Physics-constrained neural networks with minimax architecture for multiphysics dendritic growth problems in additive manufacturing

Data sparsity is the main barrier to apply deep neural networks to solve complex scientific and engineering problems, where it is expensive to obtain a large amount of high-fidelity training data from experiments or simulations. A new approach of physics-constrained neural networks (PCNNs) was recently developed to alleviate the data sparsity issue by applying the physics-based models as the constraints to guide the training. Constraints are incorporated as different loss terms in the total loss function. However, how to ensure the convergence during the training is still a challenge for PCNNs to predict complex multiphysics phenomena. The causes are the unbalanced gradients from different losses, unstable training resulting from tightly coupled multiphysics, and high dimensionality of the parameter space. In this work, a new sequential training scheme is proposed to accelerate the convergence of our previously developed physics-constrained neural networks with minimax architecture (PCNN-MMs) for solving multiphysics problems. A new training algorithm called the Dual-Dimer with compressive sampling (DD-CS) algorithm is developed to improve the convergence of the training by escaping the local minima. The novel training scheme and algorithm for PCNN-MMs are demonstrated with two examples of dendritic growth in metal additive manufacturing. The comparison shows that the sequential training scheme enables better convergence than the original concurrent training scheme. The DD-CS algorithm has the potential to improve the convergence of the training by escaping the local minimum and converging to a better one after proper parameter tuning.