Scientific Applications Leveraging Randomized Linear Algebra

TL;DR

This paper discusses how Randomized Numerical Linear Algebra (RNLA) techniques can address large-scale linear algebra challenges in scientific fields like imaging, genomics, and dynamical systems, highlighting future research directions.

Contribution

It provides a high-level overview of RNLA applications in science, identifies open challenges, and suggests future research directions for integrating RNLA into real-world problems.

Findings

RNLA effectively addresses large-scale linear algebra bottlenecks.

Open challenges include creating structure-aware RNLA algorithms.

Future directions involve hardware co-design and software infrastructure development.

Abstract

This report showcases the role of, and future directions for, the field of Randomized Numerical Linear Algebra (RNLA) in a selection of scientific applications. These applications span the domains of imaging, genomics and dynamical systems, and are thematically connected by needing to perform linear algebra routines on large-scale matrices (with up to quantillions of entries). At such scales, the linear algebra routines face typical bottlenecks: memory constraints, data access latencies, and substantial floating-point operation costs. RNLA routines are discussed at a high-level to demonstrate how these routines are able to solve the challenges faced by traditional linear algebra routines, and, consequently, address the computational problem posed in the underlying application. For each application, RNLA's open challenges and possible future directions are also presented, which broadly fall into the categories: creating structure-aware RNLA algorithms; co-designing RNLA algorithms with hardware and mixed-precision considerations; and advancing modular, composable software infrastructure. Ultimately, this report serves two purposes: it invites domain scientists to engage with RNLA; and it offers a guide for future RNLA research grounded in real applications.