With the recent wave of digitalization, specifically in the context of safety-critical applications, there has been a growing need for computationally efficient, accurate, generalizable, and trustworthy models. Physics-based models have traditionally been used extensively for simulating and understanding complex phenomena. However, these models though trustworthy and generalizable to a wide array of problems, are not ideal for real-time. To address this issue, the physics-based models are simplified. Unfortunately, these simplifications, like reducing the dimension of the problem (3D to 2D) or linearizing the highly non-linear characteristics of the problem, can degrade model accuracy. Data-driven models, on the other hand, can exhibit better computational efficiency and accuracy. However, they fail to generalize and operate as blackbox, limiting their acceptability in safety-critical applications. In the current article, we demonstrate how we can use a data-driven approach to correct for the two kinds of simplifications in a physics-based model. To demonstrate the methodology's effectiveness, we apply the method to model several elasticity problems. The results show that the hybrid approach, which we call the corrective source term approach, can make erroneous physics-based models more accurate and certain. The hybrid model also exhibits superior performance in terms of accuracy, model uncertainty, and generalizability when compared to its end-to-end data-driven modeling counterpart.

翻译：随着近年来数字化浪潮的兴起，特别是在安全关键应用背景下，对计算高效、精确、可泛化且可信赖模型的需求日益增长。基于物理的模型传统上被广泛用于模拟和理解复杂现象。然而，尽管这些模型具有可信赖性且能泛化至各类问题，却难以满足实时性要求。为解决此问题，物理模型往往被简化。遗憾的是，这些简化——如降低问题维度（三维降至二维）或线性化高度非线性特征——可能降低模型精度。相比之下，数据驱动模型虽展现出更好的计算效率与精度，但其作为黑箱模型难以泛化，限制了在安全关键应用中的可接受性。本文展示如何利用数据驱动方法校正物理模型中两类典型简化。为验证方法有效性，我们将该方法应用于多种弹性问题的建模。结果表明，这种我们称为“校正源项方法”的混合模型能使存在误差的物理模型变得更精确、更确定。与纯端到端数据驱动模型相比，该混合模型在精度、模型不确定性及泛化能力方面均表现出更优性能。