Introduction

By most estimates, physics commands the largest single pool of computational resources in the open access domain. The majority of this comprises computations of electronic structure, molecular simulations, Monte Carlo variants for statistical mechanics, and continuum physics models for fluids and solids. Ordinary and partial differential equations appear in most of these categories, for many of the physics models and across scales. The quest to understand properties and mechanisms dominates this effort, supported by a smaller, but according to some opinions, a deeper search into computational methods and numerical algorithms. In this monograph we are concerned with data-driven modelling for continuum physics studies that have at their foundation a mathematical model such as a differential, master balance, or other form of equation. These studies are centered around continuum physics problems in the context of non-biological and biological materials, as well as in fluids. The systematic use of data, backed by mathematics, has been part of this landscape of computational continuum physics.