arXiv AI July 2, 2026 By Xin-Yang Liu, Xiantao Fan, Jian-Xun Wang

A Multi-Resolution Finite-Volume Inspired Deep Learning Framework for Spatiotemporal Dynamics Prediction

arXiv:2607. 00460v1 Announce Type: cross Abstract: Predicting complex spatiotemporal dynamics in physical processes often demands computationally expensive numerical methods or data-driven neural networks that suffer from high training costs, error accumulation, and limited generalizability to unseen parameters.

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

arXiv Machine Learning

Jun 3

Flow Learners for PDEs: Toward a Physics-to-Physics Paradigm for Scientific Computing

arXiv:2604. 07366v2 Announce Type: replace Abstract: Partial differential equations (PDEs) govern nearly every physical process in science and engineering, but solving them at scale remains prohibitively expensive.

By Yilong Dai, Shengyu Chen, Xiaowei Jia, Runlong Yu

diffusion 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

Jun 2

Flowers: A Warp Drive for Neural PDE Solvers

arXiv:2603. 04430v2 Announce Type: replace Abstract: We introduce Flowers, a neural architecture for learning PDE solution operators built entirely from multihead warps.

By Till Muser, Alexandra Spitzer, Matti Lassas, Maarten V. de Hoop, Ivan Dokmani\'c

llms benchmarks

arXiv Machine Learning

Jul 22

Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics

arXiv:2510. 25306v3 Announce Type: replace Abstract: Partial physical knowledge--governing structures known, constitutive relations or their combinations not--pervades spatiotemporal systems.

By Xizhe Wang, Xiaobin Song, Hongbo Zhao, Qingshan Jia, Qianchuan Zhao, Hao Sun, Benben Jiang

rag benchmarks

arXiv Machine Learning

Jun 11

HAMNO: A Hierarchical Adaptive Multi-scale Neural Operator with Physics-Informed Learning for Dynamical Systems

arXiv:2606. 11963v1 Announce Type: new Abstract: Neural operators provide a powerful framework for learning solution mappings of partial differential equations directly in function space.

By Mostafa Bamdad, Mohammad Sadegh Eshaghi, Timon Rabczuk

arXiv AI

Jul 17

LIGO-PINN: Learned Initialization via Gated Optimization to Alleviate Convergence Failures in Physics Informed Neural Networks

arXiv:2607. 14233v1 Announce Type: cross Abstract: Physics-informed neural networks (PINNs) have had a broad research impact in modeling domains governed by partial differential equations (PDE).

By Nilay Anurag, Shital Adhikari, Taniya Kapoor, Nikhil Muralidhar

benchmarks

Related stories

Flow Learners for PDEs: Toward a Physics-to-Physics Paradigm for Scientific Computing

Physics-Informed Laplace Neural Operator for Solving Partial Differential Equations

Flowers: A Warp Drive for Neural PDE Solvers

Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics

HAMNO: A Hierarchical Adaptive Multi-scale Neural Operator with Physics-Informed Learning for Dynamical Systems

LIGO-PINN: Learned Initialization via Gated Optimization to Alleviate Convergence Failures in Physics Informed Neural Networks