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Recent advances in Deep Learning (DL) have significantly impacted the field of materials modelling. DL tools have been recently considered as promising tools to address the complex relationships among processing, microstructure and property of materials. The thermal stability of polycrystalline materials is a highly interesting and complex problem that could be addressed using DL techniques. The Multi-Phase-Field (MPF) method has emerged as a powerful tool for addressing grain growth phenomena from multiple perspectives. Unlike sharp-interface based methods, the MPF approach bypasses the need for detailed information on individual grains. In this work, we use DL to address issues related to MPF simulations of grain growth including numerical efficiency, computing speed, and resource consumption. This presents specific challenges for high-performance computing (HPC) due to the large datasets and complex computations required by both MPF and DL methods. We study various 3D microstructure settings with the goal of accelerating the simulation process while exploring different physical effects. In particular, the impact of grain boundary and triple junction energies on grain growth are to be investigated. The results will be presented in terms of the evolving size and shape distribution of the grains.
We present PINNs-MPF framework, an application of Physics-Informed Neural Networks (PINNs) to handle Multi-Phase-Field (MPF) simulations of microstructure evolution. A combination of optimization techniques within PINNs and in direct relation to MPF method are extended and adapted. The numerical resolution is realized through a multi-variable time-series problem by using fully discrete resolution. Within each interval, space, time, and phases/grains are treated separately, constituting discrete subdomains. PINNs-MPF is equipped with an extended multi-networking (parallelization) concept to subdivide the simulation domain into multiple batches, with each batch associated with an independent NN trained to predict the solution. To ensure continuity across the spatio-temporal-phasic subdomains, a Master NN efficiently is to handle interactions among the multiple networks and facilitates the transfer of learning. A pyramidal training approach is proposed to the PINN community as a dual-impact method: to facilitate the initialization of training when dealing with multiple networks, and to unify the solution through an extended transfer of learning. Furthermore, a comprehensive approach is adopted to specifically focus the attention on the interfacial regions through a dynamic meshing process, significantly simplifying the tuning of hyper-parameters, serving as a key concept for addressing MPF problems using machine learning. We perform a set of systematic simulations that benchmark foundational aspects of MPF simulations, i.e., the curvature-driven dynamics of a diffuse interface, in the presence and absence of an external driving force, and the evolution and equilibrium of a triple junction. The proposed PINNs-MPF framework successfully reproduces benchmark tests with high fidelity and Mean Squared Error (MSE) loss values ranging from 10^−6 to 10^−4 compared to ground truth solutions.
