用AI自动发现可解释的材料本构模型，精准捕捉复杂粘弹性行为。
Inelastic Constitutive Kolmogorov-Arnold Networks: A generalized framework for automated discovery of interpretable inelastic material models
- 基于柯尔莫哥洛夫-阿诺德网络，自动从数据中提取解析形式的本构方程。
- 在合成与实验数据上准确复现VHB 4910/4905材料的粘弹性响应。
- 支持温度等额外信息输入，适合材料工艺与服役条件研究。
固体力学中的关键问题是确定材料的本构关系，即应变历史与应力之间的关系。近年来机器学习在此领域取得显著进展。本文提出非弹性柯尔莫哥洛夫-阿诺德网络（iCKAN），一种新型人工神经网络架构，可自动发现描述材料弹性和非弹性行为的符号化本构定律。该方法能将材料测试数据转化为闭合数学形式的弹性与非弹性势函数。我们在合成数据及黏弹性聚合物VHB 4910和VHB 4905的实验数据上验证了iCKAN的优势。结果表明，iCKAN能精确捕捉复杂的黏弹性行为，同时保持物理可解释性。iCKAN的一大优势在于不仅能处理力学数据，还可整合材料的任意附加信息（如温度依赖性），未来可用于探究特定加工或服役条件对材料性能的影响。
原文摘要 · Abstract (English)
A key problem of solid mechanics is the identification of the constitutive law of a material, that is, the relation between strain history and stress. Machine learning has lead to considerable advances in this field lately. Here we introduce inelastic Constitutive Kolmogorov-Arnold Networks (iCKANs). This novel artificial neural network architecture can discover in an automated manner symbolic constitutive laws describing both the elastic and inelastic behavior of materials. That is, it can translate data from material testing into corresponding elastic and inelastic potential functions in closed mathematical form. We demonstrate the advantages of iCKANs using both synthetic data and experimental data of the viscoelastic polymer materials VHB 4910 and VHB 4905. The results demonstrate that iCKANs accurately capture complex viscoelastic behavior while preserving physical interpretability. It is a particular strength of iCKANs that they can process not only mechanical data but also arbitrary additional information available about a material (e.g., about temperature-dependent behavior). This makes iCKANs a powerful tool to discover in the future also how specific processing or service conditions affect the properties of materials.
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