Related papers: Gaussian process surrogate with physical law-corre…
Multi-robot systems require scalable and federated methods to model complex environments under computational and communication constraints. Gaussian Processes (GPs) offer robust probabilistic modeling, but suffer from cubic computational…
Inverse design optimization aims to infer system parameters from observed solutions, posing critical challenges across domains such as semiconductor manufacturing, structural engineering, materials science, and fluid dynamics. The lack of…
Bayesian optimization (BO) has well-documented merits for optimizing black-box functions with an expensive evaluation cost. Such functions emerge in applications as diverse as hyperparameter tuning, drug discovery, and robotics. BO hinges…
Sparse variational Gaussian processes (GPs) construct tractable posterior approximations to GP models. At the core of these methods is the assumption that the true posterior distribution over training function values ${\bf f}$ and inducing…
Topology optimization (TO) provides a principled mathematical approach for optimizing the performance of a structure by designing its material spatial distribution in a pre-defined domain and subject to a set of constraints. The majority of…
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…
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…
Neural networks have emerged as powerful surrogates for solving partial differential equations (PDEs), offering significant computational speedups over traditional methods. However, these models suffer from a critical limitation: error…
We introduce Deep Jump Gaussian Processes (DJGP), a novel method for surrogate modeling of a piecewise continuous function on a high-dimensional domain. DJGP addresses the limitations of conventional Jump Gaussian Processes (JGP) in…
Gaussian processes (GPs), implemented through multivariate Gaussian distributions for a finite collection of data, are the most popular approach in small-area spatial statistical modelling. In this context they are used to encode…
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…
We use a Gaussian Process Regression (GPR) strategy that was recently developed [3,16,17] to analyze different types of curves that are commonly encountered in parametric eigenvalue problems. We employ an offline-online decomposition…
Gaussian process surrogates are a popular alternative to directly using computationally expensive simulation models. When the simulation output consists of many responses, dimension-reduction techniques are often employed to construct these…
While Bayesian inference is the gold standard for uncertainty quantification and propagation, its use within physical chemistry encounters formidable computational barriers. These bottlenecks are magnified for modeling data with many…
This article discusses prior distributions for the parameters of Gaussian processes (GPs) that are widely used as surrogate models to emulate expensive computer simulations. The parameters typically involve mean parameters, a variance…
We propose a novel probabilistic framework, termed LVM-GP, for uncertainty quantification in solving forward and inverse partial differential equations (PDEs) with noisy data. The core idea is to construct a stochastic mapping from the…
High-fidelity numerical simulations of partial differential equations (PDEs) given a restricted computational budget can significantly limit the number of parameter configurations considered and/or time window evaluated for modeling a given…
Deep Gaussian processes (DGPs) are popular surrogate models for complex nonstationary computer experiments. DGPs use one or more latent Gaussian processes (GPs) to warp the input space into a plausibly stationary regime, then use typical GP…
Machine learning (ML) techniques have recently gained significant attention for solving compliance minimization (CM) problems. However, these methods typically provide poor feature boundaries, are very expensive, and lack a systematic…
In this paper, we develop a computational multiscale to solve the parabolic wave approximation with heterogeneous and variable media. Parabolic wave approximation is a technique to approximate the full wave equation. One benefit of the…