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We introduce a nonequilibrium off--lattice model for anisotropic phenomena in fluids. This is a Lennard--Jones generalization of the driven lattice--gas model in which the particles' spatial coordinates vary continuously. A comparison…

Statistical Mechanics · Physics 2016-08-16 M. Díez--Minguito , P. L. Garrido , J. Marro

We present a new approach for constructing a data-driven surrogate model and using it for Bayesian parameter estimation in partial differential equation (PDE) models. We first use parameter observations and Gaussian Process regression to…

Numerical Analysis · Mathematics 2020-07-15 Jing Li , Alexandre M Tartakovsky

In this paper we present a novel analysis of variance Gaussian process (ANOVA-GP) emulator for models governed by partial differential equations (PDEs) with high-dimensional random inputs. Gaussian process (GP) is a widely used surrogate…

Computational Engineering, Finance, and Science · Computer Science 2020-05-14 Chen Chen , Qifeng Liao

The stochastic partial differential equation approach to Gaussian processes (GPs) represents Mat\'ern GP priors in terms of $n$ finite element basis functions and Gaussian coefficients with sparse precision matrix. Such representations…

Computation · Statistics 2022-04-11 Daniel Sanz-Alonso , Ruiyi Yang

We perturb with an additive Gaussian white noise the Hamiltonian system associated to a cubic anharmonic oscillator. The stochastic system is assumed to start from initial conditions that guarantee the existence of a periodic solution for…

Probability · Mathematics 2019-07-26 Enrico Bernardi , Alberto Lanconelli

Gaussian Processes (GPs) are expressive models for capturing signal statistics and expressing prediction uncertainty. As a result, the robotics community has gathered interest in leveraging these methods for inference, planning, and…

Robotics · Computer Science 2023-08-29 Francesco Crocetti , Jeffrey Mao , Alessandro Saviolo , Gabriele Costante , Giuseppe Loianno

On anisotropic lattices, where generally the lattice is rather coarse in spatial directions, a parametrized classically perfect action could help reducing lattice artifacts considerably. We investigate the possibility of constructing such…

High Energy Physics - Lattice · Physics 2009-10-31 Philipp Rufenacht , Urs Wenger

The solutions of Hamiltonian equations are known to describe the underlying phase space of a mechanical system. In this article, we propose a novel spatio-temporal model using a strategic modification of the Hamiltonian equations,…

Methodology · Statistics 2026-02-17 Satyaki Mazumder , Sayantan Banerjee , Sourabh Bhattacharya

Gaussian process regression is widely applied in computational science and engineering for surrogate modeling owning to its kernel-based and probabilistic nature. In this work, we propose a Bayesian approach that integrates the variability…

Machine Learning · Computer Science 2025-01-03 Dongwei Ye , Weihao Yan , Christoph Brune , Mengwu Guo

The Gaussian process state-space model (GPSSM) has attracted extensive attention for modeling complex nonlinear dynamical systems. However, the existing GPSSM employs separate Gaussian processes (GPs) for each latent state dimension,…

Machine Learning · Computer Science 2023-09-06 Zhidi Lin , Juan Maroñas , Ying Li , Feng Yin , Sergios Theodoridis

Bayesian inference on non-Gaussian data is often non-analytic and requires computationally expensive approximations such as sampling or variational inference. We propose an approximate inference framework primarily designed to be…

Machine Learning · Computer Science 2022-10-12 Marius Hobbhahn , Philipp Hennig

We propose an efficient variational method for $Z_2$ lattice gauge theory based on the matrix product ansatz. The method is applied to ladder and square lattices. The Gauss law needs to be imposed on quantum states to guarantee gauge…

High Energy Physics - Lattice · Physics 2007-05-23 Takanori Sugihara

Stochastic averaging problems with Gaussian forcing have been studied thoroughly for many years, but far less attention has been paid to problems where the stochastic forcing has infinite variance, such as an {\alpha}-stable noise forcing.…

Dynamical Systems · Mathematics 2017-05-24 William F. Thompson , Rachel A. Kuske , Adam. H. Monahan

We present a Gaussian Process - Latent Class Choice Model (GP-LCCM) to integrate a non-parametric class of probabilistic machine learning within discrete choice models (DCMs). Gaussian Processes (GPs) are kernel-based algorithms that…

Econometrics · Economics 2023-08-02 Georges Sfeir , Filipe Rodrigues , Maya Abou-Zeid

We use two non-perturbative methods to obtain the anisotropy derivatives of the coupling constants (the anisotropy coefficients) of SU(3) lattice gauge theory. These coefficients appear in the derivative formulae for the energy density and…

High Energy Physics - Lattice · Physics 2009-10-31 J. Engels , F. Karsch , T. Scheideler

Gaussian process (GP) audio source separation is a time-domain approach that circumvents the inherent phase approximation issue of spectrogram based methods. Furthermore, through its kernel, GPs elegantly incorporate prior knowledge about…

Audio and Speech Processing · Electrical Eng. & Systems 2018-11-22 Pablo A. Alvarado , Mauricio A. Álvarez , Dan Stowell

We introduce a method to investigate the static and dynamic properties of both Abelian and non-Abelian lattice gauge models in 1+1 dimensions. Specifically, we identify a set of transformations that disentangle different degrees of freedom,…

High Energy Physics - Lattice · Physics 2018-09-27 P. Sala , T. Shi , S. Kühn , M. C. Bañuls , E. Demler , J. I. Cirac

We introduce an entirely new class of high-order methods for computational fluid dynamics (CFD) based on the Gaussian Process (GP) family of stochastic functions. Our approach is to use kernel-based GP prediction methods to…

Computational Physics · Physics 2017-05-16 Adam Reyes , Dongwook Lee , Carlo Graziani , Petros Tzeferacos

In this paper, we propose Lagrangian Gaussian Processes (LGPs) for probabilistic and data-efficient learning of dynamics via discrete forced Euler-Lagrange equations. Importantly, the geometric structure of the Lagrange-d'Alembert…

Machine Learning · Computer Science 2026-05-08 Jan-Hendrik Ewering , Kathrin Flaßkamp , Niklas Wahlström , Thomas B. Schön , Thomas Seel

Atomic Compton profiles (CPs) are a very important property which provide us information about the momentum distribution of atomic electrons. Therefore, for CPs of heavy atoms, relativistic effects are expected to be important, warranting a…

Atomic Physics · Physics 2009-11-13 Prerit Jaiswal , Alok Shukla