具有物理约束的符号回归用于从实验数据中发现多模水 retention 曲线的闭式方程
Physics-constrained symbolic regression for discovering closed-form equations of multimodal water retention curves from experimental data
AI总结：
本文提出了一种受物理约束的机器学习框架，通过符号回归自动从实验数据中发现多模水保留曲线的闭式方程，提升多孔材料水保留特性的建模能力。
摘要：
对多模孔径分布的多孔材料非饱和行为建模带来了重大挑战，因为标准水力模型通常无法捕捉其复杂的多尺度特性。一种常见的解决方法是叠加单模保留函数，每个函数针对特定孔径范围进行定制；然而，这种方法需要为每个模式单独进行参数识别，这限制了可解释性和通用性，尤其是在数据稀少的情况下。在本工作中，我们提出了一种根本不同的方法：一种用于元模型的受物理约束的机器学习框架，能够自动从实验数据中发现多模水保留曲线的闭式数学表达式。数学表达式表示为二叉树并通过遗传编程进行进化，而物理约束被嵌入到损失函数中，以指导符号回归器朝向物理上一致且数学上稳健的解决方案。我们的结果表明，所提出的框架可以发现能够有效表示具有不同孔结构的多孔材料水保留特性的闭式方程。为了支持第三方验证、应用和扩展，我们将在开源存储库中公开完整的实现。
英文摘要：
Modeling the unsaturated behavior of porous materials with multimodal pore size distributions presents significant challenges, as standard hydraulic models often fail to capture their complex, multi-scale characteristics. A common workaround involves superposing unimodal retention functions, each tailored to a specific pore size range; however, this approach requires separate parameter identification for each mode, which limits interpretability and generalizability, especially in data-sparse scenarios. In this work, we introduce a fundamentally different approach: a physics-constrained machine learning framework designed for meta-modeling, enabling the automatic discovery of closed-form mathematical expressions for multimodal water retention curves directly from experimental data. Mathematical expressions are represented as binary trees and evolved via genetic programming, while physical constraints are embedded into the loss function to guide the symbolic regressor toward solutions that are physically consistent and mathematically robust. Our results demonstrate that the proposed framework can discover closed-form equations that effectively represent the water retention characteristics of porous materials with varying pore structures. To support third-party validation, application, and extension, we make the full implementation publicly available in an open-source repository.
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