arXiv Machine Learning June 5, 2026 By Brandon Yee, Pairie Koh, Jack Rodriguez, Mihir Tekal

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

Read the original on arXiv Machine Learning →

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.

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

arXiv Machine Learning

Jun 3

Are Deep Learning Based Hybrid PDE Solvers Reliable? Why Training Paradigms and Update Strategies Matter

arXiv:2602. 06842v2 Announce Type: replace-cross Abstract: Deep learning-based hybrid iterative methods (DL-HIMs) integrate classical numerical solvers with neural operators, utilizing their complementary spectral biases to accelerate convergence.

By Yuhan Wu, Jan Willem van Beek, Victorita Dolean, Alexander Heinlein

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

Jul 3

An Optimisation Framework for the Well-Conditioned Training of Physics-Informed Neural Networks

arXiv:2607. 02194v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) have emerged as a promising route to solve partial differential equations, yet they have struggled to reach the precision of classical solvers.

By Joseph Webb, Sadok Jerad, Coralia Cartis

arXiv Machine Learning

Jun 5

On the training of physics-informed neural operators for solving parametric partial differential equations

arXiv:2606. 06164v1 Announce Type: new Abstract: Physics-informed neural operators (PINOs) aim to learn solution operators for partial differential equations by using the governing physics as supervision, rather than relying solely on paired input-output simulation data.

By Nanxi Chen, Chuanjie Cui, Airong Chen, Sifan Wang, Rujin Ma

llms computer-vision benchmarks

arXiv Machine Learning

Aug 12

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

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.

By Hengbo Xiao, Jiale Liu, Jiahao Song, Guannan He

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Jun 4

On the training of physics-informed neural operators for solving parametric partial differential equations

Physics-informed neural operators (PINOs) aim to learn solution operators for partial differential equations by using the governing physics as supervision, rather than relying solely on paired input-output simulation data. By incorporating physical constraints into the training objective, PINOs combine the cross-instance generalization of neural operators with the data efficiency of physics-informed learning.

llms computer-vision benchmarks

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Physics-Informed Laplace Neural Operator for Solving Partial Differential Equations

An Optimisation Framework for the Well-Conditioned Training of Physics-Informed Neural Networks

On the training of physics-informed neural operators for solving parametric partial differential equations

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

On the training of physics-informed neural operators for solving parametric partial differential equations