玻璃硬度：通过符号推理告知机器学习预测成分和负载效应
Glass Hardness: Predicting Composition and Load Effects via Symbolic Reasoning-Informed Machine Learning
摘要：
玻璃硬度随着化学成分和施加的载荷以非线性方式变化，这种现象称为压痕尺寸效应（ISE），这是定量预测的挑战。在这里，使用一个超过约策展的数据集。3000无机玻璃的文献，包括组成，压痕载荷，和硬度，我们开发机器学习（ML）模型来预测组成和载荷依赖性的维氏硬度。有趣的是，当对训练过程中看不见的新玻璃成分进行测试时，标准数据驱动的ML模型未能捕获ISE。为了解决这一差距，我们结合了一个经验表达式（伯恩哈特定律）来描述ISE与ML，以开发一个框架，该框架包含了代表ML中域推理的符号定律，即符号推理通知ML过程（SRIMP）。我们表明，由此产生的SRIMP在预测ISE方面优于数据驱动的ML模型。最后，我们解释SRIMP模型，以了解玻璃网络形成者和改性剂对成分和负载依赖性（ISE）和负载无关性硬度的贡献。将硬度解卷积为负载相关和负载无关项为全面理解玻璃中的成分和ISE铺平了道路，从而能够加速发现具有目标硬度的新玻璃成分。
英文摘要：
Glass hardness varies in a non-linear fashion with the chemical composition and applied load, a phenomenon known as the indentation size effect (ISE), which is challenging to predict quantitatively. Here, using a curated dataset of over approx. 3000 inorganic glasses from the literature comprising the composition, indentation load, and hardness, we develop machine learning (ML) models to predict the composition and load dependence of Vickers hardness. Interestingly, when tested on new glass compositions unseen during the training, the standard data-driven ML model failed to capture the ISE. To address this gap, we combined an empirical expression (Bernhardt law) to describe the ISE with ML to develop a framework that incorporates the symbolic law representing the domain reasoning in ML, namely Symbolic Reasoning-Informed ML Procedure (SRIMP). We show that the resulting SRIMP outperforms the data-driven ML model in predicting the ISE. Finally, we interpret the SRIMP model to understand the contribution of the glass network formers and modifiers toward composition and load-dependent (ISE) and load-independent hardness. The deconvolution of the hardness into load-dependent and load-independent terms paves the way toward a holistic understanding of composition and ISE in glasses, enabling the accelerated discovery of new glass compositions with targeted hardness.
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