State-of-the-art machine-learning-based models are a popular choice for modeling and forecasting energy behavior in buildings because given enough data, they are good at finding spatiotemporal patterns and structures even in scenarios where the complexity prohibits analytical descriptions. However, their architecture typically does not hold physical correspondence to mechanistic structures linked with governing physical phenomena. As a result, their ability to successfully generalize for unobserved timesteps depends on the representativeness of the dynamics underlying the observed system in the data, which is difficult to guarantee in real-world engineering problems such as control and energy management in digital twins. In response, we present a framework that combines lumped-parameter models in the form of linear time-invariant (LTI) state-space models (SSMs) with unsupervised reduced-order modeling in a subspace-based domain adaptation (SDA) framework. SDA is a type of transfer-learning (TL) technique, typically adopted for exploiting labeled data from one domain to predict in a different but related target domain for which labeled data is limited. We introduce a novel SDA approach where instead of labeled data, we leverage the geometric structure of the LTI SSM governed by well-known heat transfer ordinary differential equations to forecast for unobserved timesteps beyond observed measurement data. Fundamentally, our approach geometrically aligns the physics-derived and data-derived embedded subspaces closer together. In this initial exploration, we evaluate the physics-based SDA framework on a demonstrative heat conduction scenario by varying the thermophysical properties of the source and target systems to demonstrate the transferability of mechanistic models from a physics-based domain to a data domain.

翻译：最先进的基于机器学习的模型是建筑能源行为建模与预测的常用选择，因为只要有足够的数据，即使面对复杂到无法进行解析描述的场景，它们也能出色地发现时空模式和结构。然而，其架构通常与支配物理现象的机理结构缺乏物理对应关系。因此，它们对未观测时间步长成功泛化的能力取决于数据中观测系统动态的代表性，这在数字孪生中的控制与能源管理等实际工程问题中难以保证。针对这一问题，我们提出一种将线性时不变状态空间模型形式的集总参数模型与子空间领域自适应框架中无监督降阶建模相结合的框架。子空间领域自适应是一种迁移学习技术，通常用于利用一个领域中的标注数据，来预测另一个不同但相关且标注数据有限的目标领域。我们引入一种新颖的子空间领域自适应方法，该方法不依赖标注数据，而是利用由经典热传导常微分方程支配的线性时不变状态空间模型的几何结构，来预测超出观测测量数据的未观测时间步长。从根本上说，我们的方法将物理推导和数据推导的嵌入子空间在几何上更紧密地对齐。在此初步探索中，我们通过改变源系统与目标系统的热物理性质，在演示性热传导场景下评估基于物理的子空间领域自适应框架，以证明机理模型从物理领域到数据领域的可迁移性。