School of Environmental, Civil, Agricultural and Mechanical Engineering, College of Engineering, University of Georgia, Athens, GA 30602, USA.
Department of Epidemiology and Biostatistics, College of Public Health, University of Georgia, Athens, GA 30602, USA.
Acta Biomater. 2024 Oct 15;188:276-296. doi: 10.1016/j.actbio.2024.09.005. Epub 2024 Sep 17.
We introduce a data-driven framework to automatically identify interpretable and physically meaningful hyperelastic constitutive models from sparse data. Leveraging symbolic regression, our approach generates elegant hyperelastic models that achieve accurate data fitting with parsimonious mathematic formulas, while strictly adhering to hyperelasticity constraints such as polyconvexity/ellipticity. Our investigation spans three distinct hyperelastic models-invariant-based, principal stretch-based, and normal strain-based-and highlights the versatility of symbolic regression. We validate our new approach using synthetic data from five classic hyperelastic models and experimental data from the human brain cortex to demonstrate algorithmic efficacy. Our results suggest that our symbolic regression algorithms robustly discover accurate models with succinct mathematic expressions in invariant-based, stretch-based, and strain-based scenarios. Strikingly, the strain-based model exhibits superior accuracy, while both stretch-based and strain-based models effectively capture the nonlinearity and tension-compression asymmetry inherent to the human brain tissue. Polyconvexity/ellipticity assessment affirm the rigorous adherence to convexity requirements both within and beyond the training regime. However, the stretch-based models raise concerns regarding potential convexity loss under large deformations. The evaluation of predictive capabilities demonstrates remarkable interpolation capabilities for all three models and acceptable extrapolation performance for stretch-based and strain-based models. Finally, robustness tests on noise-embedded data underscore the reliability of our symbolic regression algorithms. Our study confirms the applicability and accuracy of symbolic regression in the automated discovery of isotropic hyperelastic models for the human brain and gives rise to a wide variety of applications in other soft matter systems. STATEMENT OF SIGNIFICANCE: Our research introduces a pioneering data-driven framework that revolutionizes the automated identification of hyperelastic constitutive models, particularly in the context of soft matter systems such as the human brain. By harnessing the power of symbolic regression, we have unlocked the ability to distill intricate physical phenomena into elegant and interpretable mathematical expressions. Our approach not only ensures accurate fitting to sparse data but also upholds crucial hyperelasticity constraints, including polyconvexity, essential for maintaining physical relevance.
我们介绍了一个数据驱动的框架，可以从稀疏数据中自动识别可解释和具有物理意义的超弹性本构模型。利用符号回归，我们的方法生成了优雅的超弹性模型，这些模型可以用简洁的数学公式实现精确的数据拟合，同时严格遵守超弹性约束，如多凸性/椭圆性。我们的研究涵盖了三个不同的超弹性模型——不变量基、主拉伸基和正应变基，并强调了符号回归的通用性。我们使用来自五个经典超弹性模型的合成数据和来自人类大脑皮层的实验数据来验证我们的新方法，以证明算法的有效性。我们的结果表明，我们的符号回归算法在不变量基、拉伸基和应变基场景中稳健地发现了具有简洁数学表达式的准确模型。引人注目的是，应变基模型表现出更高的准确性，而拉伸基和应变基模型都有效地捕捉到了人类脑组织固有的非线性和拉压不对称性。多凸性/椭圆性评估证实了在训练范围内和范围外都严格遵守凸性要求。然而，拉伸基模型在大变形下存在潜在的凸性损失问题。对预测能力的评估表明，所有三个模型都具有出色的内插能力，而拉伸基和应变基模型的外推性能也可以接受。最后，对嵌入噪声数据的稳健性测试强调了我们的符号回归算法的可靠性。我们的研究证实了符号回归在自动发现各向同性超弹性模型中的适用性和准确性，为其他软物质系统中的广泛应用提供了可能。
