Proposal for an analytical framework for gradient systems using Neural reduced potential

Abstract

Many natural phenomena can be modeled as gradient systems, which follow the gradient of a potential function that depends only on the state of the system. Scientists have constructed reduced models of potential functions that reflect the typical features of the phenomena, without contradicting them. However, such modeling requires a large amount of experimental data and specialized knowledge, making it challenging. In this study, we propose a framework to estimate a reduced potential function in a data-driven manner and verify that it is consistent with the phenomenon and contains useful features. First, we estimate the reduced potential function of an unknown physical phenomenon in a data-driven manner using a deep learning model inspired by Hamiltonian Neural Networks (HNN). Then, we try to validate the validity of the obtained reduced potential function and extract useful information to describe the phenomenon. As an example of verifying the usefulness of our proposed framework, we present a case where we apply the proposed framework to numerical calculation data of magnetic domain pattern formation.