MLPs to Find Extrema of Functionals
This provides a novel computational approach for solving optimization problems in physics and related fields, though it appears incremental as it adapts existing MLP techniques to functional extrema.
The authors developed a new numerical method using multilayer perceptrons (MLPs) to find extrema of functionals, demonstrating it in three physics scenarios with applicability to second-order differentiable functions and some non-differentiable cases.
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.