An Adaptive Random Fourier Features approach Applied to Learning Stochastic Differential Equations
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866913950733434880 |
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| author | Douglas, Owen Kammonen, Aku Pandey, Anamika Tempone, Raúl |
| author_facet | Douglas, Owen Kammonen, Aku Pandey, Anamika Tempone, Raúl |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_15442 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Adaptive Random Fourier Features approach Applied to Learning Stochastic Differential Equations Douglas, Owen Kammonen, Aku Pandey, Anamika Tempone, Raúl Machine Learning 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. |
| title | An Adaptive Random Fourier Features approach Applied to Learning Stochastic Differential Equations |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2507.15442 |