Conventional neural network elastoplasticity models are often perceived as lacking interpretability. This paper introduces a two-step machine learning approach that returns mathematical models interpretable by human experts. In particular, we introduce a surrogate model where yield surfaces are expressed in terms of a set of single-variable feature mappings obtained from supervised learning. A post-processing step is then used to re-interpret the set of single-variable neural network mapping functions into mathematical form through symbolic regression. This divide-and-conquer approach provides several important advantages. First, it enables us to overcome the scaling issue of symbolic regression algorithms. From a practical perspective, it enhances the portability of learned models for partial differential equation solvers written in different programming languages. Finally, it enables us to have a concrete understanding of the attributes of the materials, such as convexity and symmetries of models, through automated derivations and reasoning. Numerical examples have been provided, along with an open-source code to enable third-party validation.

翻译：传统的神经网络弹塑性模型常被认为缺乏可解释性。本文提出一种两步机器学习方法，能够返回可被人类专家理解的数学模型。具体而言，我们引入了一种代理模型，其中屈服面通过监督学习获得的单变量特征映射集合表示。随后，通过符号回归的后处理步骤，将单变量神经网络映射函数集合重新解释为数学形式。这种分治策略提供了若干重要优势。首先，它使我们能够克服符号回归算法的规模扩展问题。从实践角度看，该方法增强了学习模型在不同编程语言编写的偏微分方程求解器中的可移植性。最后，通过自动推导与推理，我们能够具体理解材料属性，例如模型的凸性与对称性。本文提供了数值示例及开源代码，以便第三方验证。