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Heating, ventilation, and air conditioning (HVAC) systems account for a significant portion of energy consumption in developed countries. Accurately identifying their dynamics is crucial for developing effective controllers. However, it is challenging due to the system’s nonlinearities and variations across building types. Data-driven approaches have shown great promise in modeling the dynamics of HVAC systems, replacing traditional ordinary differential equations. However, relying solely on data can lead to poor generalization, particularly when the training data is limited or when unknown disturbances, such as weather conditions and occupant behavior, are present. Physics-informed machine learning (PIML) techniques have been developed for integrating physical principles into machine learning methods to improve the accuracy and data efficiency of modeling of dynamical systems. This paper investigates PIML techniques that incorporate three different physical properties: monotonicity, boundedness, and system structure. These models are benchmarked against physics-agnostic machine learning (PAML) approaches and the gray-box modeling technique to further highlight the performance of PIML models in terms of accuracy, robustness, and data efficiency for modeling HVAC systems from real data. Experimental data collected from a real-world HVAC system are used for systematically studying and analyzing thirteen gray-box, PAML, and PIML modeling techniques in different scenarios. Our results demonstrate that PIML models outperform PAML models in predicting the temperature dynamics of HVAC systems, especially when the training data is limited, unreliable, or noisy, with accurate and robust performance. Furthermore, we identify which physical properties are the most beneficial for enhancing machine learning performance for HVAC system identification. 

Data-driven approaches are increasingly popular for identifying dynamical systems due to improved accuracy and availability of sensor data. However, relying solely on data for identification does not guarantee that the identified systems will maintain their physical properties or that the predicted models will generalize well. In this paper, we propose a novel method for data-driven system identification by integrating a neural network as the first-order derivative of the learned dynamics in a Taylor series instead of learning the dynamical function directly. In addition, for dynamical systems with known monotonic properties, our approach can ensure monotonicity by constraining the neural network derivative to be non-positive or non-negative to the respective inputs, resulting in Monotonic Taylor Neural Networks (MTNN). Such constraints are enforced by either a specialized neural network architecture or regularization in the loss function for training. The proposed method demonstrates better performance compared to methods without the physics-based monotonicity constraints when tested on experimental data from an HVAC system and a temperature control testbed. Furthermore, MTNN shows good performance in a control application of a model predictive controller for a nonlinear MIMO system, illustrating the practical application of our method. 

This data set contains measurements from real HVAC (heating, ventilation, and air conditioning) systems of real buildings in the US.  Each ZIP file contains CSV data files of a building for different scenarios.  Refer to the README file in each ZIP file for details. The document `data_info.pdf` provides explanations of the variables/columns in the data files. This work was supported by the U.S. National Science Foundation (NSF) under grants 2514584 and 2513096. 

The deep operator network (DeepONet) architecture is a promising approach for learning functional operators, that can represent dynamical systems described by ordinary or partial differential equations. However, it has two major limitations, namely its failures to account for initial conditions and to guarantee the temporal causality – a fundamental property of dynamical systems. This paper proposes a novel causal deep operator network (Causal-DeepONet) architecture for incorporating both the initial condition and the temporal causality into data-driven learning of dynamical systems, overcoming the limitations of the original DeepONet approach. This is achieved by adding an independent root network for the initial condition and independent branch networks conditioned, or switched on/off, by time-shifted step functions or sigmoid functions for expressing the temporal causality. The proposed architecture was evaluated and compared with two baseline deep neural network methods and the original DeepONet method on learning the thermal dynamics of a room in a building using real data. It was shown to not only achieve the best overall prediction accuracy but also enhance substantially the accuracy consistency in multistep predictions, which is crucial for predictive control. 

Physics-informed machine learning (PIML) is a set of methods and tools that systematically integrate machine learning (ML) algorithms with physical constraints and abstract mathematical models developed in scientific and engineering domains. As opposed to purely data-driven methods, PIML models can be trained from additional information obtained by enforcing physical laws such as energy and mass conservation. More broadly, PIML models can include abstract properties and conditions such as stability, convexity, or invariance. The basic premise of PIML is that the integration of ML and physics can yield more effective, physically consistent, and data-efficient models. This paper aims to provide a tutorial-like overview of the recent advances in PIML for dynamical system modeling and control. Specifically, the paper covers an overview of the theory, fundamental concepts and methods, tools, and applications on topics of: 1) physics-informed learning for system identification; 2) physics-informed learning for control; 3) analysis and verification of PIML models; and 4) physics-informed digital twins. The paper is concluded with a perspective on open challenges and future research opportunities.