Genetic Programming meets Linear Algebra How genetic programming can be used to find improved iterative numerical methods

Iterative schemes play central role in solving large scale simulations in science and engineering. Development of such methods over the past few hundreds of years faces inevitable difficulty of manual design. Herein, we report, for the first time, iterative schemes that are automatically evolved by genetic programming (GP) and outperform the well-known iterative methods. To cope with the diversity of the systems of linear equations, the proposed technique is applied on a sparse system in 1D and 2D domains and on a non-sparse asymmetric system. Our proof-of-principle experiments demonstrate GP evolved schemes that converge up to 4 times faster than the conventional GaussSeidel scheme. Our work paves the way towards automatic design of efficient iterative solvers for large scale systems of linear equations.