A transition-density-based operator learning method for Fokker-Planck equations with various initial conditions

תקציר מקורי באנגליתarXiv:2606.09434v2 Announce Type: replace Abstract: Solving Fokker-Planck equations (FPEs) for multiple initial conditions typically requires repeated computations, leading to substantial computational costs. In this work, we propose a transition-density-based operator learning method to efficiently approximate the solution operator of FPEs with various initial conditions. The core idea is to learn the transition probability density function (PDF) of the underlying stochastic differential equation (SDE), from which the solution associated with a new initial distribution can be obtained through the Chapman-Kolmogorov equation without retraining the model. A major challenge in learning the transition PDF lies in the singular behavior induced by the Dirac initial condition. To address it, we