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.

中文翻译：

---

由自主设计/自我改进的神经网络实现的离线多尺度不饱和多孔力学模型

通过人工神经网络 (ANN) 进行的监督机器学习已在许多涉及多相流和多孔力学的地质力学应用中广受欢迎。对于非饱和多孔力学问题，多物理场性质和水力学定律的复杂性使得设计深度神经网络的最佳设置、架构和超参数变得困难。本文提出了一种元建模方法，该方法利用深度强化学习 (DRL) 来自动发现最佳神经网络设置，从而最大化机器学习本构律的预定义性能指标。该元建模框架被转换为具有明确定义的状态（代表提议的神经网络 (NN) 设置的状态子集）、动作和奖励的马尔可夫决策过程 (MDP)。遵循选择规则，通过 NN 以 DRL 表示的人工智能 (AI) 代理通过在选择环境中采取一系列动作和接收反馈信号（奖励）进行自我学习。通过利用蒙特卡洛树搜索 (MCTS) 来更新策略/价值网络，AI 代理取代人工建模者来处理原本耗时的试错过程，从而从高维参数空间。该方法用于为不饱和多孔力学问题生成两个关键的本构定律：（1）具有独特润湿和干燥路径的路径相关保留曲线。(2) 微孔中的流动，由各向异性渗透率张量控制。