arXiv Machine Learning

Data-driven sparse identification of governing PDEs via knockoff filters and multi-criteria trade-offs

arXiv:2605. 26631v2 Announce Type: replace-cross Abstract: We propose KO-PDE-IDENT, a data-driven framework for identifying parsimonious partial differential equations (PDEs) with false discovery rate (FDR) control.

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

Jul 7

Counterfactual Operator Relevance for PDE Discovery: Screening, Pruning, and Identifiability

arXiv:2506. 20181v2 Announce Type: replace Abstract: We study operator relevance in data-driven partial differential equation (PDE) discovery.

By Ronald Katende

efficiency

arXiv Machine Learning

Jul 28

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.

By Baptiste Mathevon, Farah Cherfaoui, Amaury Habrard, Marc Sebban

safety

arXiv Machine Learning

Jun 5

PyCC.id: A package for hypothesis-driven equation discovery with structural identifiability

arXiv:2606. 05191v1 Announce Type: new Abstract: Data-driven equation discovery is fundamentally an inverse problem that seeks to infer the governing differential equations of a system directly from time-series measurements.

By Federico J. Gonzalez

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

Jul 31

Learning features from Newton's algorithm: a way to accelerate nonlinear parametrized PDE solvers

arXiv:2607. 28036v1 Announce Type: new Abstract: It is well known that Newton's method converges faster when the initial guess is closer to a root of a system of nonlinear equations.

By R\'emy Vallot (CB, Michelin), Florian de Vuyst (BMBI), Thibault Dairay (CB, Michelin), Mathilde Mougeot (CB, ENSIIE, ENS Paris Saclay)

arXiv Machine Learning

Aug 3

Freeze, Then Select: Structured Field Adapters and Stability-Validated Weak Selection for PDE Discovery from Sparse Observations

arXiv:2607. 29665v1 Announce Type: new Abstract: PDE discovery from sparse observations requires reconstructing a continuous field and selecting the correct differential terms.

By Juncheng Zhong, Chenghuang Shen, Jianfeng Liu, Zhengdong Xiao, Longjiu Luo, Qianrong Wang, Wenjun Xu, Wenlian Lu

diffusion

arXiv Machine Learning

6d 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 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

6d ago

Sparse Orthogonal Regression Technique: A Spectral Framework for Equation Discovery, Approximation, and Integration

arXiv:2608. 13504v1 Announce Type: new Abstract: We develop the Sparse Orthogonal Regression Technique (SORT), a sparse spectral framework for learning orthonormal-basis expansions from noisy and irregularly sampled data.

By Sabin Roman, Ljupco Todorovski, Saso Dzeroski

arXiv Machine Learning

Jun 11

How Low Can You Go? Active Learning for Sparse Model Discovery in the Ultra-Low-Data Limit

arXiv:2606. 12182v1 Announce Type: new Abstract: Identifying the governing equations of complex dynamical systems remains a fundamental challenge across science and engineering.

By Ana Larra\~naga, Urban Fasel, Steven L. Brunton

arXiv Machine Learning

Jun 17

Operator Boosting Produces Pareto-Efficient PDE Surrogates

arXiv:2606. 17460v1 Announce Type: new Abstract: Neural operators are widely used as surrogate solution maps for partial differential equations (PDEs), but full-size models can be costly to store, deploy, and evaluate in many-query scientific workflows.

By Lennon J. Shikhman

benchmarks

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