Computational models of high-dimensional systems arise in a rich variety of engineering and scientific contexts. For example, computational fluid dynamics (CFD) and finite element (FE) analysis have become indispensable tools for many engineering applications. Unfortunately, high-fidelity simulations are often computationally prohibitive for parametric and timecritical applications such as design, design optimization, control, and virtual testing. Moreover, even when adequate computational resources are available, simulations often provide too little understanding of the solutions they produce.
Our research group is focused on developing theoretical and computational tools for low-dimensional and low-rank models of multi-scale and multi-physics problems.