arXiv Machine Learning

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

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.

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

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.

diffusion benchmarks

arXiv AI

Jun 4

Curvature-aware dynamic precision approach for physics-informed neural networks

arXiv:2606. 04736v1 Announce Type: cross Abstract: Physics-informed neural networks (PINNs) have become a promising framework for simulating partial differential equations (PDEs) by embedding physical laws directly into neural network training.

By Yingjie Shao, Ioannis N. Athanasiadis, George van Voorn, Taniya Kapoor

rag benchmarks

arXiv Machine Learning

Jul 9

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

arXiv:2607. 07623v1 Announce Type: new Abstract: Nonlinear least-squares optimization is central to regression, physics-informed neural networks, and other machine-learning tasks.

By Jianing Liu, Dong H. Zhang

diffusion benchmarks

arXiv Machine Learning

Jul 27

Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers

arXiv:2607. 22004v1 Announce Type: new Abstract: Energy natural gradient descent (ENGD) aligns parameter updates with the curvature of an underlying function-space energy, but existing formulations assume an unconstrained Euclidean parameter domain.

By Zhangyong Liang, Huanhuan Gao

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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

Jul 28

Learning from the Descent Direction: Adaptive Gradient Descent under One-Sided H\"older Regularity

arXiv:2607. 22906v1 Announce Type: new Abstract: We study adaptive gradient descent for continuously differentiable, possibly nonconvex objectives under one-sided H\"older regularity.

By Arzu Ahmadova, Ismail Huseynov

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arXiv Machine Learning

Jun 2

Physics-Informed Residuals for Adaptive Mesh Refinement in Finite-Difference PDE Solvers

arXiv:2606. 02475v1 Announce Type: cross Abstract: Classical finite-difference solvers remain reliable tools for partial differential equations, but their efficiency depends on where mesh resolution is placed.

By Henry Kasumba, Ronald Katende

benchmarks

arXiv Machine Learning

Jul 28

Variational Boosting for Physics-Informed Neural Networks

arXiv:2607. 23940v1 Announce Type: new Abstract: Physics-Informed Neural Networks (PINNs) solve differential equations by minimizing the residual of a nonlinear operator over a neural parameterization of the solution.

By Pavlos Protopapas, Kaylee Vo

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arXiv Machine Learning

Jun 4

Loss-Conditional PINNs for Parametric PDE Families

arXiv:2606. 04420v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) approximate solutions of ODEs and PDEs by minimising a weighted combination of residual, boundary, initial, and data losses.

By Anna Lazareva, Alexander Tarakanov

arXiv Machine Learning

Jul 7

Directional Curvature from Armijo Backtracking: A Low-Cost Sharpness Probe and a Calibration-Free Learning-Rate Safeguard for Adam

arXiv:2607. 03998v1 Announce Type: new Abstract: The local sharpness of the loss, the top Hessian eigenvalue $\lambda_1$, determines the largest stable gradient step, but measuring it normally requires Lanczos or Hessian-vector iterations.

By Ashmitha R, J\"org Frochte

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arXiv AI

Aug 3

A user's guide to PINNs in geometric analysis: lessons from the asymptotic Plateau problem

arXiv:2607. 28733v1 Announce Type: cross Abstract: This proceedings contribution elaborates on the findings of arXiv:2605.

By Tancredi Schettini Gherardini

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