相关论文: Gaussian Process Port-Hamiltonian Systems: Bayesia…

In this paper, we propose a novel Gaussian process-based moving horizon estimation (MHE) framework for unknown nonlinear systems. On the one hand, we approximate the system dynamics by the posterior means of the learned Gaussian processes…

Partial differential equations (PDEs) are important tools to model physical systems and including them into machine learning models is an important way of incorporating physical knowledge. Given any system of linear PDEs with constant…

Gaussian process state-space models (GP-SSMs) are a very flexible family of models of nonlinear dynamical systems. They comprise a Bayesian nonparametric representation of the dynamics of the system and additional (hyper-)parameters…

Hamiltonian systems are differential equations which describe systems in classical mechanics, plasma physics, and sampling problems. They exhibit many structural properties, such as a lack of attractors and the presence of conservation…

Modeling stochastic traffic behaviors at the microscopic level, such as car-following and lane-changing, is a crucial task to understand the interactions between individual vehicles in traffic streams. Leveraging a recently developed theory…

An important issue in model-based control design is that an accurate dynamic model of the system is generally nonlinear, complex, and costly to obtain. This limits achievable control performance in practice. Gaussian process (GP) based…

Probabilistic models such as Gaussian processes (GPs) are powerful tools to learn unknown dynamical systems from data for subsequent use in control design. While learning-based control has the potential to yield superior performance in…

We propose a principled algorithm for robust Bayesian filtering and smoothing in nonlinear stochastic dynamic systems when both the transition function and the measurement function are described by non-parametric Gaussian process (GP)…

This paper proposes a receding horizon active learning and control problem for dynamical systems in which Gaussian Processes (GPs) are utilized to model the system dynamics. The active learning objective in the optimization problem is…

Probabilistic approaches for handling count-valued time sequences have attracted amounts of research attentions because their ability to infer explainable latent structures and to estimate uncertainties, and thus are especially suitable for…

We extend deterministic port-Hamiltonian systems (PHS) to a stochastic framework by means of stochastic differential equations. As the dissipation inequality plays a crucial role for deterministic PHS, we develop several passivity concepts…

We develop a new Bayesian framework based on deep neural networks to be able to extrapolate in space-time using historical data and to quantify uncertainties arising from both noisy and gappy data in physical problems. Specifically, the…

Gaussian Processes (GPs) provide a convenient framework for specifying function-space priors, making them a natural choice for modeling uncertainty. In contrast, Bayesian Neural Networks (BNNs) offer greater scalability and extendability…

Estimating state of health is a critical function of a battery management system but remains challenging due to the variability of operating conditions and usage requirements of real applications. As a result, techniques based on fitting…

Variational inference techniques based on inducing variables provide an elegant framework for scalable posterior estimation in Gaussian process (GP) models. Besides enabling scalability, one of their main advantages over sparse…

Sequential learning with Gaussian processes (GPs) is challenging when access to past data is limited, for example, in continual and active learning. In such cases, errors can accumulate over time due to inaccuracies in the posterior,…

This tutorial provides a systematic introduction to Gaussian process learning-based model predictive control (GP-MPC), an advanced approach integrating Gaussian process (GP) with model predictive control (MPC) for enhanced control in…

Differential equations based on physical principals are used to represent complex dynamic systems in all fields of science and engineering. Through repeated use in both academics and industry, these equations have been shown to represent…

Recent advances in sensing and imaging technologies have enabled the collection of high-dimensional spatiotemporal data across complex geometric domains. However, effective modeling of such data remains challenging due to irregular spatial…

In this paper we design discrete port-Hamiltonian systems systematically in two different ways, by applying discrete gradient methods and splitting methods respectively. The discrete port-Hamiltonian systems we get satisfy a discrete notion…