arXiv Machine Learning

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement

arXiv:2607. 23753v1 Announce Type: new Abstract: Partial differential equation (PDE) discovery aims to identify from data the governing law of a physical system.

arXiv AI

Aug 25

When Does AI for PDEs Yield Scientific Evidence?

arXiv:2608.22504v1 Announce Type: new Abstract: Existing AI-for-PDE benchmarks primarily assess models in terms of predictive or approximation accuracy. In physics research, however, AI outputs often...

By Wenshuo Wang

benchmarks

arXiv Machine Learning

2d ago

Residuals Are Not Enough: Limits of Physics-Informed Pre-Training for Scientific Foundation Models

arXiv:2503.19081v2 Announce Type: replace Abstract: Scientific foundation models (SciFMs) aim to learn generalizable representations of physical systems governed by partial differential equations (PD...

By Serge Kotchourko, Amin Totounferoush, Michael W. Mahoney, Steffen Staab

arXiv Machine Learning

Jun 9

Data-driven discovery of governing differential equations across physical systems

arXiv:2606. 09638v1 Announce Type: new Abstract: Differential equations play a critical role in scientific discovery because they provide a mathematical framework to describe the behaviour of physical phenomena.

By Siyu Lou, Hao Xu, Wenguan Wang, Lu Lu, Hao Sun, Yang Liu, Linfeng Zhang, Dongxiao Zhang, Yuntian Chen

arXiv Machine Learning

Jul 1

Joint discovery of governing partial differential equations from multi-source datasets by competitive optimization

arXiv:2606. 30699v1 Announce Type: new Abstract: Discovering governing equations directly from observational data is a key step towards interpretable scientific machine learning.

By Hao Xu, Siyu Lou, Yuntian Chen, Dongxiao Zhang

arXiv Machine Learning

2d ago

Geometry-physics confounding impairs PDE learning across varying domains

arXiv:2609.38623v1 Announce Type: new Abstract: Learning partial differential equation (PDE) dynamics across varying domains is central to predictive modelling and data-driven discovery of governing...

By Yinghao Cheng, Gengxiang Chen, Xu Liu, Qinglu Meng, Yixin Jing, Xiangguo Tang, Wenping Mou, Lihui Wang, Yingguang Li

benchmarks

arXiv Machine Learning

Jul 27

Latent PDE mapping for efficient physics-informed learning across geometries with limited data

arXiv:2607. 22215v1 Announce Type: new Abstract: In this study, we introduce latent PDE mapping, a broadly applicable physics-informed learning technique designed to enable efficient geometric generalization with sparse training data.

By Ingvild Askim Adde, Mary M. Maleckar, Gabriel Balaban

benchmarks

arXiv Machine Learning

2d ago

The limits of exactness: On the failure of automatic differentiation in physics-informed machine learning

arXiv:2609.33078v2 Announce Type: replace Abstract: Automatic differentiation (AD) lets neural networks compute derivatives of governing equations to machine precision, and this precision has made it...

By Ameya D. Jagtap

diffusion

arXiv Machine Learning

Jun 9

ERBench: A Benchmark and Testsuite for Equation Discovery Algorithms

arXiv:2606. 09276v1 Announce Type: new Abstract: Equation discovery aims to automate the discovery of scientific models in the form of mathematical equations from data.

By Paul Kahlmeyer, Henrik Voigt, Michael Habeck, Joachim Giesen

benchmarks

arXiv Machine Learning

Jul 14

LLM-PDESR: Robust PDE Discovery via Subdomain Weighted Residuals and LLM-Guided Symbolic Hypothesis Generation

arXiv:2607. 10546v1 Announce Type: new Abstract: Discovering governing partial differential equations (PDEs) from noisy observational data is a fundamental challenge in scientific machine learning.

By Jinyang Du, Hao Ma, Xiaohu Shi, Bo Yang, Yanchun Liang, Heow Pueh Lee, Chunguo Wu

llms benchmarks

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

Jun 19

Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System

arXiv:2606. 19754v1 Announce Type: new Abstract: Partial differential equations (PDEs) play a central role in modeling complex physical, biological, and engineering systems.

By Zhiwen Yu, Derong Yang, Liujian Zhang, Kaixiang Yang, Peilin Zhan, Jianmin Lv, Jane You, C. L. Philip Chen

arXiv Machine Learning

Aug 14

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

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