Quantifying biomechanical properties of the human vasculature could deepen our understanding of cardiovascular diseases. Standard nonlinear regression in constitutive modeling requires considerable high-quality data and an explicit form of the constitutive model as prior knowledge. By contrast, we propose a novel approach that combines generative deep learning with Bayesian inference to efficiently infer families of constitutive relationships in data-sparse regimes. Inspired by the concept of functional priors, we develop a generative adversarial network (GAN) that incorporates a neural operator as the generator and a fully-connected neural network as the discriminator. The generator takes a vector of noise conditioned on measurement data as input and yields the predicted constitutive relationship, which is scrutinized by the discriminator in the following step. We demonstrate that this framework can accurately estimate means and standard deviations of the constitutive relationships of the murine aorta using data collected either from model-generated synthetic data or ex vivo experiments for mice with genetic deficiencies. In addition, the framework learns priors of constitutive models without explicitly knowing their functional form, providing a new model-agnostic approach to learning hidden constitutive behaviors from data.

翻译：量化人体血管系统的生物力学特性有助于深化我们对心血管疾病的理解。传统本构建模中的非线性回归方法需要大量高质量数据，且需预先明确本构模型的具体形式作为先验知识。相比之下，我们提出了一种融合生成式深度学习与贝叶斯推断的新方法，可在数据稀疏条件下高效推断本构关系族。受函数先验概念的启发，我们构建了生成对抗网络（GAN），其生成器采用神经算子结构，判别器则为全连接神经网络。生成器以测量数据为条件输入噪声向量，输出预测的本构关系，并由判别器在后续步骤中进行鉴别。实验表明，该框架能够利用模型生成的合成数据或来自基因缺陷小鼠离体实验的数据，准确估计小鼠主动脉本构关系的均值与标准差。此外，该框架无需明确本构模型的具体函数形式即可学习其先验分布，为从数据中挖掘隐藏本构行为提供了一种全新的模型无关方法。