{"ID":2892168,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.15442","arxiv_id":"2507.15442","title":"An Adaptive Random Fourier Features approach Applied to Learning Stochastic Differential Equations","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 Itô 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.","short_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 Itô di...","url_abs":"https://arxiv.org/abs/2507.15442","url_pdf":"https://arxiv.org/pdf/2507.15442v1","authors":"[\"Owen Douglas\",\"Aku Kammonen\",\"Anamika Pandey\",\"Raúl Tempone\"]","published":"2025-07-21T09:52:33Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[\"Diffusion Model\"]","has_code":false}