标题： 广义不变量遇见本构神经网络：一种用于超弹性材料的新框架 显示英文标题

标题： Generalized invariants meet constitutive neural networks: A novel framework for hyperelastic materials

摘要： 确定给定材料的超弹性模型的主要挑战在于选择不变量以及选择应变能函数如何在这些不变量上进行函数依赖。 在这里，我们引入了一个新的数据驱动框架，该框架同时发现各向同性不可压缩超弹性材料的适当不变量和本构模型。 我们的方法直接从实验观察中识别出一类广义不变量中最合适的不变量以及相应的应变能函数。 与之前依赖于固定不变量选择或顺序拟合过程的方法不同，我们的方法将发现过程整合到一个单一的神经网络架构中。 通过观察可能的不变量的连续族，该模型可以灵活适应不同的材料行为。 我们使用橡胶和脑组织的流行基准数据集来证明这种方法的有效性。 对于橡胶，该方法恢复了一个以拉伸为主的形式，与经典模型一致。 对于脑组织，它识别出对小拉伸敏感的形式，捕捉了软生物材料的非线性剪切响应特性。 与传统和基于神经网络的模型相比，我们的框架在广泛的变形状态下提供了改进的预测精度和可解释性。 这种统一策略为超弹性中的自动且物理上有意义的模型发现提供了一个强大的工具。 显示英文摘要

摘要： The major challenge in determining a hyperelastic model for a given material is the choice of invariants and the selection how the strain energy function depends functionally on these invariants. Here we introduce a new data-driven framework that simultaneously discovers appropriate invariants and constitutive models for isotropic incompressible hyperelastic materials. Our approach identifies both the most suitable invariants in a class of generalized invariants and the corresponding strain energy function directly from experimental observations. Unlike previous methods that rely on fixed invariant choices or sequential fitting procedures, our method integrates the discovery process into a single neural network architecture. By looking at a continuous family of possible invariants, the model can flexibly adapt to different material behaviors. We demonstrate the effectiveness of this approach using popular benchmark datasets for rubber and brain tissue. For rubber, the method recovers a stretch-dominated formulation consistent with classical models. For brain tissue, it identifies a formulation sensitive to small stretches, capturing the nonlinear shear response characteristic of soft biological matter. Compared to traditional and neural-network-based models, our framework provides improved predictive accuracy and interpretability across a wide range of deformation states. This unified strategy offers a robust tool for automated and physically meaningful model discovery in hyperelasticity.