Parameter Estimation in Stochastic Differential Equations via Wiener Chaos Expansion and Stochastic Gradient Descent
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866912986460848128 |
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| author | Delgado-Vences, Francisco Pavón-Español, José Julián Ornelas, Arelly |
| author_facet | Delgado-Vences, Francisco Pavón-Español, José Julián Ornelas, Arelly |
| contents | This study addresses the inverse problem of parameter estimation for Stochastic Differential Equations (SDEs) by minimizing a regularized discrepancy functional via Stochastic Gradient Descent (SGD). To achieve computational efficiency, we leverage the Wiener Chaos Expansion (WCE), a spectral decomposition technique that projects the stochastic solution onto an orthogonal basis of Hermite polynomials. This transformation effectively maps the stochastic dynamics into a hierarchical system of deterministic functions, termed the \textit{propagator}. By reducing the stochastic inference task to a deterministic optimization problem, our framework circumvents the heavy computational burden and sampling requirements of traditional simulation-based methods like MCMC or MLE. The robustness and scalability of the proposed approach are demonstrated through numerical experiments on various non-linear SDEs, including models for individual biological growth. Results show that the WCE-SGD framework provides accurate parameter recovery even from discrete, noisy observations, offering a significant paradigm shift in the efficient modeling of complex stochastic systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_27019 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Parameter Estimation in Stochastic Differential Equations via Wiener Chaos Expansion and Stochastic Gradient Descent Delgado-Vences, Francisco Pavón-Español, José Julián Ornelas, Arelly Machine Learning Probability Methodology 60H10, 60H35, 62F12, 65C30 This study addresses the inverse problem of parameter estimation for Stochastic Differential Equations (SDEs) by minimizing a regularized discrepancy functional via Stochastic Gradient Descent (SGD). To achieve computational efficiency, we leverage the Wiener Chaos Expansion (WCE), a spectral decomposition technique that projects the stochastic solution onto an orthogonal basis of Hermite polynomials. This transformation effectively maps the stochastic dynamics into a hierarchical system of deterministic functions, termed the \textit{propagator}. By reducing the stochastic inference task to a deterministic optimization problem, our framework circumvents the heavy computational burden and sampling requirements of traditional simulation-based methods like MCMC or MLE. The robustness and scalability of the proposed approach are demonstrated through numerical experiments on various non-linear SDEs, including models for individual biological growth. Results show that the WCE-SGD framework provides accurate parameter recovery even from discrete, noisy observations, offering a significant paradigm shift in the efficient modeling of complex stochastic systems. |
| title | Parameter Estimation in Stochastic Differential Equations via Wiener Chaos Expansion and Stochastic Gradient Descent |
| topic | Machine Learning Probability Methodology 60H10, 60H35, 62F12, 65C30 |
| url | https://arxiv.org/abs/2603.27019 |