具有物理信息的高斯过程回归用于混凝土本构建模：一种数据驱动的改进现象模型
Physics-Informed Gaussian Process Regression for the Constitutive Modeling of Concrete: A Data-Driven Improvement to Phenomenological Models
AI总结：
本文提出了一种基于物理信息的高斯过程回归方法，用于改进混凝土的本构建模，通过引入约束条件提升模型的准确性和可靠性，同时保持模型的可解释性和效率。
摘要：
理解并建模混凝土的本构行为对于土木和国防应用至关重要，然而广泛使用的现象模型如Karagozian与Case混凝土（KCC）模型依赖于经验校准的失效表面，这些模型在模型形式上缺乏灵活性，并且相关的不确定性量化也存在问题。本文开发了一个具有物理信息的框架，该框架保留了KCC模型的模块弹性塑性结构，同时用一个受约束的高斯过程回归（GPR）替代其经验性失效表面，该替代模型可以直接从实验可获得的观测值中学习。在不同围压水平下的三轴压缩数据用于训练，然后在训练集中未包含的围压水平上评估该替代模型，以评估其泛化能力。结果表明，无约束的GPR在接近训练条件附近插值良好，但在外推时会恶化并违反基本的物理约束，即使在加入模拟数据后也是如此。相比之下，一个结合基于导数的约束的物理信息GPR，这些约束与已知的材料行为一致，显示出显著更好的准确性和可靠性，包括在超出训练范围的更高围压水平上。对这些约束的概率强制执行也减少了预测方差，在数据稀缺的地区产生了更紧的置信区间。总体而言，所提出的方法提供了一个稳健、具有不确定性的替代模型，它在不牺牲KCC模型的可解释性和数值效率的情况下提高了泛化能力和校准效率，为改进混凝土的本构模型提供了实用的途径。
英文摘要：
Understanding and modeling the constitutive behavior of concrete is crucial for civil and defense applications, yet widely used phenomenological models such as Karagozian \& Case concrete (KCC) model depend on empirically calibrated failure surfaces that lack flexibility in model form and associated uncertainty quantification. This work develops a physics-informed framework that retains the modular elastoplastic structure of KCC model while replacing its empirical failure surface with a constrained Gaussian Process Regression (GPR) surrogate that can be learned directly from experimentally accessible observables. Triaxial compression data under varying confinement levels are used for training, and the surrogate is then evaluated at confinement levels not included in the training set to assess its generalization capability. Results show that an unconstrained GPR interpolates well near training conditions but deteriorates and violates essential physical constraints under extrapolation, even when augmented with simulated data. In contrast, a physics-informed GPR that incorporates derivative-based constraints aligned with known material behavior yields markedly better accuracy and reliability, including at higher confinement levels beyond the training range. Probabilistic enforcement of these constraints also reduces predictive variance, producing tighter confidence intervals in data-scarce regimes. Overall, the proposed approach delivers a robust, uncertainty-aware surrogate that improves generalization and streamlines calibration without sacrificing the interpretability and numerical efficiency of the KCC model, offering a practical path toward an improved constitutive models for concrete.
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