Abstract: We discussed two-parameter inverse problems for a class of coupled models of temperature field and crystallization coupling model, proposed stable numerical algorithms to identify nucleation rate and growth rate, and verified anti-noise performance of the proposed algorithms. We embedded the coupled model into the loss function of a deep neural network, updated the neural network parameters based on loss function minimization, and obtained approximate solution to the forward problem. For the inverse problem, we constructed a loss function with regularization terms and proposed a regularized physics-informed neural networks (PINNs) algorithm. The numerical results show that the regularized PINNs algorithm can effectively solve the inverse problem of the temperature field and crystallization coupling model, and has noise resistance stability.

Key words: temperature field and crystallization coupling model, inverse problem, regularized PINNs algorithm, inversion of nucleation rate and growth rate