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      MLPs to Find Extrema of Functionals

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          Abstract

          Multilayer perceptron (MLP) is a class of networks composed of multiple layers of perceptrons, and it is essentially a mathematical function. In this paper, we introduce a physical term, namely Action, into MLP. The Action is technically a functional which maps from the MLP itself to a scalar quantity. Then, we use gradient-based optimization of MLPs as a numerical method to approximate the extremal function minimizing the value of action. As an application demonstration, we emulate a few physical systems which follow the principle of least action. Significantly, our approach requires no experimental data, only equations of actions and boundary conditions.

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          Journal
          01 July 2020
          Article
          2007.00530

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

          Custom metadata
          cs.CE

          Applied computer science

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