论文标题
弹性成像中非均匀材料识别的物理信息神经网络
Physics-Informed Neural Networks for Nonhomogeneous Material Identification in Elasticity Imaging
论文作者
论文摘要
我们应用物理知识的神经网络（PINN）来解决非均匀材料的鉴定问题。我们专注于具有弹性成像背景的问题，在该问题中，人们试图根据准静态负载下的全场位移测量值鉴定软组织的非均匀机械性能。在我们的模型中，我们应用两个独立的神经网络，一个用于近似于相应的正向问题的解，另一个用于近似于未知的材料参数字段。作为概念证明，我们验证了不可压缩的超弹性组织的典型平面应变问题的模型。结果表明，PINN有效地恢复了机械性能的未知分布。通过在我们的模型中采用两个神经网络，我们扩展了PINN的材料鉴定的能力，以包括非均匀材料参数字段，从而使PINN在代表复杂材料特性方面具有更大的灵活性。
We apply Physics-Informed Neural Networks (PINNs) for solving identification problems of nonhomogeneous materials. We focus on the problem with a background in elasticity imaging, where one seeks to identify the nonhomogeneous mechanical properties of soft tissue based on the full-field displacement measurements under quasi-static loading. In our model, we apply two independent neural networks, one for approximating the solution of the corresponding forward problem, and the other for approximating the unknown material parameter field. As a proof of concept, we validate our model on a prototypical plane strain problem for incompressible hyperelastic tissue. The results show that the PINNs are effective in accurately recovering the unknown distribution of mechanical properties. By employing two neural networks in our model, we extend the capability of material identification of PINNs to include nonhomogeneous material parameter fields, which enables more flexibility of PINNs in representing complex material properties.
