Structure-preserving Randomized Neural Networks for Incompressible Magnetohydrodynamics Equations
This paper proposes Structure-Preserving Randomized Neural Networks (SP-RaNN), a novel framework that reformulates the solution of incompressible magnetohydrodynamic equations into a linear least-squares problem to eliminate nonconvex optimization while automatically and exactly satisfying divergence-free constraints, thereby achieving superior accuracy, stability, and convergence compared to traditional and deep learning-based methods.