MLPs to Find Extrema of Functionals

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.