Related papers: Gaussian process surrogate with physical law-corre…

This paper addresses the challenge of reconstructing full-field structural mode shapes from sparse sensor data. While Gaussian Process Regression (GPR) offers a robust non-parametric framework for spatial interpolation and uncertainty…

Let $P$ be a linear differential operator over $\mathcal{D} \subset \mathbb{R}^d$ and $U = (U_x)_{x \in \mathcal{D}}$ a second order stochastic process. In the first part of this article, we prove a new necessary and sufficient condition…

We introduce a simple, rigorous, and unified framework for solving nonlinear partial differential equations (PDEs), and for solving inverse problems (IPs) involving the identification of parameters in PDEs, using the framework of Gaussian…

Excessive loads near wounds produce pathological scarring and other complications. Presently, stress cannot easily be measured by surgeons in the operating room. Instead, surgeons rely on intuition and experience. Predictive computational…

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…

We analyze a novel multi-level version of a recently introduced compressed sensing (CS) Petrov-Galerkin (PG) method from [H. Rauhut and Ch. Schwab: Compressive Sensing Petrov-Galerkin approximation of high-dimensional parametric operator…

In the present work, a new methodology is proposed for building surrogate parametric models of engineering systems based on modular assembly of pre-solved modules. Each module is a generic parametric solution considering parametric…

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…

Generating simulated training data needed for constructing sufficiently accurate surrogate models to be used for efficient optimization or parameter identification can incur a huge computational effort in the offline phase. We consider a…

Gaussian processes (GPs) are powerful and widely used probabilistic regression models, but their effectiveness in practice is often limited by the choice of kernel function. This kernel function is typically handcrafted from a small set of…

Deep Gaussian processes (DGPs) are increasingly popular as predictive models in machine learning (ML) for their non-stationary flexibility and ability to cope with abrupt regime changes in training data. Here we explore DGPs as surrogates…

Machine learning (ML) has been increasingly used for topology optimization (TO). However, most existing ML-based approaches focus on simplified benchmark problems due to their high computational cost, spectral bias, and difficulty in…

With the development of new remote sensing technology, large or even massive spatial datasets covering the globe become available. Statistical analysis of such data is challenging. This article proposes a semiparametric approach to model…

In recent years, surrogate models have been successfully used in likelihood-free inference to decrease the number of simulator evaluations. The current state-of-the-art performance for this task has been achieved by Bayesian Optimization…

Artificial intelligence (AI) for fluid mechanics has become attractive topic. High-fidelity data is one of most critical issues for the successful applications of AI in fluid mechanics, however, it is expensively obtained or even…

Surrogate models provide a quick-to-evaluate approximation to complex computational models and are essential for multi-query problems like design optimisation. The inputs of current deterministic computational models are usually…

Gaussian processes (GPs) are non-parametric Bayesian models that are widely used for diverse prediction tasks. Previous work in adding strong privacy protection to GPs via differential privacy (DP) has been limited to protecting only the…

Gaussian processes (GPs) are widely used in nonparametric regression, classification and spatio-temporal modeling, motivated in part by a rich literature on theoretical properties. However, a well known drawback of GPs that limits their use…

Gaussian Processes (GPs) are powerful non-parametric Bayesian models for regression of scalar fields, formulated under the assumption that measurement locations are perfectly known and the corresponding field measurements have Gaussian…

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)…