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arXiv · 2507.15442

An Adaptive Random Fourier Features approach Applied to Learning Stochastic Differential Equations

Owen Douglas·Aku Kammonen·Anamika Pandey·Raúl Tempone
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Abstract

This work proposes a training algorithm based on adaptive random Fourier features (ARFF) with Metropolis sampling and resampling \cite{kammonen2024adaptiverandomfourierfeatures} for learning drift and diffusion components of stochastic differential equations from snapshot data. Specifically, this study considers It\^{o} diffusion processes and a likelihood-based loss function derived from the Euler-Maruyama integration introduced in \cite{Dietrich2023} and \cite{dridi2021learningstochasticdynamicalsystems}. This work evaluates the proposed method against benchmark problems presented in \cite{Dietrich2023}, including polynomial examples, underdamped Langevin dynamics, a stochastic susceptible-infected-recovered model, and a stochastic wave equation. Across all cases, the ARFF-based approach matches or surpasses the performance of conventional Adam-based optimization in both loss minimization and convergence speed. These results highlight the potential of ARFF as a compelling alternative for data-driven modeling of stochastic dynamics.

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Owen Douglas, Aku Kammonen, Anamika Pandey, Raúl Tempone. 2025-07-21. An Adaptive Random Fourier Features approach Applied to Learning Stochastic Differential Equations. https://arxiv.org/abs/2507.15442

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