Operator learning for solving Fokker-Planck equations with various initial conditions
Researchers have developed a new framework using conditional normalizing flows and physics-informed neural networks (PINNs) to solve the Fokker-Planck equation (FPE). This method efficiently approximates the solution operator for various initial conditions by reformulating the problem to approximate a transition probability density function (PDF). The approach utilizes the PDF of an associated linearized stochastic differential equation as a base distribution for the normalizing flow, improving accuracy especially for early time points and mitigating numerical instabilities. AI
IMPACT This research introduces a novel approach for solving complex differential equations, potentially advancing AI's capabilities in scientific simulation and modeling.