[2604.05230] Curvature-Aware Optimization for High-Accuracy Physics-Informed Neural Networks

Computer Science > Machine Learning arXiv:2604.05230 (cs) [Submitted on 6 Apr 2026] Title:Curvature-Aware Optimization for High-Accuracy Physics-Informed Neural Networks Authors:Anas Jnini, Elham Kiyani, Khemraj Shukla, Jorge F. Urban, Nazanin Ahmadi Daryakenari, Johannes Muller, Marius Zeinhofer, George Em Karniadakis View a PDF of the paper titled Curvature-Aware Optimization for High-Accuracy Physics-Informed Neural Networks, by Anas Jnini and 7 other authors View PDF HTML (experimental) Abstract:Efficient and robust optimization is essential for neural networks, enabling scientific machine learning models to converge rapidly to very high accuracy -- faithfully capturing complex physical behavior governed by differential equations. In this work, we present advanced optimization strategies to accelerate the convergence of physics-informed neural networks (PINNs) for challenging partial (PDEs) and ordinary differential equations (ODEs). Specifically, we provide efficient implementations of the Natural Gradient (NG) optimizer, Self-Scaling BFGS and Broyden optimizers, and demonstrate their performance on problems including the Helmholtz equation, Stokes flow, inviscid Burgers equation, Euler equations for high-speed flows, and stiff ODEs arising in pharmacokinetics and pharmacodynamics. Beyond optimizer development, we also propose new PINN-based methods for solving the inviscid Burgers and Euler equations, and compare the resulting solutions against high-order numerical m...