Transfer learning enhanced physics informed neural network for phase-field modeling of fracture

TL;DR

This paper introduces a novel physics-informed neural network method that minimizes variational energy and employs transfer learning for efficient and accurate phase-field modeling of fracture, improving upon traditional residual-based PINNs.

Contribution

The paper proposes a variational energy minimization approach with boundary condition enforcement and transfer learning for fracture modeling, enhancing accuracy and training efficiency over existing PINNs.

Findings

The proposed method closely matches literature results across four fracture problems.

It outperforms residual-based PINNs in accuracy for initial problems.

Efficient scheme for variational energy computation using CAD models and Gauss quadrature.

Abstract

We present a new physics informed neural network (PINN) algorithm for solving brittle fracture problems. While most of the PINN algorithms available in the literature minimize the residual of the governing partial differential equation, the proposed approach takes a different path by minimizing the variational energy of the system. Additionally, we modify the neural network output such that the boundary conditions associated with the problem are exactly satisfied. Compared to conventional residual based PINN, the proposed approach has two major advantages. First, the imposition of boundary conditions is relatively simpler and more robust. Second, the order of derivatives present in the functional form of the variational energy is of lower order than in the residual form. Hence, training the network is faster. To compute the total variational energy of the system, an efficient scheme that takes as input a geometry described by spline based CAD model and employs Gauss quadrature rules for numerical integration has been proposed. Moreover, we utilize the concept of transfer learning to obtain the crack path in an efficient manner. The proposed approach is used to solve four fracture mechanics problems. For all the examples, results obtained using the proposed approach match closely with the results available in the literature. For the first two examples, we compare the results obtained using the proposed approach with the conventional residual based neural network results. For both the problems, the proposed approach is found to yield better accuracy compared to conventional residual based PINN algorithms.