arXiv Machine Learning July 10, 2026 By Youngjae Park, Jaemin Kim, Junghwa Hong

Coupling-Robust Accuracy in Multiphysics Physics Informed Neural Networks via Kronecker-Preconditioned Optimization

Read the original on arXiv Machine Learning →

arXiv:2605. 23391v2 Announce Type: replace Abstract: Physics-informed neural networks (PINNs) for coupled multiphysics systems suffer systematic accuracy degradation as inter-equation coupling strengthens.

Summary generated by The Flow from the publisher's feed. The full article lives at arXiv Machine Learning.

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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

Jun 11

Hybrid Iterative Neural Low-Regularity Integrator for Nonlinear Dispersive Equations

arXiv:2605. 04853v2 Announce Type: replace Abstract: We propose HIN-LRI, a hybrid framework that augments a classical numerical solver with a neural operator trained to correct the solver's structured truncation error.

By Zhangyong Liang, Huanhuan Gao

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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

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arXiv Machine Learning

Aug 12

Dual Space Preconditioning for Gradient Descent in the Overparameterized Regime

arXiv:2603. 10485v3 Announce Type: replace-cross Abstract: In this work, we study the convergence properties of the Dual Space Preconditioned Gradient Descent, encompassing optimizers such as Normalized Gradient Descent and Gradient Clipping.

By Reza Ghane, Danil Akhtiamov, Babak Hassibi

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arXiv Machine Learning

Jun 2

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise

arXiv:2605. 18528v2 Announce Type: replace-cross Abstract: A growing lesson from neural network optimization is that optimizer design should respect how the model is parametrized.

By Jiayu Zhang, Tianyi Lin

arXiv Machine Learning

Jun 15

Robin-Neumann Coupling of PINN and FEM Solvers: A Steklov-Poincar\'e View, with Application to Fluid-Structure Interaction with Contact

arXiv:2606. 14181v1 Announce Type: cross Abstract: Physics-informed neural networks (PINNs) are meshless and carry moving geometry and topology change through resampling of collocation points; the finite-element method (FEM) is the workhorse for boundary-fitted discretisations.

By Mikel Landajuela

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

Hybrid Iterative Neural Low-Regularity Integrator for Nonlinear Dispersive Equations

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

Dual Space Preconditioning for Gradient Descent in the Overparameterized Regime

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise

Robin-Neumann Coupling of PINN and FEM Solvers: A Steklov-Poincar\'e View, with Application to Fluid-Structure Interaction with Contact