A thermodynamically consistent machine learning-based finite element solver for phase-field approach

In this article, a thermodynamics-based data-driven approach utilizing machine learning is proposed to accelerate multiscale phase-field simulations. To obtain training data, the interface propagation kinetics, integrated into a physics-based phase-field model, are monolithically solved using a finite element method-based code developed within the Python-based open-source platform FEniCS. The admissible sets of internal state variables (e.g., stress, strain, order parameter, and its gradient) are extracted from the simulations and then utilized to identify the deformation fields of the microstructure at a given state in a thermodynamics-based artificial neural network. Finally, the high performance of the proposed machine learning-enhanced solver is illustrated through detailed comparisons with nanostructural calculations at the nanoscale. Unlike previous methods, the current analysis is not restricted by specific morphologies and boundary conditions, given the length and time scales required to reproduce these results.