AI and the World's Hard Problems · Mathematics · arXiv · 2026-10-26
Weak adversarial tensor neural network for high-dimensional Fokker-Planck equations
Solving high-dimensional stationary Fokker-Planck equations is hard, because the integrals needed for loss and normalization are costly to approximate accurately with Monte Carlo integration. The authors propose WATNN, which combines a weak adversarial formulation with tensor neural networks whose quadrature uses a small number of fixed points and avoids sampling error. On four high-dimensional problems it reaches mean relative errors of 1.50% to 7.93% in only a few minutes.