arXiv Machine Learning By Chenhao Si, Kang An, Shiqian Ma, Ming Yan

From Non-Convex Self-Concordant Regularization to Scalable Quasi-Newton Training of PINNs

Read the original on arXiv Machine Learning →

arXiv:2608. 04206v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) often require high-accuracy quasi-Newton refinement to obtain reliable partial differential equation solutions, but their residual objectives can exhibit indefinite, nearly singular, and poorly scaled local curvature.

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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
Hugging Face Trending Papers
Jul 8

Higher-Order Geometric Updates for Levenberg-Marquardt Method via Riemann Normal Coordinates

Nonlinear least-squares optimization is central to regression, physics-informed neural networks, and other machine-learning tasks. Such problems have a natural geometric interpretation, model predictions form a manifold in data space, while the chosen parameterization can introduce parameter-effects curvature that becomes a dominant source of nonlinearity.