arXiv Machine Learning

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.

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 Machine Learning

Sep 22

Discretization-independent operator learning for partial differential equations

arXiv:2507.07292v2 Announce Type: replace Abstract: We develop a new and general encode-approximate-reconstruct operator learning model that leverages learned neural representations of bases for inpu...

By Jacob Hauck, Yanzhi Zhang

arXiv Machine Learning

Jun 16

ANCHOR: Error-Controlled Adaptive Numerical Correction for Neural Operator Time Marching

arXiv:2512. 19643v2 Announce Type: replace Abstract: Numerical simulation of time-dependent partial differential equations (PDEs) is central to scientific and engineering applications, but high-fidelity solvers are often prohibitively expensive for long-horizon or time-critical settings.

By Rajyasri Roy, Dibyajyoti Nayak, Somdatta Goswami

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

arXiv Machine Learning

Jul 7

Learning rate adaptive stochastic gradient descent optimization methods: numerical simulations for deep learning methods for partial differential equations and convergence analyses

arXiv:2406. 14340v2 Announce Type: replace-cross Abstract: The standard stochastic gradient descent (SGD) optimization method, as well as adaptive methods such as the Adam optimizer fail to converge if the learning rates do not converge to zero (particularly, in the situation of constant learning rates).

By Steffen Dereich, Arnulf Jentzen, Adrian Riekert

arXiv Machine Learning

Jul 21

One-shot acceleration of transient PDE solvers via online-learned preconditioners

arXiv:2509. 08765v4 Announce Type: replace-cross Abstract: Data-driven acceleration of scientific computing workflows has been a high-profile aim of machine learning (ML) for science, with numerical simulation of transient partial differential equations (PDEs) being one of the main applications.

By Mikhail Khodak, Min Ki Jung, Brian Wynne, Edmond Chow, Egemen Kolemen

reinforcement-learning

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

1d 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 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 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

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

Aug 26

Physics-Integrated Operator Learning via Gaussian Splatting Representations

arXiv:2608.24049v1 Announce Type: new Abstract: Neural operators provide efficient surrogates for spatiotemporal PDE systems, but purely data-driven formulations often accumulate substantial errors d...

By Jihao Zhang, Junyi Guo, Jian-Xun Wang

diffusion benchmarks

Related stories