arXiv Machine Learning August 12, 2026 By Hengbo Xiao, Jiale Liu, Jiahao Song, Guannan He

DEFT: Data-Efficient Frequency-domain Top-k Sampling via Inverse Discrete Fourier Transform for Spatiotemporal Dynamical Systems Modeling

Read the original on arXiv Machine Learning →

arXiv:2608. 11019v1 Announce Type: new Abstract: Modeling spatiotemporal dynamical systems governed by partial differential equations (PDEs) poses two major challenges: it either requires expensive physics-based simulators that entail iterative numerical solving at high computational cost, or it depends on abundant training data, yet purely data-driven models often generalize poorly to downstream dynamic operating conditions.

Summary generated by The Flow from the publisher's feed. The full article lives at arXiv Machine Learning.

arXiv Machine Learning

Jun 5

When Attention Beats Fourier: Multi-Scale Transformers for PDE Solving on Irregular Domains

arXiv:2605. 08318v2 Announce Type: replace Abstract: We study the problem of \emph{architecture selection} for deep learning models trained to solve partial differential equations (PDEs), asking when transformer-based architectures with learned attention outperform Fourier-domain neural operators.

By Brandon Yee, Pairie Koh, Jack Rodriguez, Mihir Tekal

llms diffusion benchmarks safety

arXiv Machine Learning

5d ago

Physics-Informed Laplace Neural Operator for Solving Partial Differential Equations

arXiv:2602. 12706v2 Announce Type: replace Abstract: Neural operators have emerged as fast surrogate solvers for parametric partial differential equations (PDEs).

By Heechang Kim, Qianying Cao, Hyomin Shin, Seungchul Lee, George Em Karniadakis, Minseok Choi

rag diffusion benchmarks

arXiv Machine Learning

6d ago

Distillation of Foundation Models for Time-dependent PDEs

arXiv:2608. 11937v1 Announce Type: new Abstract: Foundation models for time-dependent partial differential equations (PDEs) are trained on large and diverse collections of physical systems and can generalize effectively to new downstream tasks.

By Daniel Musekamp, Boshra Ariguib, Andrei Manolache, Mathias Niepert

fine-tuning efficiency benchmarks

arXiv AI

Jun 10

Learning Where to Simulate: Generative Active Sampling for Online PDE Surrogate Training

arXiv:2606. 09949v1 Announce Type: cross Abstract: Data-driven PDE surrogates are trained with data produced by numerical PDE solvers.

By Pierre Cesar (DATAMOVE), Sofya Dymchenko (DATAMOVE), Abhishek Purandare (DATAMOVE), Bruno Raffin (DATAMOVE)

diffusion

arXiv AI

Jun 3

Physics-informed diffusion models in spectral space

arXiv:2602. 09708v2 Announce Type: replace-cross Abstract: We propose physics-informed spectral diffusion (PISD), a methodology that combines generative latent diffusion models with physics-informed machine learning to generate solutions of partial differential equations (PDEs) conditioned on partial observations, which includes, in particular, forward and inverse PDE problems.

By Davide Gallon, Philippe von Wurstemberger, Patrick Cheridito, Arnulf Jentzen

diffusion

arXiv AI

Jun 30

Physics-Informed Distillation of Diffusion Models for PDE-Constrained Generation

arXiv:2505. 22391v2 Announce Type: replace-cross Abstract: Modeling physical systems in a generative manner offers several advantages, including the ability to handle partial observations, generate diverse solutions, and address both forward and inverse problems.

By Yi Zhang, Peng Wang, Difan Zou

diffusion efficiency benchmarks

Related stories

When Attention Beats Fourier: Multi-Scale Transformers for PDE Solving on Irregular Domains

Physics-Informed Laplace Neural Operator for Solving Partial Differential Equations

Distillation of Foundation Models for Time-dependent PDEs

Learning Where to Simulate: Generative Active Sampling for Online PDE Surrogate Training

Physics-informed diffusion models in spectral space

Physics-Informed Distillation of Diffusion Models for PDE-Constrained Generation