Gaussian Processes

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Inducing Permutation Invariant Priors in Bayesian Optimization for Carbon Capture and Storage Applications
May 4, 2026Sofianos Panagiotis Fotias, Vassilis GaganisBayesian Optimization Gaussian Processes
School of Mining and Metallurgical Engineering, National Technical University of Athens, Athens, 15773, Greece
Sequential Inference for Gaussian Processes: A Signal Processing Perspective
Apr 30, 2026Daniel Waxman, Fernando Llorente, Petar M. DjurićGaussian Processes Gaussian Process Regression
1Basis Research Institute · 3Computing and Data Sciences Directorate, Brookhaven National Laboratory · Department of Electrical and Computer Engineering, Stony Brook University
Predicting Covariate-Driven Spatial Deformation for Nonstationary Gaussian Processes
Apr 30, 2026Minghao Gu, Weizhi Lin, Qiang HuangGaussian Processes
Daniel J. Epstein Department of Industrial & Systems Engineering, Univeristy of Southern California · Charles W. Davidson College of Engineering, San José State University
Phase Transitions in the Fluctuations of Functionals of Random Neural Networks
Apr 21, 2026Simmaco Di Lillo, Leonardo Maini, Domenico MarinucciGaussian Processes
RoMaDS - Department of Mathematics, University of Rome Tor Vergata, Rome, Italy
An Efficient Spatial Branch-and-Bound Algorithm for Global Optimization of Gaussian Process Posterior Mean Functions
Apr 21, 2026Wei-Ting Tang, Akshay Kudva, Calvin Tsay +1Bayesian Optimization Global Optimization
Department of Chemical and Biological Engineering, University of Wisconsin-Madison, 1415 Engineering Drive, Madison, 53706, Wisconsin, USA. · Department of Chemical and Biomolecular Engineering, The Ohio State University, 151 W. Woodruf Avenue, Columbus, 43210, Ohio, USA. · Department of Computing, Imperial College London, Exhibition Rd, South Kensington, SW7 2AZ, London, United Kingdom.
GP-4DGS: Probabilistic 4D Gaussian Splatting from Monocular Video via Variational Gaussian Processes
Apr 3, 2026Mijeong Kim, Jungtaek Kim, Bohyung Han3D Gaussian Splatting Dynamic Scene Reconstruction
1ECE and 2IPAI, Seoul National University, Korea · University of Wisconsin–Madison, USA
Time-adaptive infinite-dimensional Gaussian process regression on manifolds
Mar 22, 2026MD Ruiz-Medina, AE Madrid, A Torres-Signes +1Empirical Bayes Bayesian Inference
Posterior Sampling Reinforcement Learning with Gaussian Processes for Continuous Control: Sublinear Regret Bounds for Unbounded State Spaces
Mar 9, 2026Hamish Flynn, Joe Watson, Ingmar Posner +1RL Control Regret Minimization in RL
Carnegie Mellon University · University of Oxford · Technical University of Darmstadt +2
Regular Fourier Features for Nonstationary Gaussian Processes
Feb 26, 2026Arsalan Jawaid, Abdullah Karatas, Jörg SeewigFourier Feature Embeddings Gaussian Processes
Institute of Measurement and Sensor Technology, University of Kaiserslautern-Landau, Kaiserslautern, Germany · Independent Researcher, Mannheim, Germany
Improving Forecasts of Suicide Attempts for Patients with Little Data
Nov 22, 2025Genesis Hang, Annie Chen, Hope Neveux +2Latent Variable Models Gaussian Processes
Wellesley College · Harvard University
Warm-Starting Iterative Gaussian Processes for Faster Sequential Inference
Nov 20, 2025Alan Yufei Dong, Jihao Andreas Lin, José Miguel Hernández-LobatoEfficient Inference Gaussian Processes
Department of Engineering, University of Cambridge
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

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Inducing Permutation Invariant Priors in Bayesian Optimization for Carbon Capture and Storage Applications

Sofianos Panagiotis Fotias, Vassilis Gaganis

School of Mining and Metallurgical Engineering, National Technical University of Athens, Athens, 15773, Greece

Bayesian Optimization Gaussian Processes

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Bayesian Optimization is an iterative method, tailored to optimizing expensive black box objective functions. Surrogate models like Gaussian Processes, which are the gold standard in Bayesian Optimization, can be inefficient for inputs with permutation symmetries, as the most common kernels employed are better suited for vector inputs rather than unordered sets of items. Motivated by this issue, we turn to permutation invariant Bayesian Optimization for well placement in Carbon Capture and Storage projects. The high fidelity black box simulator is instructed to operate wells under group control, giving rise to permutation symmetries within injector and producer groups that cannot be exploited with standard GP kernels. In this work, our main contribution is a novel Gaussian Process kernel (GP-Perm) that encodes permutation invariance by comparing sets through a stable divergence between their induced empirical representations, and can be combined with standard kernels for additional vector-valued inputs. As a learned invariant baseline, we also consider a Deep Kernel Learning model (DKL-DS) using the Deep Sets architecture to learn a permutation-invariant embedding. We evaluate the proposed methodology across 8 use cases, comprising seven synthetic benchmarks and one realistic CCS case study (Johansen formation)

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