arXiv AI

WaSP: Wasserstein Data Synthesis Pipeline for Solver-Free Operator Learning

arXiv AI

Jun 26

Error-Conditioned Neural Solvers

arXiv:2606. 27354v1 Announce Type: cross Abstract: Neural surrogate models offer fast approximate mappings from PDE parameters to solutions, but they typically treat solving as a purely statistical task: once trained, they struggle to correct their own constraint violations and extrapolate beyond the training distribution.

By Haina Jiang, Liam Wang, Peng-Chen Chen, Min Seop Kwak, Seungryong Kim, Brian Bell, Jeong Joon Park

arXiv Machine Learning

Jun 25

A Zeroth-Order Deep Learning Method for Fully Nonlinear Parabolic Partial Differential Equations with Unknown Coefficients

arXiv:2606. 24999v1 Announce Type: new Abstract: High-dimensional partial differential equations (PDEs) with unknown coefficients arise widely in scientific machine learning, including continuous-time reinforcement learning, yet solving them efficiently in a data-driven way remains challenging.

By Yanwei Jia, Du Ouyang, Huy\^en Pham, Xun Yu Zhou

reinforcement-learning safety

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

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 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

arXiv AI

Jul 15

Learning to Discretize: Diffusion-Based Adaptive Mesh with Spectral Guidance

arXiv:2607. 11974v1 Announce Type: cross Abstract: Most neural partial differential equation (PDE) surrogates learn how fields evolve after a grid has already been chosen.

By Zixuan Shen (Central South University), Bingchuan Wang (Central South University), Zhi Wang (Nanjing University), Yong Wang (Central South University)

diffusion

arXiv Machine Learning

Sep 22

Learning Physics from an Imperfect Ancestor

arXiv:2609.24947v1 Announce Type: new Abstract: Neural operators evaluate parametric partial differential equations cheaply but degrade sharply outside their training distribution. Physics-informed n...

By S. Mohammad Mousavi, Teeratorn Kadeethum, Nikolaos Bouklas, Somdatta Goswami

efficiency

arXiv Machine Learning

2d ago

Backward-Consistent Diffusion Sampling for Sparsely Observed PDE Inverse Problems

arXiv:2610.04624v2 Announce Type: replace Abstract: Recovering Partial Differential Equation (PDE) coefficient fields from extremely sparse observations is a severely ill-posed inverse problem for wh...

By Yida Pan, Muhammad H. Ashiq, Chanyong Jung, Yixuan Jia, Jonah M. Miller, Qing Qu, Ismail Alkhouri

diffusion benchmarks

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

Sep 22

Predicting Out-of-Distribution Generalization of Neural Operators via Observable Spectral Error Decomposition

arXiv:2609. 23529v1 Announce Type: new Abstract: Neural operators have emerged as powerful surrogates for solving partial differential equations (PDEs), yet their reliability under distribution shift remains a critical barrier to deployment.

By Hang-Cheng Dong, Pengcheng Cheng

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 AI

Aug 25

One-Step Evolution for Long-Time Extrapolation: An Error-Bound-Informed and Prior-Guided Neural Residual Framework for Autonomous PDEs

arXiv:2608.22026v1 Announce Type: new Abstract: Accurate simulation of the long-time evolution of systems governed by partial differential equations (PDEs) is central to scientific computing. Among e...

By Maqun Zhang, Feng Gao, Wankun Chen, Hui Yu, Yanhai Gan, Junyu Dong

agents benchmarks

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