Physics-Informed Deep Learning Method for Surrogate Modeling in Elastic Mechanics (Advances in Applied Mathematics and Mechanics, 2025)
In this paper, we utilize Physics-Informed Neural Networks (PINNs) without any labeled data to solve the fourth-order partial differential equation governingthe bending of thin plates. We meticulously formulate and apply our framework to thebending problem of elastic thin plates. Our findings indicate that defining each solution variable through an independent network, meaning without shared network parameters, yields superior performance compared to a single-network model with multiple outputs. During the training process, we discovered that more accurate resultswere achieved by adjusting the network architecture to strictly satisfy the boundaryconditions, rather than incorporating them as part of the loss function. Remarkably,the PINNs are capable of obtaining relatively good results without the use of any labeled data during training, irrespective of whether soft or hard constraints are applied.In the end, the neural network’s predictions for plate deflection, stress, strain, bending,and shear force all have errors less than 5% compared to the analytical solutions. Inthe algorithm implementation phase, we leverage the Python library DeepXDE, whichfacilitates the training of PINNs by providing an efficient and expedited process.