Surrogate modeling and uncertainty quantification tasks for PDE systems are most often
considered as supervised learning problems where input and output data pairs are used for …

Abstract Machine learning (ML) methods have become an important tool for modelling and
forecasting complex high-dimensional spatiotemporal datasets such as those found in …

We present a deep learning framework for quantifying and propagating uncertainty in
systems governed by non-linear differential equations using physics-informed neural …

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

Uncertainty quantification serves a central role for simulation-based analysis of physical,
engineering, and biological applications using mechanistic models. From a broad …

Through the previous three editions, Handbook of Differential Equations has proven an
invaluable reference for anyone working within the field of mathematics, including …

Summary Markov chain Monte Carlo (MCMC) methods provide consistent approximations of
integrals as the number of iterations goes to∞. MCMC estimators are generally biased after …

The Matern Model: A Journey Through Statistics, Numerical Analysis and Machine Learning
Page 1 Statistical Science 2024, Vol. 39, No. 3, 469–492 https://doi.org/10.1214/24-STS923 © …

Gaussian process regression underpins countless academic and industrial applications of
machine learning and statistics, with maximum likelihood estimation routinely used to select …

We introduce a priori Sobolev-space error estimates for the solution of arbitrary nonlinear,
and possibly parametric, PDEs that are defined in the strong sense, using Gaussian process …