Estimating condition number with Graph Neural Networks
This provides a faster solution for numerical analysts and engineers dealing with sparse matrix computations, though it appears incremental as it applies GNNs to an existing bottleneck.
The paper tackles the problem of fast condition number estimation for sparse matrices using graph neural networks (GNNs), achieving a computational complexity of O(nnz + n) and demonstrating significant speedup over traditional methods like Hager-Higham and Lanczos in experiments.
In this paper, we propose a fast method for estimating the condition number of sparse matrices using graph neural networks (GNNs). To enable efficient training and inference of GNNs, our proposed feature engineering for GNNs achieves $\mathrm{O}(\mathrm{nnz} + n)$, where $\mathrm{nnz}$ is the number of non-zero elements in the matrix and $n$ denotes the matrix dimension. We propose two prediction schemes for estimating the matrix condition number using GNNs. The extensive experiments for the two schemes are conducted for 1-norm and 2-norm condition number estimation, which show that our method achieves a significant speedup over the Hager-Higham and Lanczos methods.