An offline multi-scale unsaturated poromechanics model enabled by self-designed/self-improved neural networks

Supervised machine learning via artificial neural network (ANN) has gained significant popularity for many geomechanics applications that involves multi-phase flow and poromechanics. For unsaturated poromechanics problems, the multi-physics nature and the complexity of the hydraulic laws make it difficult to design the optimal setup, architecture, and hyper-parameters of the deep neural networks. This paper presents a meta-modeling approach that utilizes deep reinforcement learning (DRL) to automatically discover optimal neural network settings that maximize a pre-defined performance metric for the machine learning constitutive laws. This meta-modeling framework is cast as a Markov Decision Process (MDP) with well-defined states (subsets of states representing the proposed neural network (NN) settings), actions, and rewards. Following the selection rules, the artificial intelligence (AI) agent, represented in DRL via NN, self-learns from taking a sequence of actions and receiving feedback signals (rewards) within the selection environment. By utilizing the Monte Carlo Tree Search (MCTS) to update the policy/value networks, the AI agent replaces the human modeler to handle the otherwise time-consuming trial-and-error process that leads to the optimized choices of setup from a high-dimensional parametric space. This approach is applied to generate two key constitutive laws for the unsaturated poromechanics problems: (1) the path-dependent retention curve with distinctive wetting and drying paths. (2) The flow in the micropores, governed by an anisotropic permeability tensor. Numerical experiments have shown that the resultant ML-generated material models can be integrated into a finite element (FE) solver to solve initial-boundary-value problems as replacements of the hand-craft constitutive laws.

Automated summary

This paper presents a meta-modeling approach that utilizes deep reinforcement learning to automatically discover optimal neural network settings for the machine learning constitutive laws. By replacing the human modeler to handle the optimized choices of setup, the AI agent self-learns from taking a sequence of actions within the selection environment. The resulting ML-generated material models can be integrated into a finite element solver to solve initial-boundary-value problems.