Accelerated Solutions of Coupled Phase-Field Problems using Generative Adversarial Networks

TL;DR

This paper introduces a novel neural network framework using GANs with ConvLSTM layers to efficiently solve coupled phase-field PDEs, specifically the Cahn-Hilliard equations, offering mesh-independent and scalable solutions for microstructural evolution.

Contribution

The paper presents a new encoder-decoder GAN-based neural network approach with ConvLSTM layers for solving coupled PDEs, improving scalability and mesh-independence over existing methods.

Findings

The proposed model accurately predicts microstructural evolution.

The neural network solutions are mesh and scale-independent.

The framework reduces computational costs compared to traditional methods.

Abstract

Multiphysics problems such as multicomponent diffusion, phase transformations in multiphase systems and alloy solidification involve numerical solution of a coupled system of nonlinear partial differential equations (PDEs). Numerical solutions of these PDEs using mesh-based methods require spatiotemporal discretization of these equations. Hence, the numerical solutions are often sensitive to discretization parameters and may have inaccuracies (resulting from grid-based approximations). Moreover, choice of finer mesh for higher accuracy make these methods computationally expensive. Neural network-based PDE solvers are emerging as robust alternatives to conventional numerical methods because these use machine learnable structures that are grid-independent, fast and accurate. However, neural network based solvers require large amount of training data, thus affecting their generalizabilty and scalability. These concerns become more acute for coupled systems of time-dependent PDEs. To address these issues, we develop a new neural network based framework that uses encoder-decoder based conditional Generative Adversarial Networks with ConvLSTM layers to solve a system of Cahn-Hilliard equations. These equations govern microstructural evolution of a ternary alloy undergoing spinodal decomposition when quenched inside a three-phase miscibility gap. We show that the trained models are mesh and scale-independent, thereby warranting application as effective neural operators.