[2604.06081] A machine learning framework for uncovering stochastic nonlinear dynamics from noisy data

Computer Science > Machine Learning arXiv:2604.06081 (cs) [Submitted on 7 Apr 2026] Title:A machine learning framework for uncovering stochastic nonlinear dynamics from noisy data Authors:Matteo Bosso, Giovanni Franzese, Kushal Swamy, Maarten Theulings, Alejandro M. Aragón, Farbod Alijani View a PDF of the paper titled A machine learning framework for uncovering stochastic nonlinear dynamics from noisy data, by Matteo Bosso and Giovanni Franzese and Kushal Swamy and Maarten Theulings and Alejandro M. Arag\'on and Farbod Alijani View PDF Abstract:Modeling real-world systems requires accounting for noise - whether it arises from unpredictable fluctuations in financial markets, irregular rhythms in biological systems, or environmental variability in ecosystems. While the behavior of such systems can often be described by stochastic differential equations, a central challenge is understanding how noise influences the inference of system parameters and dynamics from data. Traditional symbolic regression methods can uncover governing equations but typically ignore uncertainty. Conversely, Gaussian processes provide principled uncertainty quantification but offer little insight into the underlying dynamics. In this work, we bridge this gap with a hybrid symbolic regression-probabilistic machine learning framework that recovers the symbolic form of the governing equations while simultaneously inferring uncertainty in the system parameters. The framework combines deep symbolic regr...