Session

DescriptionThe aim of this minisymposium is to discuss the latest research at the intersection of parallel computing and high-dimensional approximation. High-dimensional approximation drives e.g. uncertainty quantification and machine learning as well as big data and simulations of complex physics models. It is well-known that approximation of functions of growing dimension has the challenge of the curse of dimensionality. Over the last decades, many powerful mathematical tools have been developed to do weaken or overcome this. These include, but are not limited to sparse approximation, (quasi) Monte Carlo, multi-level (multigrid) / multi-fidelity techniques, (sparse) tensor product and low-rank approximations, hierarchical matrices, compressed sensing and meshfree methods. There is a growing interest to solve high-dimensional approximation problems at large scale. While many of the discussed methods have good or even optimal approximation properties and complexities for larger dimensions, some have been primarily developed for sequential execution. However, to solve large scale approximation problems, it becomes necessary to develop fast, scalable and parallel numerical methods. This minisymposium includes contributions in high-dimensional approximation ranging from initial studies for the use of parallel techniques up to full scale parallel methods that run on large HPC clusters. We focus both on algorithmic-oriented and application-centered research.