Gaussian Process Regression

Also known as GP

Gaussian process regression (GPR) places a probability distribution over functions, with kernels encoding assumptions such as smoothness, periodicity, or shared structure; conditioning on observations yields predictions and uncertainty, especially useful when data are scarce or decisions depend on confidence. Research develops richer models—including nonstationary, additive, multi-output, deep, and physics-informed GPs—and applies them to time series, spatial fields, dynamical systems, scientific surrogates, and Bayesian optimization. Because exact inference scales cubically with sample count, scalable approaches use inducing points and variational inference, nearest-neighbor or Vecchia approximations, sparse and low-rank kernels, and streaming or distributed updates. A central tension is balancing expressive models and calibrated uncertainty against computational cost and sensitivity to kernel and hyperparameter choices; reliable uncertainty under misspecification and scalable high-dimensional inference remain open challenges.

Latest papers

111 papers14 papers in the last four weeks, down 7% on the four weeks before. 0.1% of all new papers.

Multifidelity-Augmented Gaussian Process Inputs for Surrogate Modeling from Scarce Data
Mar 23, 2026Atticus Rex, Elizabeth Qian, David PetersonSurrogate Modeling Multifidelity Modeling
School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA · School of Computational Science & Engineering, Georgia Institute of Technology, Atlanta, GA · Air Force Research Lab, Wright-Patterson AFB, Dayton, Ohio
Time-adaptive infinite-dimensional Gaussian process regression on manifolds
Mar 22, 2026MD Ruiz-Medina, AE Madrid, A Torres-Signes +1Empirical Bayes Bayesian Inference
Infinite-dimensional spherical-radial decomposition for probabilistic functions, with application to constrained optimal control and Gaussian process regression
Mar 20, 2026Kewei Wang, Georg StadlerChance-Constrained Optimization Stochastic Optimal Control
Courant Institute School of Mathematics, Computing and Data Science, New York University, New York, USA
On Additive Gaussian Processes for Wind Farm Power Prediction
Mar 18, 2026Simon M. Brealy, Lawrence A. Bull, Daniel S. Brennan +4Wind Power Forecasting Gaussian Processes
Dynamics Research Group, Department of Mechanical Engineering, The University of Sheffield, Mappin Street, Sheffield, S1 3JD, UK · Computational Statistics and Machine Learning Group, Department of Engineering, University of Cambridge, Cambridge, CB3 0FA, UK · Vattenfall R&D, Vattenfall AB, Älvkarleby, Sweden
Real-Time Online Learning for Model Predictive Control using a Spatio-Temporal Gaussian Process Approximation
Mar 18, 2026Lars Bartels, Amon Lahr, Andrea Carron +1Model Predictive Control Gaussian Processes
Institute for Dynamic Systems and Control, ETH Zürich, CH-8092 Zürich, Switzerland.
Wasserstein-type Gaussian Process Regressions for Input Measurement Uncertainty
Mar 18, 2026Hengrui Luo, Xiaoye S. Li, Yang Liu +3Gaussian Process Regression Uncertainty Quantification
Department of Statistics Rice University, Houston, TX 77005 · Lawrence Berkeley National Laboratory, Berkeley, CA 94709
Optimal uncertainty bounds for multivariate kernel regression under bounded noise: A Gaussian process-based dual function
Mar 17, 2026Amon Lahr, Anna Scampicchio, Johannes Köhler +1Kernel Methods Gaussian Process Regression
Institute for Dynamical Systems and Control, ETH Zurich, Zurich, Switzerland
Kriging via variably scaled kernels
Mar 16, 2026Gianluca Audone, Francesco Marchetti, Emma Perracchione +1Gaussian Processes Gaussian Process Regression
Faculty of Engineering and Physical Sciences, University of Southampton, United Kindom · Dipartimento di Matematica “Tullio Levi-Civita”, Universit`a di Padova, Italy · Dipartimento di Scienze Matematiche Giuseppe Luigi Lagrange, Politecnico di Torino, Italy +1
Gaussian Process Regression-based Knowledge Distillation Framework for Simultaneous Prediction of Physical and Mechanical Properties of Epoxy Polymers
Mar 12, 2026Sindu B. S., Jan HamaekersMaterials Property Prediction Polymer Property Prediction
Special and Multifunctional Structures Laboratory, CSIR-Structural Engineering Research Centre, Taramani, Chennai, Tamil Nadu, India - 600113. · Fraunhofer Institute for Algorithms and Scientific Computing SCAI, Schloss Birlinghoven, 53757 Sankt Augustin, Germany
A Unified Hierarchical Multi-Task Multi-Fidelity Framework for Data-Efficient Surrogate Modeling in Manufacturing
Mar 10, 2026Manan Mehta, Zhiqiao Dong, Yuhang Yang +1Surrogate Modeling Multifidelity Modeling
Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, United States · Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 41809, United States
Instrumental and Proximal Causal Inference with Gaussian Processes
Mar 2, 2026Yuqi Zhang, Krikamol Muandet, Dino Sejdinovic +2Proximal Causal Inference Causal Inference
Department of Statistics and Actuarial Science, University of Hong Kong, Hong Kong · Rational Intelligence Lab, CISPA Helmholtz Center for Information Security, Germany · Australian Institute for Machine Learning, Adelaide University, Australia +1
Scalable Gaussian process modeling of parametrized spatio-temporal fields
Feb 27, 2026Srinath Dama, Prasanth B. NairGaussian Processes Gaussian Process Regression
University of Toronto Institute for Aerospace Studies, 4925 Dufferin Street, Toronto, M3H 5T6, Ontario, Canada
From Shallow Bayesian Neural Networks to Gaussian Processes: General Convergence, Identifiability and Scalable Inference
Feb 26, 2026Gracielle Antunes de Araújo, Flávio B. GonçalvesNyström Method Bayesian Neural Networks
Universidade do Estado de Minas Gerais (UEMG), FaEnge – Faculdade de Engenharia. · Universidade Federal de Minas Gerais (UFMG), ICEx – Instituto de Ciências Exatas.
Generative Bayesian Computation as a Scalable Alternative to Gaussian Process Surrogates
Feb 24, 2026Nick Polson, Vadim SokolovSurrogate Modeling Gaussian Process Regression
Booth School of Business, University of Chicago. · Department of Systems Engineering and Operations Research, George Mason University.
MAST: A Multi-fidelity Augmented Surrogate model via Spatial Trust-weighting
Feb 24, 2026Ahmed Mohamed Eisa Nasr, Ali Elham, Haris Moazam SheikhSurrogate Modeling Multifidelity Modeling
Department of Aeronautics and Astronautics, University of Southampton, SO17 1BJ, Southampton, United Kingdom
Quasi-Periodic Gaussian Process Predictive Iterative Learning Control
Feb 20, 2026Unnati Nigam, Radhendushka Srivastava, Faezeh Marzbanrad +1Iterative Learning Control Robotic Control
IITB-Monash Research Academy, IIT Bombay, Mumbai, India · Department of Mathematics, IIT Bombay, Mumbai, India · Department of Electrical and Computer Systems Engineering, Monash University, Clayton, Melbourne, Australia
Nonplanar Model Predictive Control for Autonomous Vehicles with Recursive Sparse Gaussian Process Dynamics
Feb 18, 2026Ahmad Amine, Kabir Puri, Viet-Anh Le +1Model Predictive Control Residual Dynamics Learning
Department of Electrical & Systems Engineering, University of Pennsylvania, Philadelphia, PA 19104, USA
Correcting Boundary Bias and Observation Independence in Bayesian Experimental Design
Feb 2, 2026Sanna Jarl, Jens Sjölund, Jonathan J. S. Scragg +1Active Learning Adaptive Sampling
Department of Material Science & Engineering Uppsala University RISE · Department of Information Technology Uppsala University · RISE
No-Regret Gaussian Process Optimization of Time-Varying Functions
Nov 29, 2025Eliabelle Mauduit, Eloïse Berthier, Andrea SimonettoMulti-Armed Bandits Bayesian Optimization
Unit´e de Math´ematiques Appliqu´ees ENSTA, Institut Polytechnique de Paris Palaiseau, France · U2IS ENSTA, Institut Polytechnique de Paris Palaiseau, France
Deep Jump Gaussian Processes for Surrogate Modeling of High-Dimensional Piecewise Continuous Functions
Oct 24, 2025Yang Xu, Chiwoo ParkDeep Gaussian Processes Surrogate Modeling
Industrial & Systems Engineering, University of Washington, Seattle, WA, USA
Gaussian Processes and Reproducing Kernel Hilbert Spaces: Connections and Equivalences
Jun 20, 2025Motonobu Kanagawa, Philipp Hennig, Dino Sejdinovic +1Gaussian Processes Reproducing Kernel Hilbert Spaces
EURECOM · University of Tübingen, Tübingen AI Center Max Planck Institute for Intelligent Systems · Adelaide University Australian Institute for Machine Learning +1

