For its robust predictive power (compared to pure physics-based models) and sample-efficient training (compared to pure deep learning models), physics-informed deep learning (PIDL), a paradigm hybridizing physics-based models and deep neural networks (DNN), has been booming in science and engineering fields. One key challenge of applying PIDL to various domains and problems lies in the design of a computational graph that integrates physics and DNNs. In other words, how physics are encoded into DNNs and how the physics and data components are represented. In this paper, we provide a variety of architecture designs of PIDL computational graphs and how these structures are customized to traffic state estimation (TSE), a central problem in transportation engineering. When observation data, problem type, and goal vary, we demonstrate potential architectures of PIDL computational graphs and compare these variants using the same real-world dataset.

翻译：物理信息深度学习（PIDL）作为一种融合物理模型与深度神经网络（DNN）的范式，因其相较于纯物理模型具有更强的预测能力，且相较于纯深度学习模型具备更高的样本效率，在科学与工程领域蓬勃发展。将PIDL应用于不同领域和问题的关键挑战之一，在于如何设计集成物理规律与DNN的计算图结构——换言之，即物理知识如何编码到DNN中，以及物理与数据分量如何表征。本文系统梳理了PIDL计算图的多类架构设计，并展示了这些结构如何针对交通状态估计（TSE）这一交通工程核心问题进行定制化设计。针对观测数据、问题类型及目标差异，我们提出了PIDL计算图的潜在架构方案，并基于同一真实世界数据集对这些变体进行了比较分析。