相关论文: Gaussian process emulation for discontinuous respo…

We tackle the problem of quantifying failure probabilities for expensive deterministic computer experiments with stochastic inputs under a fixed budget. The computational cost of the computer simulation prohibits direct Monte Carlo (MC) and…

Uncertainty quantification based on generalized polynomial chaos has been used in many applications. It has also achieved great success in variation-aware design automation. However, almost all existing techniques assume that the parameters…

We describe a computational framework linking Uncertainty Quantification (UQ) methods for continuum problems depending on random parameters with Equation-Free (EF) methods for performing continuum deterministic numerics by acting directly…

Computer models, also known as simulators, can be computationally expensive to run, and for this reason statistical surrogates, known as emulators, are often used. Any statistical model, including an emulator, should be validated before…

This paper presents an adaptive online learning framework for systems with uncertain parameters to ensure safety-critical control in non-stationary environments. Our approach consists of two phases. The initial phase is centered on a novel…

Although machine learning is increasingly applied in control approaches, only few methods guarantee certifiable safety, which is necessary for real world applications. These approaches typically rely on well-understood learning algorithms,…

Segmentation of cardiac magnetic resonance images (MRI) is crucial for the analysis and assessment of cardiac function, helping to diagnose and treat various cardiovascular diseases. Most recent techniques rely on deep learning and usually…

Inverse Uncertainty Quantification (UQ) is a process to quantify the uncertainties in random input parameters while achieving consistency between code simulations and physical observations. In this paper, we performed inverse UQ using an…

Gaussian process regression is a popular Bayesian framework for surrogate modeling of expensive data sources. As part of a broader effort in scientific machine learning, many recent works have incorporated physical constraints or other a…

Dynamic systems described by differential equations often involve feedback among system components. When there are time delays for components to sense and respond to feedback, delay differential equation (DDE) models are commonly used. This…

This paper proposes a statistical verification framework using Gaussian processes (GPs) for simulation-based verification of stochastic nonlinear systems with parametric uncertainties. Given a small number of stochastic simulations, the…

Modern day engineering problems are ubiquitously characterized by sophisticated computer codes that map parameters or inputs to an underlying physical process. In other situations, experimental setups are used to model the physical process…

With the rapid development of modern technology, massive amounts of data with complex pattern are generated. Gaussian process models that can easily fit the non-linearity in data become more and more popular nowadays. It is often the case…

Gaussian process priors are a popular choice for Bayesian analysis of regression problems. However, the implementation of these models can be complex, and ensuring that the implementation is correct can be challenging. In this paper we…

Many fields of science and engineering rely on running simulations with complex and computationally expensive models to understand the involved processes in the system of interest. Nevertheless, the high cost involved hamper reliable and…

Gaussian Process Regression (GPR) is widely used in statistics and machine learning for prediction tasks requiring uncertainty measures. Its efficacy depends on the appropriate specification of the mean function, covariance kernel function,…

This article presents an approach to Bayesian semiparametric inference for Gaussian multivariate response regression. We are motivated by various small and medium dimensional problems from the physical and social sciences. The statistical…

The design of biological systems is hindered by uncertainty arising from both intrinsic stochasticity of biomolecular reactions and variability across laboratory or experimental conditions. In this work, we present a sequential framework to…

Gaussian processes (GPs) are a good choice for function approximation as they are flexible, robust to over-fitting, and provide well-calibrated predictive uncertainty. Deep Gaussian processes (DGPs) are multi-layer generalisations of GPs,…

We consider estimation of the parameters of a Gaussian Stochastic Process (GaSP), in the context of emulation (approximation) of computer models for which the outcomes are real-valued scalars. The main focus is on estimation of the GaSP…