Prof. Darve’s research lies at the intersection of applied mathematics and computational engineering with a focus on fast algorithms to solve complex engineering problems. One of the core areas is solving large-scale sparse linear systems, which requires novel numerical schemes, mathematics, and the design of parallel algorithms. This is key to many areas including solid mechanics, fluid mechanics, and material science. More recently, novel methods have emerged that promise to revolutionize the way scientific computing is done. They include machine learning (deep neural networks, hierarchical Gaussian processes, random forests) and statistical scientific computing. These new ideas promise to open radically new ways of expressing and solving engineering problems, going beyond what current partial differential equations models are capable of.