arXiv Machine Learning June 25, 2026 By Yanwei Jia, Du Ouyang, Huy\^en Pham, Xun Yu Zhou

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

Read the original on arXiv Machine Learning →

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.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

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 Machine Learning

6d ago

Fractional is Better: Learnable Derivative Orders in Neural Operator Learning

arXiv:2610.20363v1 Announce Type: new Abstract: Neural operators learn mappings between function spaces, enabling fast surrogate solutions to partial differential equations. Despite remarkable archit...

By Fares B. Mehouachi, Saif Eddin Jabari

benchmarks safety

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

One email a morning, machine-written

Related stories

Physics-Informed Laplace Neural Operator for Solving Partial Differential Equations

Discretization-independent operator learning for partial differential equations

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

Fractional is Better: Learnable Derivative Orders in Neural Operator Learning

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

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