenge. In this work, we make a comprehensive comparison between various FNO, ResNet, and U-Net like approaches to fluid mechanics problems in both vorticity-stream and velocity function form. For U-Nets, we transfer recent architectural improvements from computer vision, most notably from object segmentation and generative modeling. We further analyze the design considerations for using FNO layers to improve performance of U-Net architectures without major degradation of computational cost. Finally, we show promising results on generalization to different PDE parameters and time-scales with a single surrogate model. Source code for our PyTorch benchmark framework is available at https://github.com/microsoft/pdearena.
Forward citations
Cited by 16 Pith papers
-
PDEAgent-Bench: A Multi-Metric, Multi-Library Benchmark for PDE Solver Generation
PDEAgent-Bench is the first multi-metric, multi-library benchmark for AI-generated PDE solvers, evaluating executability, numerical accuracy, and efficiency across DOLFINx, Firedrake, and deal.II.
-
ELADO: Elliptic PDE Assessment Datasets for Operator Learning
ELADO provides a benchmark suite of elliptic PDE datasets designed to isolate and quantify failure modes in neural operator architectures.
-
Revisiting Neural Processes via Fourier Transform and Volterra Series
Set Fourier convolutions plus a Volterra cascade yield scalable, translation-equivariant CNPs that handle irregular inputs with global receptive fields and beat strong baselines.
-
Latent Generative Solvers for Generalizable Long-Term Physics Simulation
LGS pretrained on 2.5M trajectories across 16 systems matches deterministic baselines at one step and halves 20-step error while using far less compute and adapting to held-out higher-resolution flows.
-
Neptuna: A Comprehensive Machine Learning Framework for Benchmarking Complex Multiphase Flows
A new 2.4 TB benchmark shows no single ML surrogate dominates on shock-driven multiphase flows, and composite losses with SoftAdapt weighting improve interface and spectral fidelity.
-
Revisiting Neural Processes via Fourier Transform and Volterra Series
Introduces SFConvCNPs and SFVConvCNPs using set Fourier convolutions and Volterra expansions for translation-equivariant neural processes on irregular data with global receptive fields and linear scaling.
-
Small Models, Strong Priors: Architectural Inductive Bias for Parameter-Efficient Neural PDE Solvers
WaveLiT combines wavelet tokenization, linear attention, and multiscale pyramids to produce parameter-efficient neural PDE solvers that match much larger models on TheWell benchmarks.
-
MC$^2$: Monte Carlo Correction for Fast Elliptic PDE Solving
MC² corrects low-budget Monte Carlo solutions for elliptic PDEs with a single-pass neural network to match the accuracy of 1000× more Monte Carlo samples while outperforming classical and learned baselines.
-
Physical Fidelity Reconstruction via Improved Consistency-Distilled Flow Matching for Dynamical Systems
Distilled one-step consistency model from optimal-transport flow-matching teacher reconstructs high-fidelity dynamical system flows from low-fidelity data with 12x speedup, half the parameters, and 23.1% better SSIM t...
-
Deep Wave Network for Modeling Multi-Scale Physical Dynamics
DW-Net improves the accuracy versus computational cost Pareto front over standard U-Nets for 2D and 3D multi-scale flow benchmarks by stacking multiple waves while keeping training settings identical.
-
FluxNet: Learning Capacity-Constrained Local Transport Operators for Conservative and Bounded PDE Surrogates
FluxNet is a family of neural PDE time-steppers whose learned transport plans make discrete conservation exact and one-sided bound preservation structural, with empirical dual-bound control via a consistency-regulariz...
-
Multi-Scale Wavelet Transformers for Operator Learning of Dynamical Systems
Multi-scale wavelet transformers learn operator dynamics of chaotic systems in the wavelet domain, yielding lower errors and higher spectral fidelity on benchmarks and ERA5 climate data.
-
Flow marching for a generative PDE foundation model
Flow Marching jointly samples noise and physical time to learn a velocity field for generative PDE modeling, paired with a latent autoencoder and efficient transformer for large-scale pretraining on 2.5M trajectories.
-
LLT: Local Linear Transformer for PDE Operator Learning
Local Linear Transformer learns PDE operators by combining linear global attention with local spatial mixing, achieving competitive accuracy and lower training-step cost than prior transformers.
-
Common Task Framework For a Critical Evaluation of Scientific Machine Learning Algorithms
The paper introduces a Common Task Framework for scientific ML, benchmarks it on Kuramoto-Sivashinsky and Lorenz systems, and launches a competition on a global sea surface temperature dataset with holdout data.
-
Conditional Clifford-Steerable CNNs for PDE Modeling
Conditional Clifford-Steerable CNNs, which condition the equivariant kernel on pooled input features, improve PDE forecasting accuracy but do not prove the claimed complete kernel basis.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.