Sparse inference and active learning of stochastic differential equations from data
arXiv:2203.11010 · doi:10.1038/s41598-022-25638-9
Abstract
Automatic machine learning of empirical models from experimental data has recently become possible as a result of increased availability of computational power and dedicated algorithms. Despite the successes of non-parametric inference and neural-network-based inference for empirical modelling, a physical interpretation of the results often remains challenging. Here, we focus on direct inference of governing differential equations from data, which can be formulated as a linear inverse problem. A Bayesian framework with a Laplacian prior distribution is employed for finding sparse solutions efficiently. The superior accuracy and robustness of the method is demonstrated for various cases, including ordinary, partial, and stochastic differential equations. Furthermore, we develop an active learning procedure for the automated discovery of stochastic differential equations. In this procedure, learning of the unknown dynamical equations is coupled to the application of perturbations to the measured system in a feedback loop. We demonstrate with simulations that the active learning procedure improves the inference of empirical, Langevin-type descriptions of stochastic processes.
References in corpus (7)
- A Variational Approach to Enhanced Sampling and Free Energy Calculations
- A Unified Approach to Enhanced Sampling
- Learning the dynamics of cell-cell interactions in confined cell migration
- A New Algorithm Based Entropic Threshold for Edge Detection in Images
- Langevin equations from experimental data: the case of rotational diffusion in granular media
- Markov properties in presence of measurement noise
- Arbitrary-order finite-time corrections for the Kramers-Moyal operator