Uncertainty quantification (UQ) methods play a pivotal role in reducing the impact of
uncertainties during both optimization and decision making processes. They have been …

There is great excitement that medical artificial intelligence (AI) based on machine learning
(ML) can be used to improve decision making at the patient level in a variety of healthcare …

Over the last decade, neural networks have reached almost every field of science and
become a crucial part of various real world applications. Due to the increasing spread …

Neural networks (NNs) are currently changing the computational paradigm on how to
combine data with mathematical laws in physics and engineering in a profound way …

The posterior over Bayesian neural network (BNN) parameters is extremely high-
dimensional and non-convex. For computational reasons, researchers approximate this …

We propose a Bayesian physics-informed neural network (B-PINN) to solve both forward
and inverse nonlinear problems described by partial differential equations (PDEs) and noisy …

Data assimilation (DA) and uncertainty quantification (UQ) are extensively used in analysing
and reducing error propagation in high-dimensional spatial-temporal dynamics. Typical …

Learning the distribution of a continuous or categorical response variable y given its
covariates x is a fundamental problem in statistics and machine learning. Deep neural …

While the choice of prior is one of the most critical parts of the Bayesian inference workflow,
recent Bayesian deep learning models have often fallen back on vague priors, such as …

We propose a new class of Bayesian neural networks (BNNs) that can be trained using
noisy data of variable fidelity, and we apply them to learn function approximations as well as …