Solving Fokker–Planck equations using deep KD-tree with a small amount of data

The Fokker–Planck (FP) equation can deterministically describe the evolution of probability density function, which plays an extremely significant role in fields stochastic dynamics. Unfortunately, limited samples that arise from consideration engineering practice are inevitable, restricts solving FP equation. Accordingly, present study, a super-DL-FP framework is established to solve steady-state with small amount data, through combining deep KD-tree and DL-FP approach proposed [Chaos 30, 013133 (2020)]. It should be emphasized normalization condition great importance has considered An appropriate integral estimation for under non-uniform meshing effectively improve precision solution, but it still challenging problem, especially case data. Thus, so-called method innovatively estimate normalized random dataset. main target obtain discrete points corresponding volumes by executing multiple segmentation based on data region. Several numerical experiments comparisons implemented illustrate superior performance method. obtained results indicate algorithm accomplish higher accuracy sense lower cost than well-known algorithms like center difference scheme, Chebyshev spectrum algorithm, flow approach.