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

By Somdatta Goswami, Cosmin Anitescu, Subrata Chakraborty, Timon Rabczuk. 2019

829 citations recorded by the source corpus.

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.

Subfields: Mechanical Engineering, Mechanics of Materials, Statistical and Nonlinear Physics

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Citations in the corpus

Physics informed deep learning for computational elastodynamics without labeled data (2020, background): “It is important to note that a few recent attempts show the promise and power of PINN for addressing computational mechanics relevant challenges such as solving mechanical problems [39, 46], modeling fracture in materials [40, 47], and detecting cracks via ultrasound nondestructive testing [48].”
Physics-informed neural networks (PINNs) for fluid mechanics: a review (2021, background): “More relevant works on mechanics in general can be found in [52] for turbulent flow, [53] for phase-field fracture model, and [54] for inferring modulus in a nonhomogeneous material.”
Physics-Informed Neural Network for Modelling the Thermochemical Curing Process of Composite-Tool Systems During Manufacture (2020, methodology): “Due to these advantages, many variations of the PINN approach have been successfully used to solve PDEs in a wide range of engineering applications [24, 29–37].”
Scientific Machine Learning Through Physics–Informed Neural Networks: Where we are and What’s Next (2022, background): “When compared to the residual-based loss functions typically found in the literature, the variational energy-based loss function is simpler to minimize and so performs better (Goswami et al, 2020).”
Physics-informed deep learning for incompressible laminar flows (2020, background): “Our future work aims to address this challenge by developing a “divide-and-conquer” training scheme in the context of transfer learning, that is to divide the time domain into multiple steps and re-train the network partially while fixing the weights and the biases from the previous step [17].”
A physics-informed variational DeepONet for predicting the crack path in brittle materials (2021, methodology): “V-PINNs, which were proposed in [27], successfully implemented the crack growth problem using larger displacement increments and enabled a signiﬁcant reduction in the computational cost.”