[2507.03119] Improving ideal MHD equilibrium accuracy with physics-informed neural networks

Computer Science > Machine Learning arXiv:2507.03119 (cs) [Submitted on 3 Jul 2025 (v1), last revised 28 Mar 2026 (this version, v5)] Title:Improving ideal MHD equilibrium accuracy with physics-informed neural networks Authors:Timo Thun, Andrea Merlo, Rory Conlin, Dario Panici, Daniel Böckenhoff View a PDF of the paper titled Improving ideal MHD equilibrium accuracy with physics-informed neural networks, by Timo Thun and 4 other authors View PDF Abstract:We present a novel approach to compute three-dimensional Magnetohydrodynamic equilibria by parametrizing Fourier modes with artificial neural networks and compare it to equilibria computed by conventional solvers. The full nonlinear global force residual across the volume in real space is then minimized with first order optimizers. Already,we observe competitive computational cost to arrive at the same minimum residuals computed by existing codes. With increased computational cost,lower minima of the residual are achieved by the neural networks,establishing a new lower bound for the force residual. We use minimally complex neural networks,and we expect significant improvements for solving not only single equilibria with neural networks,but also for computing neural network models valid over continuous distributions of equilibria. Comments: Subjects: Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Plasma Physics (physics.plasm-ph) Cite as: arXiv:2507.03119 [cs.LG]   (or arXiv:2507.03119v5 [cs.LG] for this version...