Physics-informed UNets for discovering hidden elasticity in heterogeneous materials.
Physics-informed UNets for discovering hidden elasticity in heterogeneous materials.
复制标题
基于物理的 UNet，用于发现异质材料中隐藏的弹性。
DOI：
10.1016/j.jmbbm.2023.106228
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发表时间：
2024
影响因子：
3.9
通讯作者：
Laksari,Kaveh
中科院分区：
文献类型：
--
作者：
Kamali,Ali;Laksari,Kaveh
由于结构成分的不同，生物软组织往往具有复杂的力学性能。本文提出了一种新的基于神经网络的弹性力学反演模型(EL-UNET)，用于从作为输入图像的应变图、法向应力边界条件和区域物理信息中推断力学参数的空间分布。在估计各向同性线弹性的未知参数和应力分布方面，与完全连接的物理信息神经网络相比，EL-UNET在精度和计算成本方面都表现出了优越的性能。我们对EL-UNET的不同变化进行了表征，并提出了一种自适应的空间损失加权方法。为了验证我们的反演模型，我们对材料参数非均匀分布的各向同性区域进行了各种有限元模拟，以生成合成数据。在解决未知场的分布方面，EL-UNET比完全连接的物理知情实施更快和更准确。在测试的模型中，自适应空间加权模型在相同的计算时间内具有最准确的重建结果。学习到的空间权重分布明显对应于未加权模型不准确解析的区域。我们的工作证明了一种利用卷积神经网络的弹性成像的计算效率的反演算法，并为三维弹性逆问题提供了一个潜在的快速框架，这些问题已经被证明是以前提出的方法所不能实现的。
Soft biological tissues often have complex mechanical properties due to variation in structural components. In this paper, we develop a novel UNet-based neural network model for inversion in elasticity (El-UNet) to infer the spatial distributions of mechanical parameters from strain maps as input images, normal stress boundary conditions, and domain physics information. We show superior performance – both in terms of accuracy and computational cost – by El-UNet compared to fully-connected physics-informed neural networks in estimating unknown parameters and stress distributions for isotropic linear elasticity. We characterize different variations of El-UNet and propose a self-adaptive spatial loss weighting approach. To validate our inversion models, we performed various finite-element simulations of isotropic domains with heterogenous distributions of material parameters to generate synthetic data. El-UNet is faster and more accurate than the fully-connected physics-informed implementation in resolving the distribution of unknown fields. Among the tested models, the self-adaptive spatially weighted models had the most accurate reconstructions in equal computation times. The learned spatial weighting distribution visibly corresponded to regions that the unweighted models were resolving inaccurately. Our work demonstrates a computationally efficient inversion algorithm for elasticity imaging using convolutional neural networks and presents a potential fast framework for three-dimensional inverse elasticity problems that have proven unachievable through previously proposed methods.