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Gaussian process regression is a widely-applied method for function approximation and uncertainty quantification. The technique has gained popularity recently in the machine learning community due to its robustness and interpretability. The…

Machine Learning · Statistics 2022-10-12 Marcus M. Noack , James A. Sethian

As an entry for the 2012 Gordon-Bell performance prize, we report performance results of astrophysical N-body simulations of one trillion particles performed on the full system of K computer. This is the first gravitational trillion-body…

Cosmology and Nongalactic Astrophysics · Physics 2015-04-14 Tomoaki Ishiyama , Keigo Nitadori , Junichiro Makino

By conceiving physical systems as 3D many-body point clouds, geometric graph neural networks (GNNs), such as SE(3)/E(3) equivalent GNNs, have showcased promising performance. In particular, their effective message-passing mechanics make…

Machine Learning · Computer Science 2024-01-30 Weitao Du , Shengchao Liu , Xuecang Zhang

Purely data driven approaches for machine learning present difficulties when data is scarce relative to the complexity of the model or when the model is forced to extrapolate. On the other hand, purely mechanistic approaches need to…

Machine Learning · Statistics 2020-03-16 Mauricio A. Álvarez , David Luengo , Neil D. Lawrence

Quantum computers have the opportunity to be transformative for a variety of computational tasks. Recently, there have been proposals to use the unsimulatably of large quantum devices to perform regression, classification, and other machine…

In nonparametric regression, it is common for the inputs to fall in a restricted subset of Euclidean space. Typical kernel-based methods that do not take into account the intrinsic geometry of the domain across which observations are…

Methodology · Statistics 2021-11-04 David B Dunson , Hau-Tieng Wu , Nan Wu

Gaussian processes offers a convenient way to perform nonparametric reconstructions of observational data assuming only a kernel which describes the covariance between neighbouring points in a data set. We approach the ambiguity in the…

Cosmology and Nongalactic Astrophysics · Physics 2021-08-17 Reginald Christian Bernardo , Jackson Levi Said

Due to their flexibility, Gaussian processes (GPs) have been widely used in nonparametric function estimation. A prior information about the underlying function is often available. For instance, the physical system (computer model output)…

Methodology · Statistics 2017-11-21 Hassan Maatouk

Key to being able to accurately model the properties of realistic materials is being able to predict their properties in the thermodynamic limit. Nevertheless, because most many-body electronic structure methods scale as a high-order…

Chemical Physics · Physics 2024-04-04 Edgar Josué Landinez Borda , Kenneth O. Berard , Annette Lopez , Brenda Rubenstein

Gaussian processes are typically used for smoothing and interpolation on small datasets. We introduce a new Bayesian nonparametric framework -- GPatt -- enabling automatic pattern extrapolation with Gaussian processes on large…

Machine Learning · Statistics 2014-01-03 Andrew Gordon Wilson , Elad Gilboa , Arye Nehorai , John P. Cunningham

Machine-learning models based on a point-cloud representation of a physical object are ubiquitous in scientific applications and particularly well-suited to the atomic-scale description of molecules and materials. Among the many different…

Chemical Physics · Physics 2023-03-08 Filippo Bigi , Sergey N. Pozdnyakov , Michele Ceriotti

Gaussian processes are ubiquitous as the primary tool for modeling spatial data. However, the Gaussian process is limited by its $\mathcal{O}(n^3)$ cost, making direct parameter fitting algorithms infeasible for the scale of modern data…

Methodology · Statistics 2025-12-25 Ashlynn Crisp , Daniel Taylor-Rodriguez , Andrew O. Finley

We introduce a Gaussian process model of functions which are additive. An additive function is one which decomposes into a sum of low-dimensional functions, each depending on only a subset of the input variables. Additive GPs generalize…

Machine Learning · Statistics 2011-12-20 David Duvenaud , Hannes Nickisch , Carl Edward Rasmussen

Gaussian process (GP) regression provides a flexible, nonparametric framework for probabilistic modeling, yet remains computationally demanding in large-scale applications. For one-dimensional data, state space (SS) models achieve…

Machine Learning · Statistics 2025-11-07 Liang Ding , Rui Tuo , Lu Zhou

Simulating large molecular systems over long timescales requires force fields that are both accurate and efficient. In recent years, E(3) equivariant neural networks have lifted the tension between computational efficiency and accuracy of…

Chemical Physics · Physics 2025-05-22 Leif Seute , Eric Hartmann , Jan Stühmer , Frauke Gräter

Gaussian process ($GP$) regression is a widely used non-parametric modeling tool, but its cubic complexity in the training size limits its use on massive data sets. A practical remedy is to predict using only the nearest neighbours of each…

Machine Learning · Statistics 2026-04-09 Robert Allison , Tomasz Maciazek , Anthony Stephenson

We show that the output of a (residual) convolutional neural network (CNN) with an appropriate prior over the weights and biases is a Gaussian process (GP) in the limit of infinitely many convolutional filters, extending similar results for…

Machine Learning · Statistics 2019-05-07 Adrià Garriga-Alonso , Carl Edward Rasmussen , Laurence Aitchison

In nuclear and particle physics, reconciling sophisticated simulations with experimental data is vital for understanding complex systems like the Quark Gluon Plasma (QGP) generated in heavy-ion collisions. However, computational demands…

Nuclear Theory · Physics 2026-02-03 Hendrik Roch , Syed Afrid Jahan , Chun Shen

Earth observation from satellite sensory data poses challenging problems, where machine learning is currently a key player. In recent years, Gaussian Process (GP) regression has excelled in biophysical parameter estimation tasks from…

Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on…

Machine Learning · Statistics 2026-05-14 Rafael Oliveira