mlsanityData to 14 Oct 2026

FlowKac: An Efficient Neural Fokker-Planck solver using Temporal Normalizing Flows and the Feynman-Kac Formula

arXiv 2503.11427 ↗First posted 14 Mar 2025cs.LG math.DS stat.MLcited by 3

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Abstract (arXiv)

Solving the Fokker-Planck equation for high-dimensional complex dynamical systems remains a pivotal yet challenging task due to the intractability of analytical solutions and the limitations of traditional numerical methods. In this work, we present FlowKac, a novel approach that reformulates the Fokker-Planck equation using the Feynman-Kac formula, allowing to query the solution at a given point via the expected values of stochastic paths. A key innovation of FlowKac lies in its adaptive stochastic sampling scheme which significantly reduces the computational complexity while maintaining high accuracy. This sampling technique, coupled with a time-indexed normalizing flow, designed for capturing time-evolving probability densities, enables robust sampling of collocation points, resulting in a flexible and mesh-free solver. This formulation mitigates the curse of dimensionality and enhances computational efficiency and accuracy, which is particularly crucial for applications that inherently require dimensions beyond the conventional three. We validate the robustness and scalability of our method through various experiments on a range of stochastic differential equations, demonstrating significant improvements over existing techniques.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 24 of its 53 references that are in the map. First posted on arXiv 14 Mar 2025.

Builds on

24 of 53 references.

References · 24

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  2. 2022Flow Matching for Generative Modelingcited by 5,702
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12 more
  1. 2023Tackling the Curse of Dimensionality with Physics-Informed Neural Networkscited by 79
  2. 2020Algorithms for Solving High Dimensional PDEs: From Nonlinear Monte Carlo to Machine Learningcited by 77
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  5. 2018Forward-Backward Stochastic Neural Networks: Deep Learning of High-dimensional Partial Differential Equationscited by 55
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  12. 2018Unbiased deep solvers for linear parametric PDEscited by 5

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 3.

3 papers.

  1. 2026A deep learning framework for jointly solving transient Fokker-Planck equations with arbitrary parameters and initial distributionscited by 1
  2. 2026A transition-density-based operator learning method for Fokker-Planck equations with various initial conditionscited by 0
  3. 2026Deep operator learning for efficient sampling from invariant measures of stochastic differential equationscited by 0