论文标题
有效的数据采样策略和物理知识神经网络的边界条件约束，以识别固体力学中的材料特性
Effective Data Sampling Strategies and Boundary Condition Constraints of Physics-Informed Neural Networks for Identifying Material Properties in Solid Mechanics
论文作者
论文摘要
材料识别对于理解机械性能与相关机械功能之间的关系至关重要。然而，材料识别是一项具有挑战性的任务，尤其是当材料的特征在本质上是高度非线性的，这在生物组织中很常见。在这项工作中，我们通过物理知识的神经网络（PINN）确定了连续固体力学中未知的材料特性。为了提高PINN的准确性和效率，我们开发了有效的策略，以不均匀地采样观察数据。我们还研究了不同的方法，以将Dirichlet边界条件作为软约束或硬性约束。最后，我们将提出的方法应用于一组跨越线性弹性和超弹性材料空间的时间依赖性和与时间无关的固体机械示例。估计的材料参数的相对误差小于1％。因此，这项工作与各种应用有关，包括优化结构完整性和开发新型材料。
Material identification is critical for understanding the relationship between mechanical properties and the associated mechanical functions. However, material identification is a challenging task, especially when the characteristic of the material is highly nonlinear in nature, as is common in biological tissue. In this work, we identify unknown material properties in continuum solid mechanics via physics-informed neural networks (PINNs). To improve the accuracy and efficiency of PINNs, we developed efficient strategies to nonuniformly sample observational data. We also investigated different approaches to enforce Dirichlet boundary conditions as soft or hard constraints. Finally, we apply the proposed methods to a diverse set of time-dependent and time-independent solid mechanic examples that span linear elastic and hyperelastic material space. The estimated material parameters achieve relative errors of less than 1%. As such, this work is relevant to diverse applications, including optimizing structural integrity and developing novel materials.
