Optimized matrix ordering of sparse linear solver using a few-shot model for circuit simulation

Abstract

The sparse linear solver has become the bottleneck in a SPICE-like circuit simulator. A general sparse linear solver comprises pre-analysis, numeric factorization, and right-hand solving. The matrix ordering method in pre-analysis determines fill-ins and matrix structure, which is critical for the performance of numeric factorization and right-hand solving. Current leading solvers use a sequential (e.g., KLU) or completely parallel (e.g., NICSLU) framework to order the matrix, which produces non-optimal options or consumes tremendous memory. Furthermore, the criterion for judging the optimal ordering method is also controversial. In this paper, we propose a new pre-analysis framework. It redefines the criterion of the optimal ordering method and utilizes a few-shot model for inference. By performing up to 2 ordering methods from the proposed pre-analysis, our work can implement an optimal ordering method and consume much less memory than a completely parallel framework. Experimental results on 70 circuit matrices show that compared to KLU, our work achieves an average time improvement of 27.09%. Compared to NICSLU, our work achieves an average time improvement of 14.39% and an average memory improvement of 61.52% in the sequential mode, and an average time improvement of 15.74% and an average memory improvement of 55.11% in the parallel (16 threads) mode.