arXiv Machine Learning By Joseph Webb, Sadok Jerad, Coralia Cartis

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

Read the original on arXiv Machine Learning →

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.

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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.

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Error-Conditioned Neural Solvers

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By Haina Jiang, Liam Wang, Peng-Chen Chen, Min Seop Kwak, Seungryong Kim, Brian Bell, Jeong Joon Park
arXiv Machine Learning
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Adjoint Method versus Physics-Informed Neural Networks in PDE-Constrained Inverse Problems

arXiv:2606. 12337v1 Announce Type: cross Abstract: Inverse problems governed by partial differential equations (PDEs) are central to computational mechanics and are commonly solved by adjoint-based optimization, while physics-informed neural networks (PINNs) have emerged as a flexible alternative.

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arXiv Machine Learning
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Eikonal Regularisation in Physics-Informed Neural Networks for Three-Dimensional Level-Set Advection: Transferability of Two-Dimensional Design Principles

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