This survey describes probabilistic algorithms for linear algebraic computations, such as
factorizing matrices and solving linear systems. It focuses on techniques that have a proven …

Randomized algorithms for very large matrix problems have received a great deal of
attention in recent years. Much of this work was motivated by problems in large-scale data …

Operator learning aims to discover properties of an underlying dynamical system or partial
differential equation (PDE) from data. Here, we present a step-by-step guide to operator …

We present a sparse linear system solver that is based on a multifrontal variant of Gaussian
elimination and exploits low-rank approximation of the resulting dense frontal matrices. We …

We exploit the high memory bandwidth of AI-customized Cerebras CS-2 systems for seismic
processing. By leveraging low-rank matrix approximation, we fit memory-hungry seismic …

Can linear systems be solved faster than matrix multiplication? While there has been
remarkable progress for the special cases of graph structured linear systems, in the general …

Neural operators are a popular technique in scientific machine learning to learn a
mathematical model of the behavior of unknown physical systems from data. Neural …

Usually one avoids numerical algorithms involving operations with large, fully populated
matrices. Instead one tries to reduce all algorithms to matrix-vector multiplications involving …

Randomized sampling has recently been proven a highly efficient technique for computing
approximate factorizations of matrices that have low numerical rank. This paper describes …

Partial differential equations (PDE) learning is an emerging field that combines physics and
machine learning to recover unknown physical systems from experimental data. While deep …