用符号回归自动发现满足热力学条件的材料耗散势,兼顾物理可解释性与数据拟合能力。
Discovering Thermodynamically Admissible Dissipation Potentials via Grammar-Based Symbolic Regression

- 基于语法生成候选耗散势,确保热力学自洽性
- 在合成与实验数据上准确复现材料非线性软化行为
- 适合需要物理可解释性的材料建模研究者
不可逆材料的本构定律必须满足严格的热力学相容性要求。现有数据驱动方法虽有物理约束架构提供形式保证,但仍牺牲可解释性。本文提出一种符号回归框架,用于在广义标准材料(GSM)形式下,从数据中发现控制内变量演化的耗散势。基于克莱斯勒-杜汉不等式,强制要求对偶耗散势满足凸性和非负性,以确保机械耗散非负。该要求在一般次微分框架下统一处理率相关(粘弹性)与粘塑性耗散机制,包括具有真实弹性域的情况。通过扩展的凸性保持语法生成候选势函数,确保热力学相容性“构造即成立”。框架在包含牛顿流体、幂律与宾汉粘塑性真值的合成数据集上验证,覆盖过程与测量噪声;并在多应变幅值和频率下的合成橡胶振荡剪切实验数据上测试,所发现的耗散势成功再现动态模量的幅值依赖软化现象,优于校准后的线性齐纳基准模型。
原文摘要 · Abstract (English)
Constitutive laws for inelastic materials must satisfy strict thermodynamic admissibility requirements, yet current data-driven approaches sacrifice interpretability, even when formal guarantees are provided by physics-encoded architectures. We propose a symbolic regression framework for the data-driven discovery of dissipation potentials governing the evolution of internal variables within the Generalized Standard Materials (GSM) formalism. Starting from the Clausius--Duhem inequality, we enforce the thermodynamic requirements, convexity and non-negativity, that the dual dissipation potential must satisfy to guarantee non-negative mechanical dissipation. These requirements are formulated in the general subdifferential setting, encompassing rate-dependent (viscoelastic) and viscoplastic dissipative mechanisms, including potentials with genuine elastic domains, within a unified framework. Candidate potentials are generated by a composition-extended convexity-preserving grammar that guarantees thermodynamic admissibility \emph{by construction}. The framework is validated on synthetic datasets spanning Newtonian, power-law, and Bingham viscoplastic ground truths under process and measurement noise, and on experimental oscillatory shear measurements of a synthetic elastomer across multiple strain amplitudes and frequencies, where the discovered potentials reproduce the amplitude-dependent softening of the dynamic moduli and outperform a calibrated linear Zener baseline.
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