Neuroevolution-enabled adaptation of the Jacobi method for Poisson’s equation with density discontinuities

Abstract

Lacking labeled examples of working numerical strategies, adapting an iterative solver to accommodate a numerical issue, e.g., density discontinuities in the pressure Poisson equation, is non-trivial and usually involves a lot of trial and error. Here, we resort to evolutionary neural network. A evolutionary neural network observes the outcome of an action and adapts its strategy accordingly. The process requires no labeled data but only a measure of a network’s performance at a task. Applying neuro-evolution and adapting the Jacobi iterative method for the pressure Poisson equation with density discontinuities, we show that the adapted Jacobi method is able to accommodate density discontinuities.

Keywords

• Evolutionary neural network
• Jacobi method