# A physics-based domain adaptation framework for modelling and forecasting building energy systems

arXiv: https://arxiv.org/abs/2208.09456 · HTML: https://mlsanity.com/paper/2208.09456/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 58 references that are in the map.
- First posted on arXiv 19 Aug 2022.

## Builds on (most cited first, 6 of 6)

- [A Comprehensive Survey on Transfer Learning](https://mlsanity.com/paper/1911.02685/) (2019)
- [Theory-guided Data Science: A New Paradigm for Scientific Discovery from Data](https://mlsanity.com/paper/1612.08544/) (2016)
- [Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems](https://mlsanity.com/paper/2003.04919/) (2020)
- [Dynamic mode decomposition with control](https://mlsanity.com/paper/1409.6358/) (2014)
- [An introduction to domain adaptation and transfer learning](https://mlsanity.com/paper/1812.11806/) (2018)
- [Subspace Alignment For Domain Adaptation](https://mlsanity.com/paper/1409.5241/) (2014)

## Built on by (most cited first, 2 of 2)

- [Active transfer learning for structural health monitoring](https://mlsanity.com/paper/2510.27525/) (2025)
- [RESCAST-100K: A Comprehensive Dataset for Cross-Domain Residential Load and Indoor Temperature Forecasting](https://mlsanity.com/paper/2606.02852/) (2026)

## Abstract (arXiv)

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.