A machine-learning solver for modified diffusion equations

TL;DR

This paper introduces a neural network-based solver capable of approximating solutions to complex multi-variable partial differential equations, including coupled integrodifferential equations, with potential applications in polymer microstructure prediction.

Contribution

It presents a universal machine-learning approach that uses neural networks to solve multi-variable PDEs and integrodifferential equations, extending the applicability of neural solvers.

Findings

Neural networks can approximate solutions to complex PDEs.

The method is adaptable to coupled integrodifferential equations.

Potential applications include polymer microstructure modeling.

Abstract

A feed-forward neural network has a remarkable property which allows the network itself to be a universal approximator for any functions.Here we present a universal, machine-learning based solver for multi-variable partial differential equations. The algorithm approximates the target functions by neural networks and adjusts the network parameters to approach the desirable solutions.The idea can be easily adopted for dealing with multi-variable, coupled integrodifferential equations, such as those in the self-consistent field theory for predicting polymer microphase-separated structures.