arXiv Machine Learning August 19, 2026 By Jaemin Oh, Youngkyu Lee, Jerome Darbon, George Em Karniadakis

Spectrally Safe Neural Operator Warm-Starts for Large-Scale Newton Solvers

Read the original on arXiv Machine Learning →

arXiv:2606. 21828v2 Announce Type: replace-cross Abstract: Neural operators are increasingly used to warm-start Newton solvers for nonlinear PDEs, on the premise that a low test error places the initial guess inside the basin of attraction.

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.

fine-tuning

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 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 17

A Convex Quasilinearization Method for Solving Nonlinear PDEs with Physics-Informed Neural Networks

arXiv:2606. 18175v1 Announce Type: cross Abstract: We present a numerical method for the forward solution of nonlinear partial differential equations (PDEs) in which Bellman-Kalaba quasilinearization reduces the nonlinear problem to a sequence of linear subproblems, each discretized by collocation onto a trial space that is linear in its parameters and solved by a single direct linear least-squares QR factorization.

By Gbenga T. Awojinrin, Abdul-Akeem Olawoyin, Rami M. Younis

benchmarks

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

Sep 22

Cost-Accuracy Trade-offs: Neural Operator vs Classical Numerical Solver

arXiv:2609.24021v1 Announce Type: cross Abstract: Neural operators are data-driven models that learn mappings from inputs that parameterize partial differential equations, such as spatially varying c...

By Daniel Zhengyu Huang, Andrew M. Stuart

benchmarks

arXiv Machine Learning

Jun 3

Are Deep Learning Based Hybrid PDE Solvers Reliable? Why Training Paradigms and Update Strategies Matter

arXiv:2602. 06842v2 Announce Type: replace-cross Abstract: Deep learning-based hybrid iterative methods (DL-HIMs) integrate classical numerical solvers with neural operators, utilizing their complementary spectral biases to accelerate convergence.

By Yuhan Wu, Jan Willem van Beek, Victorita Dolean, Alexander Heinlein

One email a morning, machine-written

Related stories

An Optimisation Framework for the Well-Conditioned Training of Physics-Informed Neural Networks

Learning Physics from an Imperfect Ancestor

A Convex Quasilinearization Method for Solving Nonlinear PDEs with Physics-Informed Neural Networks

Error-Conditioned Neural Solvers

Cost-Accuracy Trade-offs: Neural Operator vs Classical Numerical Solver

Are Deep Learning Based Hybrid PDE Solvers Reliable? Why Training Paradigms and Update Strategies Matter