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Gaussian processes (GPs) are ubiquitous tools for modeling and predicting continuous processes in physical and engineering sciences. This is partly due to the fact that one may employ a Gaussian process as an interpolator while facilitating…

Statistics Theory · Mathematics 2025-12-16 D. Andrew Brown , Peter Kiessler , John Nicholson

Kernel models of potential energy surfaces (PES) for polyatomic molecules are often restricted by a specific choice of the kernel function. This can be avoided by optimizing the complexity of the kernel function. For regression problems…

Chemical Physics · Physics 2023-05-02 Jun Dai , Roman V. Krems

In this paper, we focus on the data-driven discovery of a general second-order particle-based model that contains many state-of-the-art models for modeling the aggregation and collective behavior of interacting agents of similar size and…

Machine Learning · Statistics 2023-11-03 Jinchao Feng , Charles Kulick , Sui Tang

Gaussian process (GP) priors are non-parametric generative models with appealing modelling properties for Bayesian inference: they can model non-linear relationships through noisy observations, have closed-form expressions for training and…

Machine Learning · Statistics 2020-01-31 Gonzalo Rios

A key challenge in the practical application of Gaussian processes (GPs) is selecting a proper covariance function. The moving average, or process convolutions, construction of GPs allows some additional flexibility, but still requires…

Machine Learning · Statistics 2022-10-19 Thomas M. McDonald , Magnus Ross , Michael T. Smith , Mauricio A. Álvarez

Ensuring safety and adapting to the user's behavior are of paramount importance in physical human-robot interaction. Thus, incorporating elastic actuators in the robot's mechanical design has become popular, since it offers intrinsic…

Robotics · Computer Science 2024-05-15 Samuel Tesfazgi , Markus Keßler , Emilio Trigili , Armin Lederer , Sandra Hirche

Off-the-shelf Gaussian Process (GP) covariance functions encode smoothness assumptions on the structure of the function to be modeled. To model complex and non-differentiable functions, these smoothness assumptions are often too…

Machine Learning · Statistics 2016-04-12 Roberto Calandra , Jan Peters , Carl Edward Rasmussen , Marc Peter Deisenroth

This paper presents a Gaussian Process (GP) framework, a non-parametric technique widely acknowledged for regression and classification tasks, to address inverse problems in mean field games (MFGs). By leveraging GPs, we aim to recover…

Computer Science and Game Theory · Computer Science 2023-12-27 Jinyan Guo , Chenchen Mou , Xianjin Yang , Chao Zhou

We introduce new Gaussian Process (GP) high-order approximations to linear operations that are frequently used in various numerical methods. Our method employs the kernel-based GP regression modeling, a non-parametric Bayesian approach to…

Computational Physics · Physics 2025-06-09 Christopher DeGrendele , Dongwook Lee

This paper presents a method for approximate Gaussian process (GP) regression with tensor networks (TNs). A parametric approximation of a GP uses a linear combination of basis functions, where the accuracy of the approximation depends on…

Machine Learning · Statistics 2023-11-01 Clara Menzen , Eva Memmel , Kim Batselier , Manon Kok

Effective forces -- derived from experimental or {\it in silico} molecular dynamics time traces -- are critical in developing reduced and computationally efficient descriptions of otherwise complex dynamical problems. Thus, designing…

Biological Physics · Physics 2019-08-29 J Shepard Bryan , Ioannis Sgouralis , Steve Pressé

Prior beliefs about the latent function to shape inductive biases can be incorporated into a Gaussian Process (GP) via the kernel. However, beyond kernel choices, the decision-making process of GP models remains poorly understood. In this…

Machine Learning · Computer Science 2023-06-07 Maximilian P. Niroomand , Luke Dicks , Edward O. Pyzer-Knapp , David J. Wales

Inference in popular nonparametric Bayesian models typically relies on sampling or other approximations. This paper presents a general methodology for constructing novel tractable nonparametric Bayesian methods by applying the kernel trick…

Machine Learning · Statistics 2011-08-15 Ferenc Huszár , Simon Lacoste-Julien

Gaussian process regression is a well-established Bayesian machine learning method. We propose a new approach to Gaussian process regression using quantum kernels based on parameterized quantum circuits. By employing a hardware-efficient…

Quantum Physics · Physics 2024-02-06 Frederic Rapp , Marco Roth

Machine learning (ML) techniques have recently gained significant attention for solving compliance minimization (CM) problems. However, these methods typically provide poor feature boundaries, are very expensive, and lack a systematic…

Machine Learning · Computer Science 2025-11-06 Xiangyu Sun , Amin Yousefpour , Shirin Hosseinmardi , Ramin Bostanabad

Gaussian processes provide a powerful probabilistic kernel learning framework, which allows learning high quality nonparametric regression models via methods such as Gaussian process regression. Nevertheless, the learning phase of Gaussian…

Numerical Analysis · Mathematics 2021-01-06 Paz Fink Shustin , Haim Avron

Gaussian Processes (GPs) are widely recognized as powerful non-parametric models for regression and classification. Traditional GP frameworks predominantly operate under the assumption that the inputs are either accurately known or subject…

Systems and Control · Electrical Eng. & Systems 2025-10-14 Muzaffar Qureshi , Tochukwu Elijah Ogri , Zachary I. Bell , Wanjiku A. Makumi , Rushikesh Kamalapurkar

Gaussian processes (GPs) enable principled computation of model uncertainty, making them attractive for safety-critical applications. Such scenarios demand that GP decisions are not only accurate, but also robust to perturbations. In this…

Machine Learning · Computer Science 2021-04-08 Andrea Patane , Arno Blaas , Luca Laurenti , Luca Cardelli , Stephen Roberts , Marta Kwiatkowska

Gaussian processes regression models are an appealing machine learning method as they learn expressive non-linear models from exemplar data with minimal parameter tuning and estimate both the mean and covariance of unseen points. However,…

Machine Learning · Computer Science 2020-08-25 Vladimir Joukov , Dana Kulić

Gaussian processes (GPs) are crucial in machine learning for quantifying uncertainty in predictions. However, their associated covariance matrices, defined by kernel functions, are typically dense and large-scale, posing significant…

Machine Learning · Computer Science 2025-04-02 Theresa Wagner , Tianshi Xu , Franziska Nestler , Yuanzhe Xi , Martin Stoll