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

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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.

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arXiv AI

Sep 1

SS-ESOAP: Self-Scaled Adaptive Preconditioning for Physics-Informed Learning

arXiv:2608.29448v1 Announce Type: cross Abstract: Physics-informed neural networks (PINNs) often face ill-conditioned objectives that limit high-accuracy training. Dense quasi-Newton methods improve...

By Guangyuan Wang, Mads Toftrup, Sebastian Loeschcke, Yixuan Wang, Anima Anandkumar

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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

Sep 2

Gradient-Update Mismatch: Rethinking Conflict-Free Training of Physics-Informed Neural Networks

The paper identifies a problem called Gradient-Update Mismatch (GUM), where optimizers can alter conflict-free gradient directions produced by gradient surgery, leading to conflicts between physics residual and boundary condition losses in Physics-Informed Neural Networks (PINNs). To address this, the authors propose Gradient-Update Alignment (GUA), which projects the optimizer’s update onto the conflict-free cone and adjusts internal optimizer state accordingly. Experiments show GUM is common across many optimizers, and GUA consistently eliminates conflicts and significantly reduces error in PINN training.

By Jing Xiao, Xinhai Chen, Qinglin Wang, Menghan Jia, Zhiquan Lai, Dongsheng Li, Jie Liu, Tiejun Li

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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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