AI RESEARCH
Neural Pushforward Samplers for the Fokker-Planck Equation on Embedded Riemannian Manifolds
arXiv CS.LG
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ArXi:2603.16239v1 Announce Type: cross We extend the Weak Adversarial Neural Pushforward (WANPF) Method to the Fokker--Planck equation posed on a compact, smoothly embedded Riemannian manifold M in $R^n$. The key observation is that the weak formulation of the Fokker--Planck equation, together with the ambient-space representation of the Laplace--Beltrami operator via the tangential projection $P(x)$ and the mean-curvature vector $H(x)$, permits all integrals to be evaluated as expectations over samples lying on M, using test functions defined globally on $R^n.