论文标题
结合基于物理和数据驱动的技术，用于使用纠正源术语方法可靠的混合分析和建模
Combining physics-based and data-driven techniques for reliable hybrid analysis and modeling using the corrective source term approach
论文作者
论文摘要
即将到来的技术，例如数字双胞胎，涉及安全至关重要应用的人工智能系统，需要准确，可解释，计算效率且可推广的模型。不幸的是，两种最常用的建模方法，基于物理学的建模（PBM）和数据驱动的建模（DDM）无法满足所有这些要求。在当前的工作中，我们演示了混合方法如何结合最佳PBM和DDM的混合方法可以导致模型可以胜过两者的模型。我们这样做是通过基于第一原则与黑匣子DDM相结合的部分微分方程，在这种情况下，深层神经网络模型补偿了未知物理。首先，我们提出了一个数学上的论点，说明为什么这种方法应该起作用，然后将混合方法应用于未知源项模拟二维热扩散问题。结果证明了该方法在准确性和概括性方面的出色性能。此外，它显示了如何在混合框架中解释DDM部分以使整体方法可靠。
Upcoming technologies like digital twins, autonomous, and artificial intelligent systems involving safety-critical applications require models which are accurate, interpretable, computationally efficient, and generalizable. Unfortunately, the two most commonly used modeling approaches, physics-based modeling (PBM) and data-driven modeling (DDM) fail to satisfy all these requirements. In the current work, we demonstrate how a hybrid approach combining the best of PBM and DDM can result in models which can outperform them both. We do so by combining partial differential equations based on first principles describing partially known physics with a black box DDM, in this case, a deep neural network model compensating for the unknown physics. First, we present a mathematical argument for why this approach should work and then apply the hybrid approach to model two dimensional heat diffusion problem with an unknown source term. The result demonstrates the method's superior performance in terms of accuracy, and generalizability. Additionally, it is shown how the DDM part can be interpreted within the hybrid framework to make the overall approach reliable.
