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

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. (C) 2021 The Author(s). Published by Elsevier Ltd on behalf of The Chinese Society of Theoretical and Applied Mechanics.

Automated summary

The study utilizes evolutionary neural network to adjust the Jacobi iterative method to accommodate density discontinuities in the pressure Poisson equation, without the need for labeled data, but simply evaluating the network's performance on the task.