Symbolic Discovery of Stochastic Differential Equations with Genetic Programming

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Main Authors: de Vries, Sigur, Keemink, Sander W., van Gerven, Marcel A. J.
Format: Preprint
Published: 2026
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author de Vries, Sigur
Keemink, Sander W.
van Gerven, Marcel A. J.
author_facet de Vries, Sigur
Keemink, Sander W.
van Gerven, Marcel A. J.
contents Automated scientific discovery aims to improve scientific understanding through machine learning. A central approach in this field is symbolic regression, which uses genetic programming or sparse regression to learn interpretable mathematical expressions to explain observed data. Conventionally, the focus of symbolic regression is on identifying ordinary differential equations. The general view is that noise only complicates the recovery of deterministic dynamics. However, explicitly learning a symbolic function of the noise component in stochastic differential equations enhances modelling capacity, increases knowledge gain and enables generative sampling. We introduce a method for symbolic discovery of stochastic differential equations based on genetic programming, jointly optimizing drift and diffusion functions via the maximum likelihood estimate. Our results demonstrate accurate recovery of governing equations, efficient scaling to higher-dimensional systems, robustness to sparsely sampled problems and generalization to stochastic partial differential equations. This work extends symbolic regression toward interpretable discovery of stochastic dynamical systems, contributing to the automation of science in a noisy and dynamic world.
format Preprint
id arxiv_https___arxiv_org_abs_2603_09597
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Symbolic Discovery of Stochastic Differential Equations with Genetic Programming
de Vries, Sigur
Keemink, Sander W.
van Gerven, Marcel A. J.
Neural and Evolutionary Computing
Symbolic Computation
Automated scientific discovery aims to improve scientific understanding through machine learning. A central approach in this field is symbolic regression, which uses genetic programming or sparse regression to learn interpretable mathematical expressions to explain observed data. Conventionally, the focus of symbolic regression is on identifying ordinary differential equations. The general view is that noise only complicates the recovery of deterministic dynamics. However, explicitly learning a symbolic function of the noise component in stochastic differential equations enhances modelling capacity, increases knowledge gain and enables generative sampling. We introduce a method for symbolic discovery of stochastic differential equations based on genetic programming, jointly optimizing drift and diffusion functions via the maximum likelihood estimate. Our results demonstrate accurate recovery of governing equations, efficient scaling to higher-dimensional systems, robustness to sparsely sampled problems and generalization to stochastic partial differential equations. This work extends symbolic regression toward interpretable discovery of stochastic dynamical systems, contributing to the automation of science in a noisy and dynamic world.
title Symbolic Discovery of Stochastic Differential Equations with Genetic Programming
topic Neural and Evolutionary Computing
Symbolic Computation
url https://arxiv.org/abs/2603.09597