A numerical comparison of simplified Galerkin and machine learning reduced order models for vaginal deformations
A numerical comparison of simplified Galerkin and machine learning reduced order models for vaginal deformations
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DOI：
10.1016/j.camwa.2023.10.018
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发表时间：
2023-12
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影响因子：
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通讯作者：
William Snyder;Alex Santiago Anaya;Justin Krometis;T. Iliescu;R. Vita
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作者：
William Snyder;Alex Santiago Anaya;Justin Krometis;T. Iliescu;R. Vita
高保真度的分娩计算机模拟仍然非常昂贵和耗时，使其无法在产科急诊期间指导决策。使用替代建模可以开发出保持高保真模型准确性的廉价计算机模拟。代理建模的两种常见方法是基于物理的降阶建模（ROM）和机器学习（ML），随着科学计算社区寻求利用其他（主要是非物理基础的）计算策略的进步，后者越来越受欢迎。虽然ROM和ML已经针对各种问题进行了比较，但据我们所知，目前缺少阴道变形模拟的比较。这项研究提供了一个基线数值比较这两个根本不同的方法之间的方法。由于每种建模方法都有许多方法，为了提供公平和自然的比较，我们从每个类别中选择一个基本模型，每个模型都允许（i）在商业软件包中直接实现，以及（ii）由该领域经验有限的从业者使用。作为ROM和ML方法的数值比较的基准，我们使用有限元（FE）建模的大鼠阴道组织进行膨胀测试的离体变形，以研究预先施加的撕裂的影响。从ROM策略出发，我们考虑一种基于底层非线性方程线性化的简化伽辽金ROM（G-ROM）。从ML策略中，我们选择前馈神经网络来创建从本构模型参数和管腔压力值到FE位移历史（在这种情况下，我们表示产生的模型ML）或位移历史的适当正交分解（POD）系数（在这种情况下，我们表示产生的模型POD-ML）的映射。G-ROM，ML和POD-ML的数值研究发生在重建制度。数值结果表明，G-ROM优于ML模型的离线中央处理器（CPU）的时间模型训练，在线CPU的时间需要生成近似值，相对于FE模型的相对误差。G-ROM实现了上级的错误性能最好的ML模型与11 POD基函数。对于更高维的POD基，G-ROM实现了比最佳ML模型低3个数量级的相对误差，而在线CPU时间仍然与最佳ML模型相同。POD-ML模型提高了ML的速度性能，在相同大小的POD基础上，在线CPU时间与G-ROM相当。然而，POD-ML模型并没有改善ML的错误性能，并且对于大小大于11的POD基，G-ROM仍然优于POD-ML模型。这项基线数值研究作为未来计算机模拟的起点，考虑最先进的G-ROM和ML策略，以及人类阴道的活体几何学、边界条件和材料特性，以及它们在分娩期间的变化。
High-fidelity computer simulations of childbirth remain prohibitively expensive and time consuming, making them impractical for guiding decision-making during obstetric emergencies. Cheap computer simulations that preserve the accuracy of high-fidelity models can be developed using surrogate modeling. Two common approaches to surrogate modeling are physics-based reduced order modeling (ROM) and machine learning (ML), with the latter gaining popularity as the scientific computing community seeks to leverage advances from other, mostly non-physics-based, computational strategies. Although ROM and ML have been compared for various problems, to our knowledge, such a comparison for simulations of vaginal deformations is currently missing. This study provides a baseline numerical comparison between methods from these two fundamentally different approaches. Since there are many methods falling into each modeling approach, to provide a fair and natural comparison, we select a basic model from each category, with each allowing (i) a straightforward implementation in commercial software packages, and (ii) use by practitioners with limited experience in the field. As a benchmark for the numerical comparison of the ROM and ML approaches, we use the finite element (FE) modeling of theex vivodeformations of rat vaginal tissue subjected to inflation testing to study the effect of a pre-imposed tear. From the ROM strategies, we consider a simplified Galerkin ROM (G-ROM) that is based on the linearization of the underlying nonlinear equations. From the ML strategies, we select a feed-forward neural network to create mappings from constitutive model parameters and luminal pressure values to either the FE displacement history (in which case we denote the resulting model ML) or the proper orthogonal decomposition (POD) coefficients of the displacement history (in which case we denote the resulting model POD-ML). The numerical investigation of G-ROM, ML, and POD-ML takes place in the reconstructive regime. The numerical results show that the G-ROM outperforms the ML model in terms of offline central processing unit (CPU) time for model training, online CPU time required to generate approximations, and relative error with respect to the FE models. The G-ROM achieves superior error performance to the best ML model with 11 POD basis functions. With higher-dimensional POD bases, the G-ROM achieves a relative error 3 orders of magnitude lower than that of the best ML model with an online CPU time still on the same order of magnitude as the best ML model. The POD-ML model improves on the speed performance of the ML, having online CPU times comparable to those of the G-ROM given the same size of POD bases. However, the POD-ML model does not improve on the error performance of the ML and is still outperformed by the G-ROM for POD bases of size greater than 11. This baseline numerical investigation serves as a starting point for future computer simulations that consider state-of-the-art G-ROM and ML strategies, and thein vivogeometry, boundary conditions, and material properties of the human vagina, as well as their changes during labor.