Reproduce “Predicting Crack Nucleation and Propagation in Brittle Materials Using Deep Operator Networks with Diverse Trunk Architectures” on OpenResearch

About this paper

Elham Kiyani, Manav Manav, Nikhil Kadivar, Laura De Lorenzis, George Em Karniadakis

Researchers from Brown University and ETH Zurich developed Deep Operator Networks (DeepONets) with varied trunk architectures to predict crack nucleation and propagation in brittle materials, achieving accurate forecasts for complex crack behaviors in 1D and 2D scenarios. These models demonstrated reduced computational and data costs, particularly with a physics-informed approach, for predicting displacement and phase fields.

Key insights

• The two-step training process for DeepONets successfully converges and enables the network's trunk to learn physically meaningful basis functions that represent fracture fields.
• Incorporating the phase-field energy functional into the DeepONet's loss significantly reduces the amount of high-fidelity training data needed while maintaining prediction accuracy.
• DeepONet architectures, particularly the two-step variant, can generalize effectively to predict diverse and complex brittle fracture phenomena, including nucleation, kinking, and branching, from limited training datasets.

Summary by alphaXiv.