发布时间：

2026-07-01

DOI码：

10.1016/j.neunet.2025.107508

所属单位：

国家数字化学习工程技术研究中心

论文名称：

Physics-informed multi-output Gaussian process for dynamical system

发表刊物：

Neural Networks

关键字：

Gaussian process;Physical prior knowledge;Multi-output modeling;Dynamical system

摘要：

Learning accurate dynamics models is crucial for model-based reinforcement learning. Gaussian processes (GPs), as a probabilistic modeling approach, have been widely used for dynamical system modeling. However, standard GPs are designed for single-output scenarios, modeling each dimension of a dynamical system independently and failing to capture dependencies among them. Multi-output GPs address this limitation by jointly modeling multiple outputs, capturing their correlations, and enabling information transfer across dimensions. As a result, each output can leverage information from others to improve modeling accuracy. Existing multi-output GPs typically capture the correlation between multiple outputs using covariance functions, but this approach often lacks interpretability in the context of dynamical system modeling. This paper proposes a physics-informed multi-output Gaussian process (P-MO-GP) for dynamical system modeling. P-MO-GP incorporates a physical model derived from the Lagrangian method as prior knowledge and models each dimension of the dynamical system as a GP with the mean function defined by the discretized physical model. The mean functions of all dimensions share the same parameter, namely the physical parameter. P-MO-GP treats all hyperparameters (the physical parameter, kernel parameters, and noise variances) as random variables and adopts a fully Bayesian framework. With a probabilistic graphical model, we prove that when the physical parameter is unknown, all dimensions of the dynamical system become dependent. We propose an interpretable and principled approach to correlating all dimensions of a dynamical system by leveraging the natural assumption that all dimensions share a common physical parameter. Through extensive simulations, we demonstrate that the proposed model, P-MO-GP, learns more accurate dynamics models, achieves better control performance, and is more robust to observation noise than both single-output GPs and existing multi-output GPs.

合写作者：

何彬

第一作者：

汤胜兵

论文类型：

期刊论文

通讯作者：

余新国

论文编号：

1973035289144332288

文献类型：

00001

页面范围：

107508

ISSN号：

0893-6080

是否译文：

否

发表时间：

2025-09-01

收录刊物：

其他（ESI、Scopus、OA）、EI、SCI