Constitutive relation remains one of the most important, yet fundamental challenges in the study of granular materials. Instead of using closed-form phenomenological models or numerical multiscale modelling, machine learning has emerged as an alternative paradigm to revolutionise the constitutive modelling of granular materials. However, deep neural networks (DNNs) require massive training data and often fail to make credible extrapolations. This study aims to develop a deep active learning strategy to (i) identify unreliable forecasts without knowing the ground truth; and (ii) continuously improve and verify a data-driven constitutive model until the desired generalisation is satisfied. The role of active learning in constitutive modelling is instantiated through three scenarios: (i) off-line strain-stress data pool of granular materials; (ii) interactive constitutive training and strain-stress data labelling; and (iii) finite element modelling (FEM) driven by deep learning-based constitutive models. The results confirm the capability of active learning in advancing data-driven constitutive modelling of granular materials toward developing a faithful surrogate constitutive model with less data. The same active learning strategy can also be applied to other data-centric applications across various science and engineering fields.

本构关系仍然是粒状材料研究中最重要但最基本的挑战之一。机器学习不是使用封闭形式的现象学模型或数值多尺度建模，而是作为一种替代范例出现，以彻底改变颗粒材料的本构建模。然而，深度神经网络 (DNN) 需要大量训练数据，而且往往无法做出可靠的推断。本研究旨在开发一种深度主动学习策略，以 (i) 在不知道基本事实的情况下识别不可靠的预测；(ii) 不断改进和验证数据驱动的本构模型，直到满足所需的泛化。主动学习在本构建模中的作用通过三个场景实例化：（i）颗粒材料的离线应变应力数据池；(ii) 交互式本构训练和应变应力数据标记；(iii) 由基于深度学习的本构模型驱动的有限元建模 (FEM)。结果证实了主动学习在推进颗粒材料的数据驱动本构建模方面的能力，以开发具有较少数据的忠实替代本构模型。同样的主动学习策略也可以应用于各个科学和工程领域的其他以数据为中心的应用程序。