A Physics-based Domain Adaptation framework for modelling and forecasting building energy systems

State-of-the-art machine-learning based models are a popular choice for modelling and forecasting energy behaviour 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, machine-learning based models for building energy forecasting have difficulty generalizing to out-of-sample scenarios that are not represented in the data because their architecture typically does not hold physical correspondence to mechanistic structures linked with governing phenomena of energy transfer. Thus, their ability to forecast for unseen initial conditions and boundary conditions wholly depends on the representativeness in the data, which is not guaranteed in building measurement data. Consequently, these limitations impede their application to real-world engineering applications such as energy management in Digital Twins. In response, we present a Domain Adaptation framework that aims to leverage well-known understanding of phenomenon governing energy behavior in buildings to forecast for out of sample scenarios beyond building measurement data. More specifically, we represent mechanistic knowledge of energy behavior using low-rank linear time-invariant state space models and subsequently leverage their governing structure to forecast for a target energy system for which only building measurement data is available. We achieve this by aligning the Physics-derived subspace that governs global state space behavior closer towards the target subspace derived from the measurement data. In this initial exploration we focus on linear energy systems; we test the subspace-based DA framework on a 1D heat conduction scenario by varying the thermophysical properties of the source and target systems to demonstrate the transferability of mechanistic models from Physics to measurement data.