 |
Center for Nonlinear Studies |
Constitutive responses of geological interfaces are important for a wide spectrum of problems that involve spatial domain with embedded discontinuity, such as fracture surfaces, slip lines, joints, and faults. We introduce a new “meta-modeling” framework that employs both supervised learning and deep reinforcement learning (DRL) to generate mechanical constitutive models for interfaces. The constitutive models are conceptualized as information flow in directed graphs. The process of writing constitutive models is simplified as a sequence of forming graph edges with the goal of maximizing the model score (a function of accuracy, robustness and forward prediction quality). Thus meta-modeling can be formulated as a Markov decision process with well-defined states, actions, rules, and rewards. By using neural networks to estimate policies and state values, the computer agent is able to efficiently self-improve the constitutive models generated through self-playing, in the same way AlphaGo Zero (the algorithm that outplayed the world champion in the game of Go) improves its gameplay. Our numerical examples show that this automated meta-modeling framework not only produces models which outperform existing cohesive models on benchmark traction–separation data, but is also capable of detecting hidden mechanisms among micro-structural features and incorporating them in constitutive models to improve the forward prediction accuracy.
In order to further introduce intelligence into data collection, we extend our method to a “multi-agent meta-modeling” framework to provide guidance on database generation and constitutive modeling at the same time. The modeler agent in the framework focuses on evaluating all modeling options (from domain experts’ knowledge or machine learning) in a directed multigraph of elasto-plasticity theory, and finding the optimal path that links the source of the directed graph (e.g., strain history) to the target (e.g., stress). Meanwhile, the data agent, who focuses on collecting data from real or virtual experiments, interacts with the modeler agent sequentially and generate the database for model calibration to optimize the prediction accuracy. This treatment enables us to emulate an idealized scientific collaboration between experimentalists and modelers to derive, implement, calibrate and validate a constitutive model for the complex responses of geomaterials.
Host: Kane Bennett