Parameter estimation in stochastic differential equations via Wiener chaos expansion and stochastic gradient descent

This study addresses the inverse problem of parameter estimation for Stochastic Differential Equations by minimizing a regularized discrepancy functional via Stochastic Gradient Descent. To achieve computational efficiency, we leverage the Wiener Chaos Expansion, 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 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 Markov chain Monte Carlo or Maximum Likelihood Estimation. The robustness and scalability of the proposed approach are demonstrated through numerical experiments on various non-linear Stochastic Differential Equations, including models for individual biological growth. Results show that the Wiener Chaos Expansion-Stochastic Gradient Descent framework provides accurate parameter recovery even from discrete, noisy observations, offering a significant paradigm shift in the efficient modeling of complex stochastic systems.