Gaussian process learning of nonlinear dynamics
(2024) In Communications in Nonlinear Science and Numerical Simulation 138.- Abstract
One of the pivotal tasks in scientific machine learning is to represent underlying dynamical systems from time series data. Many methods for such dynamics learning explicitly require the derivatives of state data, which are not directly available and can be approximated conventionally by finite differences. However, the discrete approximations of time derivatives may result in poor estimations when state data are scarce and/or corrupted by noise, thus compromising the predictiveness of the learned dynamical models. To overcome this technical hurdle, we propose a new method that learns nonlinear dynamics through a Bayesian inference of characterizing model parameters. This method leverages a Gaussian process representation of states, and... (More)
One of the pivotal tasks in scientific machine learning is to represent underlying dynamical systems from time series data. Many methods for such dynamics learning explicitly require the derivatives of state data, which are not directly available and can be approximated conventionally by finite differences. However, the discrete approximations of time derivatives may result in poor estimations when state data are scarce and/or corrupted by noise, thus compromising the predictiveness of the learned dynamical models. To overcome this technical hurdle, we propose a new method that learns nonlinear dynamics through a Bayesian inference of characterizing model parameters. This method leverages a Gaussian process representation of states, and constructs a likelihood function using the correlation between state data and their derivatives, yet prevents explicit evaluations of time derivatives. Through a Bayesian scheme, a probabilistic estimate of the model parameters is given by the posterior distribution, and thus a quantification is facilitated for uncertainties from noisy state data and the learning process. Specifically, we will discuss the applicability of the proposed method to several typical scenarios for dynamical systems: identification and estimation with an affine parametrization, nonlinear parametric approximation without prior knowledge, and general parameter estimation for a given dynamical system.
(Less)
- author
- Ye, Dongwei and Guo, Mengwu LU
- organization
- publishing date
- 2024
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Bayesian inference, Data-driven discovery, Dynamical systems, Gaussian process, Uncertainty quantification
- in
- Communications in Nonlinear Science and Numerical Simulation
- volume
- 138
- article number
- 108184
- publisher
- Elsevier
- external identifiers
-
- scopus:85198015221
- ISSN
- 1007-5704
- DOI
- 10.1016/j.cnsns.2024.108184
- language
- English
- LU publication?
- yes
- additional info
- Publisher Copyright: © 2024 The Author(s)
- id
- 0fe8c565-8eaa-45c5-89e3-9971bf09a15d
- date added to LUP
- 2024-07-30 19:01:37
- date last changed
- 2024-08-28 11:53:24
@article{0fe8c565-8eaa-45c5-89e3-9971bf09a15d,
abstract = {{<p>One of the pivotal tasks in scientific machine learning is to represent underlying dynamical systems from time series data. Many methods for such dynamics learning explicitly require the derivatives of state data, which are not directly available and can be approximated conventionally by finite differences. However, the discrete approximations of time derivatives may result in poor estimations when state data are scarce and/or corrupted by noise, thus compromising the predictiveness of the learned dynamical models. To overcome this technical hurdle, we propose a new method that learns nonlinear dynamics through a Bayesian inference of characterizing model parameters. This method leverages a Gaussian process representation of states, and constructs a likelihood function using the correlation between state data and their derivatives, yet prevents explicit evaluations of time derivatives. Through a Bayesian scheme, a probabilistic estimate of the model parameters is given by the posterior distribution, and thus a quantification is facilitated for uncertainties from noisy state data and the learning process. Specifically, we will discuss the applicability of the proposed method to several typical scenarios for dynamical systems: identification and estimation with an affine parametrization, nonlinear parametric approximation without prior knowledge, and general parameter estimation for a given dynamical system.</p>}},
author = {{Ye, Dongwei and Guo, Mengwu}},
issn = {{1007-5704}},
keywords = {{Bayesian inference; Data-driven discovery; Dynamical systems; Gaussian process; Uncertainty quantification}},
language = {{eng}},
publisher = {{Elsevier}},
series = {{Communications in Nonlinear Science and Numerical Simulation}},
title = {{Gaussian process learning of nonlinear dynamics}},
url = {{http://dx.doi.org/10.1016/j.cnsns.2024.108184}},
doi = {{10.1016/j.cnsns.2024.108184}},
volume = {{138}},
year = {{2024}},
}