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FlowKac

Code for the paper

"FlowKac: Convergent Fokker-Planck Solutions via Temporal Normalizing Flows and Feynman-Kac Formula"

FlowKac is a novel approach that reformulates the Fokker-Planck equation using the Feynman-Kac formula to obtain a loss function based on expected values of stochastic paths. FlowKac offers efficient and accurate sampling capability of stochastic paths by using the properties of stochastic flows and Taylor expansions. This sampling technique coupled with a time-indexed normalizing flow, enables solving the Fokker-Plank equation for complex dynamics.

Acknowledgements

The code make use of codes from the following papers

FENG, Xiaodong, ZENG, Li, et ZHOU, Tao. "Solving time dependent Fokker-Planck equations via temporal normalizing flow" (2021) [arxiv]

TANG, Kejun, WAN, Xiaoliang, et LIAO, Qifeng. "Adaptive deep density approximation for Fokker-Planck equations". Journal of Computational Physics, 2022, vol. 457, p. 111080. https://github.com/xlwan/KRnet

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