A data-driven ANN method estimates low-lying Fokker-Planck and Koopman eigenfunctions from Monte Carlo density relaxations, and is used to define a stochastic asymptotic phase for the noisy Lorenz system.
An efficient data-driven solver for Fokker-Planck equations: algorithm and analysis
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abstract
Computing the invariant probability measure of a randomly perturbed dynamical system usually means solving the stationary Fokker-Planck equation. This paper studies several key properties of a novel data-driven solver for low-dimensional Fokker-Planck equations proposed in [15]. Based on these results, we propose a new `block solver' for the stationary Fokker-Planck equation, which significantly improves the performance of the original algorithm. Some possible ways of reducing numerical artifacts caused by the block solver are discussed and tested with examples.
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Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions
A data-driven ANN method estimates low-lying Fokker-Planck and Koopman eigenfunctions from Monte Carlo density relaxations, and is used to define a stochastic asymptotic phase for the noisy Lorenz system.