Accelerating sparse linear algebra with graph neural networks

We aim to accelerate sparse linear algebra by harnessing the power of machine learning, specifically graph neural networks (GNNs).

Sparse linear algebra is pivotal in solving large-scale computational problems but requires experts to carefully craft algorithms on a case-by-case basis.

Our approach provides an alternative, more accessible, route to highly efficient solvers with the potential to have a major impact throughout science and engineering.

The underlying idea is to leverage the inherent graph structure of sparse matrices to create graph neural networks that learn task-adapted algorithms from a dataset of computational problems.

Through this integration of machine learning with sparse linear algebra, we hope to unlock unprecedented efficiency and scalability in solving sparse linear systems.

To achieve this, the project has three strategically linked research aims: (1) developing techniques for learning task-adapted Krylov subspace methods, (2) developing techniques for learning task-adapted multilevel graph representations, and (3) scaling these techniques to realistic, large-scale computational problems.

While we will focus on applications in radiotherapy and battery research to spearhead the method development, the resulting methods will be immediately useful in a wide range of fields, from optimization and computational physics to machine learning.