标题： 关于多保真度和降维神经 emulator 对生理边界条件推断的性能 显示英文标题

标题： On the performance of multi-fidelity and reduced-dimensional neural emulators for inference of physiologic boundary conditions

摘要： 在心血管建模中求解反问题尤其具有挑战性，因为运行高保真模拟的计算成本非常高昂。 在这项工作中，我们专注于贝叶斯参数估计，并探索不同的方法来通过利用低保真近似来降低从后验分布采样的计算成本。 一种常见的方法是为高保真模拟本身构建一个代理模型。 另一种方法是构建高保真和低保真模型之间差异的代理模型。 这种差异通常更容易被近似，可以用全连接神经网络或使代理模型能够在较低维度空间中构建的非线性降维技术来建模。 第三种可能的方法是将高保真模型与代理模型之间的差异视为随机噪声，并使用归一化流估计其分布。 这使得我们可以通过修改似然函数将近似误差纳入贝叶斯反问题中。 我们通过比较五种不同的方法（这些方法是上述方法的变化形式）与完全由高保真模型得出的后验分布来验证它们在解析测试案例中的表现，评估准确性和计算成本。 最后，我们在两个复杂度逐渐增加的心血管实例中展示了我们的方法：一个集总参数Windkessel模型和一个患者特定的三维解剖结构。 显示英文摘要

摘要： Solving inverse problems in cardiovascular modeling is particularly challenging due to the high computational cost of running high-fidelity simulations. In this work, we focus on Bayesian parameter estimation and explore different methods to reduce the computational cost of sampling from the posterior distribution by leveraging low-fidelity approximations. A common approach is to construct a surrogate model for the high-fidelity simulation itself. Another is to build a surrogate for the discrepancy between high- and low-fidelity models. This discrepancy, which is often easier to approximate, is modeled with either a fully connected neural network or a nonlinear dimensionality reduction technique that enables surrogate construction in a lower-dimensional space. A third possible approach is to treat the discrepancy between the high-fidelity and surrogate models as random noise and estimate its distribution using normalizing flows. This allows us to incorporate the approximation error into the Bayesian inverse problem by modifying the likelihood function. We validate five different methods which are variations of the above on analytical test cases by comparing them to posterior distributions derived solely from high-fidelity models, assessing both accuracy and computational cost. Finally, we demonstrate our approaches on two cardiovascular examples of increasing complexity: a lumped-parameter Windkessel model and a patient-specific three-dimensional anatomy.