Sparse inference and active learning of stochastic differential equations from data
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2022
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866911897131941888 |
|---|---|
| author | Huang, Yunfei Mabrouk, Youssef Gompper, Gerhard Sabass, Benedikt |
| author_facet | Huang, Yunfei Mabrouk, Youssef Gompper, Gerhard Sabass, Benedikt |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_11010 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Sparse inference and active learning of stochastic differential equations from data Huang, Yunfei Mabrouk, Youssef Gompper, Gerhard Sabass, Benedikt Statistical Mechanics Quantitative Methods 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. |
| title | Sparse inference and active learning of stochastic differential equations from data |
| topic | Statistical Mechanics Quantitative Methods |
| url | https://arxiv.org/abs/2203.11010 |