Surrogate modelling is a powerful tool to replace computationally expensive nonlinear numerical simulations, with fast representations thereof, for inverse analysis, model-based control or optimization. For some problems, it is required that the surrogate model describes a complete output field. To construct such surrogate models, proper orthogonal decomposition (POD) can be used to reduce the dimensionality of the output data. The accuracy of the surrogate models strongly depends on the (pre)processing actions that are used to prepare the data for the dimensionality reduction. In this work, POD-based surrogate models with Radial Basis Function interpolation are used to model high-dimensional FE data fields. The effect of (pre)processing methods on the accuracy of the result field is systematically investigated. Different existing methods for surrogate model construction are compared with a novel method. Special attention is given to data fields consisting of several physical meanings, e.g. displacement, strain and stress. A distinction is made between the errors due to truncation and due to interpolation of the data. It is found that scaling the data per physical part substantially increases the accuracy of the surrogate model.

中文翻译：

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评估基于 POD 的非线性 FEM 模拟场的替代模型

代理建模是一种强大的工具，可以替代计算成本高的非线性数值模拟，并具有快速表示，用于逆向分析、基于模型的控制或优化。对于某些问题，需要代理模型描述一个完整的输出字段。为了构建这样的代理模型，可以使用适当的正交分解 (POD) 来降低输出数据的维数。代理模型的准确性在很大程度上取决于用于为降维准备数据的（预）处理操作。在这项工作中，基于 POD 的具有径向基函数插值的代理模型用于对高维 FE 数据场进行建模。系统地研究了（预）处理方法对结果字段准确性的影响。将用于替代模型构建的不同现有方法与一种新方法进行比较。特别注意由几个物理含义组成的数据字段，例如位移、应变和应力。由截断和由于数据插值引起的错误之间存在区别。发现按物理部分缩放数据可显着提高代理模型的准确性。