The curse of dimensionality and the blessings of sparsity and Monte Carlo sampling: From polynomial approximation to deep learning in high dimensions In data science and scientific computing, the approximation of high-dimensional functions from pointwise samples is a ubiquitous task,

Optimization and Learning in the Design of Preconditioners Computer simulation algorithms are a major tool in many areas of science and industry, particularly in areas where the behaviour of fluids or complex materials governs the physical processes of interest.  A

Conservative Hamiltonian Monte Carlo Markov Chain Monte Carlo (MCMC) methods enable us to extract meaningful statistics from complex distributions which frequently appear in parameter estimation, Bayesian statistics, statistical mechanics and machine learning. Similar to how flipping a coin, or rolling a

Semisupervised machine learning algorithms and their application to geoscience classification problems In recent years, many disciplines have been challenged with trying to efficiently extract meaning, or value, out of large datasets. Technological advances have improved data storage capabilities as well