Equivariant geometric learning paradigm for interpretable polycrystal plasticity models of energetic materials with evolving microstructures
Abstract
We propose a new equivariant geometric learning paradigm in which microstructural data for crystals and grain boundaries are represented by node-weighted and edge-weighted hypergraphs such that a set of non-traditional low-dimensional descriptors can be incorporated into a semi-supervised machine learning algorithm capable of predicting constitutive responses of energetic materials with evolving microstructures. To ensure the machine learning plasticity models are obeying physical principles, we will introduce a new workflow where components of the models, such as elasticity function, yield function, and plastic flow are first generated by a semi-supervised learning algorithm where the evolution of microstructural data are captured by evolutions of the geometric descriptors whose governing equations are learned from data. A new technique called equivariant graph convolutional neural network will be used to ensure that the resultant models obey material frame indifference, an important property that the classical convolutional neural network does not possess. Then, a risk-aware deep reinforcement learning will be used to infer the black-box neural networks learned functions into readable mathematical expressions through deep symbolic regression. This treatment enables us to not only empirically check for violations of mechanics principles but also to generate the mathematical proofs of the underlying thermodynamic laws for the learned models. Finally, a multi-agent non-cooperative game will be used to create computer agents capable of designing numerical experiments that calibrate and spot the hidden weaknesses of the learned models. Through repeated unmanned trial-and-error, both the accuracy (through the calibration agent that finds data to improve the models) and robustness (through the adversarial agent that exposes the weakness of the machine learning models) of the machine learning plasticity models may continuously improve until a Nash equilibrium is estimated.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Mar 07, 2023
- Source ID
- FA95502110391
Entities
People
- WaiChing Sun
Organizations
- Air Force Office of Scientific Research
- Trustees of Columbia University in the City of New York
- United States Air Force