NeuralLinearSolve.jl

NeuralLinearSolve.jl is a Julia package that uses a pretrained CNN to predict the fastest direct linear solver for a given sparse matrix.

Given a SparseMatrixCSC, the package generates a 64×64 SPY plot image and passes it through a frozen CNN to classify the matrix into one of three solver categories: UMFPACK, KLU, or Pardiso.

Installation

using Pkg
Pkg.add("NeuralLinearSolve")

Example Usage

using NeuralLinearSolve
using SparseArrays

A = sprand(1000, 1000, 0.01)

# Get the recommended solver
solver = predict_solver(A)
# e.g. :KLU

# Get the full probability distribution over solvers
probs = predict_solver_probs(A)
# e.g. Dict(:UMFPACK => 0.05, :KLU => 0.91, :Pardiso => 0.04)

The CNN was trained on timing data from the SuiteSparse Matrix Collection, comparing solve times for UMFPACK, KLU, and Pardiso across ~1000 sparse matrices. It achieved 94.2% test accuracy on held-out matrices.

Supported solvers

Symbol	Solver	LinearSolve.jl algorithm
:UMFPACK	UMFPACK (default Julia sparse solver, via SuiteSparse)	UMFPACKFactorization()
:KLU	KLU (via SuiteSparse)	KLUFactorization()
:Pardiso	MKL Pardiso (Intel MKL)	MKLPardisoFactorize()

License

MIT