做材料本构建模或计算力学的团队，终于有了一个既能保证热力学约束又不牺牲可解释性的符号回归工具，值得在实验数据上试试。
该研究提出一种基于语法符号回归的框架，用于从数据中发现满足热力学约束的耗散势函数。框架通过构造凸性保持的语法规则，自动保证候选势函数满足热力学第二定律的凸性和非负性要求，适用于率相关和率无关的耗散机制。在合成数据集和实验数据上的验证表明，该方法能准确恢复牛顿、幂律和宾汉粘塑性本构，并在弹性体振荡剪切实验中优于线性Zener模型。这项工作为数据驱动本构建模提供了兼顾可解释性和物理一致性的新路径。
Discovering Thermodynamically Admissible Dissipation Potentials via Grammar-Based Symbolic Regression
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.