Sparse Linear Algebra as a Computational Paradigm for Irregular Scientific Computation

From life sciences to data analytics and machine learning, a growing class of workloads involves irregular, data-intensive computation that maps poorly onto modern hardware, yet increasingly requires access to high-performance computing resources. This talk presents sparse linear algebra as a unifying computational paradigm for such problems. By reformulating a computation in terms of a small set of primitives, such as sparse matrix multiplication, matrix-vector products, and triangular solves, these computations become tractable at scale and portable across architectures, while hardware-specific tuning is delegated to expert-maintained libraries. In this talk, I will focus primarily on recent work on Mikado, which recasts a core operation in biobank-scale population genetics, traditionally a traversal of a large directed acyclic graph, as a sparse triangular solve. Under a topological ordering, the graph’s adjacency matrix is strictly lower triangular, and the traversal reduces to pipelined sparse matrix-vector products, cutting hours or days of CPU time down to minutes on a single GPU without custom kernels. I will conclude with open problems in the automatic discovery of sparse structure in scientific codes, its implications for hardware co-design, and the role of sparse computation in AI for science.