# Data-driven Performance Modeling of Linear Solvers for Sparse Matrices

### Jae-Seung Yeom, Jayaraman J. Thiagarajan, Abhinav Bhatele, Tzanio Kolev, Greg Bronevetsky

Performance of scientific codes is increasingly dependent
on the input problem, its data representation and the
underlying hardware with the increase in code and architectural
complexity. This makes the task of identifying the fastest algorithm
for solving a problem more challenging. In this paper,
we focus on modeling the performance of numerical libraries
used to solve a sparse linear system. We use machine learning
to develop data-driven models of performance of linear solver
implementations. These models can be used by a novice user
to identify the fastest preconditioner and solver for a given
input matrix. We use a variety of features that represent the
matrix structure, numerical properties of the matrix and the
underlying mesh or input problem as input to the model.
We model the performance of nine linear solvers and thirteen
preconditioners available in Trilinos using 1240 sparse matrices
obtained from two different sources. Our prediction models
perform significantly better than a blind classifier and black-box
SVM and k-NN classifiers.