We propose a randomized quasi-Monte Carlo (RQMC) sampling strategy for score-based learning of high-dimensional Fokker-Planck equations. The method follows a two-stage framework: the score function is first learned by conditional score matching, and the log-likelihood is then reconstructed from the learned score. To improve the empirical approximation of the expectation-type losses arising in both stages, we express them as integrals over the unit cube via the inversion transformation, which facilitates the use of RQMC quadrature rules in the empirical losses. We then analyze the transformed integrands through mixed-derivative bounds under a boundary-growth condition for a class of stochastic processes with Gaussian-transition kernels. We prove that the scrambled-net quadrature (a classical RQMC method) with a sample size N can achieve an error rate of nearly $O(N^{-1})$, beating the MC rate $O(N^{-1/2})$. Numerical experiments on high-dimensional anisotropic Ornstein-Uhlenbeck (OU) problems show that the proposed sampling strategy improves training stability and sample efficiency, and yields more accurate approximations of the score, log-likelihood, and density than the standard MC baseline.
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Funding
Guangdong Basic and Applied Basic Research Foundation(2025A1515011888, 2026B0303000003)
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Shanghai University
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