MLPs to Find Extrema of Functionals

TL;DR

This paper introduces a novel numerical method using multilayer perceptrons to efficiently find the extrema of functionals, demonstrated through physics applications and adaptable to various differentiability conditions.

Contribution

It develops a new MLP-based approach for extremum finding of functionals, extending applicability to non-differentiable points and surfaces.

Findings

Successfully applied to three physics scenarios

Applicable to second-order differentiable functions

Extendable to non-differentiable but continuous cases

Abstract

Multilayer perceptron (MLP) is a class of networks composed of multiple layers of perceptrons, and it is essentially a mathematical function. Based on MLP, we develop a new numerical method to find the extrema of functionals. As demonstrations, we present our solutions in three physic scenes. Ideally, the same method is applicable to any cases where the objective curve/surface can be fitted by second-order differentiable functions. This method can also be extended to cases where there are a finite number of non-differentiable (but continuous) points/surfaces.