Neural networks can be used as surrogates for PDE models. They can be made physics-aware by penalizing underlying equations or the conservation of physical properties in the loss function during training. Current approaches allow to additionally respect data from numerical simulations or experiments in the training process. However, this data is frequently expensive to obtain and thus only scarcely available for complex models. In this work, we investigate how physics-aware models can be enriched with computationally cheaper, but inexact, data from other surrogate models like Reduced-Order Models (ROMs). In order to avoid trusting too-low-fidelity surrogate solutions, we develop an approach that is sensitive to the error in inexact data. As a proof of concept, we consider the one-dimensional wave equation and show that the training accuracy is increased by two orders of magnitude when inexact data from ROMs is incorporated.
翻译:神经网络可以用作PDE模型的代孕器。 它们可以通过惩罚基本方程式或保护培训中损失功能中物理特性而获得物理觉悟。 目前的方法允许在培训过程中进一步尊重数字模拟或实验中的数据。 然而,这些数据往往非常昂贵,因此对于复杂的模型来说,这些数据很少可用。 在这项工作中,我们研究如何通过计算成本低廉但不准确的其他替代模型(如减序模型(ROMs))的数据来丰富物理觉悟模型。为了避免信任过低纤维替代解决方案,我们开发了一种对不精确数据错误敏感的方法。作为概念的证明,我们考虑单维波方程式,并表明当纳入来自ROM的不精确数据时,培训准确性会增加两个数量级。