Neural Pushforward Samplers for the Fokker-Planck Equation on Embedded Riemannian Manifolds
In this paper, we extend the Weak Adversarial Neural Pushforward Method to the Fokker--Planck equation on compact embedded Riemannian manifolds. The method represents the solution as a probability distribution via a neural pushforward map that is constrained to the manifold by a retraction layer, enforcing manifold membership and probability conservation by construction. Training is guided by a weak adversarial objective using ambient plane-wave test functions, whose intrinsic differential operators are derived in closed form from the geometry of the embedding, yielding a fully mesh-free and chart-free algorithm. Both steady-state and time-dependent formulations are developed, and numeric...
| Authors | Andrew Qing He, Wei Cai |
|---|---|
| Primary category | math.NA |
| Published | 17 March 2026 |
| Last updated at source | 18 March 2026 |
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