Related papers: MMGP: a Mesh Morphing Gaussian Process-based machi…

Stress prediction in porous materials and structures is challenging due to the high computational cost associated with direct numerical simulations. Convolutional Neural Network (CNN) based architectures have recently been proposed as…

In engineering design, surrogate models are widely employed to replace computationally expensive simulations by leveraging design variables and geometric parameters from computer-aided design (CAD) models. However, these models often lose…

Mesh-based Graph Neural Networks (GNNs) have recently shown capabilities to simulate complex multiphysics problems with accelerated performance times. However, mesh-based GNNs require a large number of message-passing (MP) steps and suffer…

Deep Gaussian processes (DGPs) provide a Bayesian non-parametric alternative to standard parametric deep learning models. A DGP is formed by stacking multiple GPs resulting in a well-regularized composition of functions. The Bayesian…

In this contribution we deal with the problem of learning an undirected graph which encodes the conditional dependence relationship between variables of a complex system, given a set of observations of this system. This is a very central…

Although Gaussian processes (GPs) with deep kernels have been successfully used for meta-learning in regression tasks, its uncertainty estimation performance can be poor. We propose a meta-learning method for calibrating deep kernel GPs for…

Gaussian processes (GPs) are ubiquitously used in sciences and engineering as metamodels. Standard GPs, however, can only handle numerical or quantitative variables. In this paper, we introduce latent map Gaussian processes (LMGPs) that…

Neural implicit representations, including Neural Distance Fields and Neural Radiance Fields, have demonstrated significant capabilities for reconstructing surfaces with complicated geometry and topology, and generating novel views of a…

This paper introduces an active learning framework for manifold Gaussian Process (GP) regression, combining manifold learning with strategic data selection to improve accuracy in high-dimensional spaces. Our method jointly optimizes a…

Gaussian processes (GPs) provide a powerful non-parametric framework for reasoning over functions. Despite appealing theory, its superlinear computational and memory complexities have presented a long-standing challenge. State-of-the-art…

Nonlinear finite element crash simulations are accurate but computationally expensive, limiting their use in iterative design optimisation. Machine-learning surrogate models based on graph neural networks (GNNs) offer a faster alternative.…

Gaussian processes (GPs), or distributions over arbitrary functions in a continuous domain, can be generalized to the multi-output case: a linear model of coregionalization (LMC) is one approach. LMCs estimate and exploit correlations…

Recent developments in Machine Learning approaches for modelling physical systems have begun to mirror the past development of numerical methods in the computational sciences. In this survey, we begin by providing an example of this with…

Gaussian Process (GP) regression is a flexible non-parametric approach to approximate complex models. In many cases, these models correspond to processes with bounded physical properties. Standard GP regression typically results in a proxy…

Physics-based simulation of mesh based domains remains a challenging task. State-of-the-art techniques can produce realistic results but require expert knowledge. A major bottleneck in many approaches is the step of integrating a potential…

Model selection in Gaussian processes scales prohibitively with the size of the training dataset, both in time and memory. While many approximations exist, all incur inevitable approximation error. Recent work accounts for this error in the…

Standard Gaussian Process (GP) regression, a powerful machine learning tool, is computationally expensive when it is applied to large datasets, and potentially inaccurate when data points are sparsely distributed in a high-dimensional…

Gaussian processes (GPs) are Bayesian nonparametric generative models that provide interpretability of hyperparameters, admit closed-form expressions for training and inference, and are able to accurately represent uncertainty. To model…

Simulation of the dynamics of physical systems is essential to the development of both science and engineering. Recently there is an increasing interest in learning to simulate the dynamics of physical systems using neural networks.…

A new algorithm is developed to tackle the issue of sampling non-Gaussian model parameter posterior probability distributions that arise from solutions to Bayesian inverse problems. The algorithm aims to mitigate some of the hurdles faced…