Mar 23, 2026J/K move · Enter open · S save

Multifidelity-Augmented Gaussian Process Inputs for Surrogate Modeling from Scarce Data

Atticus Rex, Elizabeth Qian, David Peterson

School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA · School of Computational Science & Engineering, Georgia Institute of Technology, Atlanta, GA · Air Force Research Lab, Wright-Patterson AFB, Dayton, Ohio

Surrogate Modeling Multifidelity Modeling Gaussian Process Regression

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Supervised machine learning describes the practice of fitting a parameterized model to labeled input-output data. Supervised machine learning methods have demonstrated promise in learning efficient surrogate models that can (partially) replace expensive high-fidelity models, making many-query analyses, such as optimization, uncertainty quantification, and inference, tractable. However, when training data must be obtained through the evaluation of an expensive model or experiment, the amount of training data that can be obtained is often limited, which can make learned surrogate models unreliable. In many engineering and scientific settings, cheaper low-fidelity models may be available, for example arising from simplified physics modeling or coarse grids. These models may be used to generate additional low-fidelity training data. The goal of multifidelity machine learning is to use both high- and low-fidelity training data to learn a surrogate model which is cheaper to evaluate than the high-fidelity model, but more accurate than any available low-fidelity model. This work proposes a new multifidelity training approach for Gaussian process regression which uses low-fidelity data to define additional features that augment the input space of the learned model. Similarly to cokriging estimators, the proposed approach conditions the high-fidelity surrogate model on the predictions of all available low-fidelity surrogate models, while benefiting from the computational efficiency of autoregressive estimators. Numerical experiments on several test problems demonstrate both increased predictive accuracy and reduced computational cost relative to the state of the art.