Physics-informed neural networks for martensitic transformation: Toward morphology-based material parameters estimation

Martensitic transformations are diffusionless phase transitions that occur through lattice distortions without altering the chemical composition, resulting in unique properties such as super-elasticity and shape memory effects. Conventional phase field solvers to model martensitic transformations are efficient for forward simulation when material parameters are known, but inverse calibration of difficult to measure parameters such as interfacial energy remains challenging under sparse or noisy morphology data. The emergence of physics-informed neural networks (PINNs) offers a promising alternative to estimate such phase-field parameters from limited morphology observations. In this paper, we developed a PINN for modeling martensitic phase transformations based on a coupled time-dependent Ginzburg–Landau (TDGL) phase-field formulation and mechanical equilibrium equations, applicable to both forward and inverse cases. By embedding the governing physical laws into the neural network training process, the PINN solves the coupled TDGL–mechanical equilibrium system for forward microstructure evolution from an initial localized perturbation and enables inverse estimation of the gradient energy coefficient under sparse sampling, partial observations, and observational noise.