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Description
We present a novel training algorithm based on adaptive random Fourier features sampling [1] for the learning of the drift and the diffusion components of stochastic differential equations (SDEs). Specifically, we considerItˆo diffusion processes and a loss function [2] derived from the Euler-Maruyama (EM) integration scheme. Promising results, improving both the loss and the training time have been observed compared to traditional gradient-based methods.
[1] Aku Kammonen, Jonas Kiessling, Petr Plech´aˇc, Mattias Sandberg, and Anders Szepessy. Adaptive randomfourier features with metropolis sampling, 2020.
[2] Felix Dietrich, Alexei Makeev, George Kevrekidis, Nikolaos Evangelou, Tom Bertalan, Sebastian Reich, andIoannis G. Kevrekidis. Learning effective stochastic differential equations from microscopic simulations:Linking stochastic numerics to deep learning, 2023.
