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

• URL: http://arxiv.org/abs/2211.12084v2
• Date: Wed, 23 Nov 2022 05:42:58 GMT
• Title: Accelerated Solutions of Coupled Phase-Field Problems using Generative Adversarial Networks
• Authors: Vir Karan, A. Maruthi Indresh, Saswata Bhattacharyya
• Abstract summary: We develop a new neural network based framework that uses encoder-decoder based conditional GeneLSTM layers to solve a system of Cahn-Hilliard microstructural equations. We show that the trained models are mesh and scale-independent, thereby warranting application as effective neural operators.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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