A surrogate model approximates the outputs of a solver of Partial Differential Equations (PDEs) with a low computational cost. In this article, we propose a method to build learning-based surrogates in the context of parameterized PDEs, which are PDEs that depend on a set of parameters but are also temporal and spatial processes. Our contribution is a method hybridizing the Proper Orthogonal Decomposition and several Support Vector Regression machines. This method is conceived to work in real-time, thus aimed for being used in the context of digital twins, where a user can perform an interactive analysis of results based on the proposed surrogate. We present promising results on two use cases concerning electrical machines. These use cases are not toy examples but are produced an industrial computational code, they use meshes representing non-trivial geometries and contain non-linearities.

翻译：代理模型能以较低计算成本近似偏微分方程求解器的输出。本文针对参数化偏微分方程提出一种构建学习型代理模型的方法，该类方程不仅依赖于参数集，同时还是时空过程。我们的贡献在于提出了一种融合本征正交分解与多个支持向量回归机的混合方法。该方法设计用于实时运算，旨在应用于数字孪生场景，使用户能基于所提出的代理模型进行交互式结果分析。我们在两个电机相关用例中展示了具有前景的结果。这些用例并非简单示例，而是由工业计算代码生成，采用表征非平凡几何结构的网格且包含非线性特征。