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Multiphysics problems such as multicomponent diffusion, phase transformationsin multiphase systems and alloy solidification involve numerical solution of acoupled system of nonlinear partial differential equations (PDEs). Numericalsolutions of these PDEs using mesh-based methods require spatiotemporaldiscretization of these equations. Hence, the numerical solutions are oftensensitive to discretization parameters and may have inaccuracies (resultingfrom grid-based approximations). Moreover, choice of finer mesh for higheraccuracy make these methods computationally expensive. Neural network-based PDEsolvers are emerging as robust alternatives to conventional numerical methodsbecause these use machine learnable structures that are grid-independent, fastand accurate. However, neural network based solvers require large amount oftraining data, thus affecting their generalizabilty and scalability. Theseconcerns become more acute for coupled systems of time-dependent PDEs. Toaddress these issues, we develop a new neural network based framework that usesencoder-decoder based conditional Generative Adversarial Networks with ConvLSTMlayers to solve a system of Cahn-Hilliard equations. These equations governmicrostructural evolution of a ternary alloy undergoing spinodal decompositionwhen quenched inside a three-phase miscibility gap. We show that the trainedmodels are mesh and scale-independent, thereby warranting application aseffective neural operators.

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