Related papers: A Bayesian neural network approach to Multi-fideli…
Gaussian process regression networks (GPRN) are powerful Bayesian models for multi-output regression, but their inference is intractable. To address this issue, existing methods use a fully factorized structure (or a mixture of such…
Deep learning tools have gained tremendous attention in applied machine learning. However such tools for regression and classification do not capture model uncertainty. In comparison, Bayesian models offer a mathematically grounded…
We introduce a novel adaptive Gaussian Process Regression (GPR) methodology for efficient construction of surrogate models for Bayesian inverse problems with expensive forward model evaluations. An adaptive design strategy focuses on…
Machine learning techniques typically rely on large datasets to create accurate classifiers. However, there are situations when data is scarce and expensive to acquire. This is the case of studies that rely on state-of-the-art computational…
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…
Challenges in multi-fidelity modeling relate to accuracy, uncertainty estimation and high-dimensionality. A novel additive structure is introduced in which the highest fidelity solution is written as a sum of the lowest fidelity solution…
While Bayesian neural networks (BNNs) hold the promise of being flexible, well-calibrated statistical models, inference often requires approximations whose consequences are poorly understood. We study the quality of common variational…
Due to their high degree of expressiveness, neural networks have recently been used as surrogate models for mapping inputs of an engineering system to outputs of interest. Once trained, neural networks are computationally inexpensive to…
Multifidelity models integrate data from multiple sources to produce a single approximator for the underlying process. Dense low-fidelity samples are used to reduce interpolation error, while sparse high-fidelity samples are used to…
We present a novel computational approach for extracting weak signals, whose exact location and width may be unknown, from complex background distributions with an arbitrary functional form. We focus on datasets that can be naturally…
In statistical modeling with Gaussian Process regression, it has been shown that combining (few) high-fidelity data with (many) low-fidelity data can enhance prediction accuracy, compared to prediction based on the few high-fidelity data…
Accurately modelling the Earth's climate has widespread applications ranging from forecasting local weather to understanding global climate change. Low-fidelity simulations of climate phenomena are readily available, but high-fidelity…
Outer loop tasks such as optimization, uncertainty quantification or inference can easily become intractable when the underlying high-fidelity model is computationally expensive. Similarly, data-driven architectures typically require large…
Bayesian model updating based on Gaussian Process (GP) models has received attention in recent years, which incorporates kernel-based GPs to provide enhanced fidelity response predictions. Although most kernel functions provide high fitting…
Recently, a Gaussian Process Regression - neural network (GPRNN) hybrid machine learning method was proposed, which is based on additive-kernel GPR in redundant coordinates constructed by rules [J. Phys. Chem. A 127 (2023) 7823]. The method…
In engineering design and scientific computing, computational cost and predictive accuracy are intrinsically coupled. High-fidelity simulations provide accurate predictions but at substantial computational costs, while lower-fidelity…
A multi-fidelity regression model is proposed for combining multiple datasets with different fidelities, particularly abundant low-fidelity data and scarce high-fidelity observations. The model builds upon recent multi-fidelity frameworks…
Across many domains of science, stochastic models are an essential tool to understand the mechanisms underlying empirically observed data. Models can be of different levels of detail and accuracy, with models of high-fidelity (i.e., high…
Modern neural networks have proven to be powerful function approximators, providing state-of-the-art performance in a multitude of applications. They however fall short in their ability to quantify confidence in their predictions - this is…
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…