A Multifidelity Function-on-Function Model Applied to an Abdominal Aortic Aneurysm
A Multifidelity Function-on-Function Model Applied to an Abdominal Aortic Aneurysm
复制标题
应用于腹主动脉瘤的多保真功能叠加模型
作者：
Christoph Striegel;J. Biehler;W. Wall;G. Kauermann
在这项工作中，我们使用函数对函数回归来预测高保真多变量计算机模拟的结果。高保真仿真发生在高清网格上，而低保真仿真发生在粗化和截断的网格上。我们通过将其应用于腹主动脉瘤的复杂有限元模拟来展示我们的方法，该模拟提供了血管在压力下的位移场。为了连接两个多维结果，我们压缩它们，然后拟合函数对函数回归模型。数据是高维的，但样本量小，这意味着只有少数模拟是可用的，而低保真度和高保真度模拟的输出都在几千个量级。为了满足这种特殊的条件，我们的压缩方法假设了一个高斯马尔可夫随机场，考虑了有限元几何，只需要很少的数据。为了解决函数到函数回归模型，我们构建了一个适当的先验，其中包含一个收缩参数，该参数自然遵循karhunen - lo<e:1>分解的贝叶斯观点。我们的模型能够在完整的网格上进行真正的多元预测，而不是诉诸于特定点的结果。
Abstract In this work, we predict the outcomes of high fidelity multivariate computer simulations from low fidelity counterparts using function-to-function regression. The high fidelity simulation takes place on a high definition mesh, while its low fidelity counterpart takes place on a coarsened and truncated mesh. We showcase our approach by applying it to a complex finite element simulation of an abdominal aortic aneurysm which provides the displacement field of a blood vessel under pressure. In order to link the two multidimensional outcomes we compress them and then fit a function-to-function regression model. The data are high dimensional but of low sample size, meaning that only a few simulations are available, while the output of both low and high fidelity simulations is in the order of several thousands. To match this specific condition our compression method assumes a Gaussian Markov random field that takes the finite element geometry into account and only needs little data. In order to solve the function-to-function regression model we construct an appropriate prior with a shrinkage parameter which follows naturally from a Bayesian view of the Karhunen–Loève decomposition. Our model enables real multivariate predictions on the complete grid instead of resorting to the outcome of specific points.
影响因子：
1
作者：
Greven, Sonja;Scheipl, Fabian
通讯作者：
Scheipl, Fabian
影响因子：
3.5
作者：
Biehler, Jonas;Gee, Michael W.;Wall, Wolfgang A.
通讯作者：
Wall, Wolfgang A.
影响因子：
3.8
作者：
Maier, A.;Gee, M. W.;Wall, W. A.
通讯作者：
Wall, W. A.