Structure-Preserving Discretizations for Fokker–Planck Equations via the Energy Dissipation Law (Satish Chandran, UCR)

Abstract: We present a new approach for deriving structure-preserving numerical discretizations of Fokker-Planck equations by establishing a connection between the Fokker-Planck equation and its semi-discrete master equation at the level of the energy-dissipation law. We determine the transition rate in the master equation via the detailed balance condition and the spatial discretization of the continuous energy-dissipation law. This approach ensures that the semi-discrete master equation satisfies the detailed balance condition and converges to the correct equilibrium. In addition to recovering existing transition rates proposed in earlier works, our framework uncovers new transition rates that have not been discussed in the current literature. This work is joint with Dr. Yiwei Wang (UCR).