Physics informed neural networks for control oriented thermal modeling of buildings

Highlights

• We propose data-driven models designed for thermal control in buildings.

• We develop and analyze variants of physics-informed neural networks (PhysNet).

• We present case studies on both simulated and real-world data.

• PhysNets are superior in prediction accuracy, training data efficiency and robustness.

Abstract

Buildings constitute more than 40% of total primary energy consumption worldwide and are bound to play an important role in the energy transition process. To unlock their potential, we need sophisticated controllers that can understand the underlying non-linear thermal dynamics of buildings, consider user comfort constraints and produce optimal control actions. A crucial challenge for developing such controllers is obtaining an accurate control-oriented model of a building. To address this challenge, we present a novel, data-driven modeling approach using physics informed neural networks. With this, we aim to combine the strengths of two prominent modeling frameworks: the interpretability of building physics models and the expressive power of neural networks. Specifically, we use measured data and prior information about building parameters to realize a neural network model that is guided by building physics and can model the temporal evolution of room temperature, power consumption as well as the hidden state, i.e., the temperature of building thermal mass. The main research contributions of this work are: (1) we propose two new variants of physics informed neural network architectures for the task of control-oriented thermal modeling of buildings, (2) we show that training these architectures is data-efficient, requiring less training data compared to conventional, non-physics informed neural networks, and (3) we show that these architectures achieve more accurate predictions than conventional neural networks for longer prediction horizons (as needed for effective control). We test the prediction performance of the proposed architectures using both simulated and real-word data to demonstrate (2) and (3) and argue that the proposed physics informed neural network architectures can be used for control-oriented modeling.

Introduction

According to the recent IPCC report on climate change, global temperature is expected to reach the 1.5 °C threshold in the next decades [1]. In the fight against climate change, the energy and power sector is going through numerous changes such as phasing out of coal-based generation, the addition of renewable energy sources and decentralization of generation and storage units. Concurrently, there is a growing need for efficient and flexible energy consumption that can accommodate the energy generated by intermittent renewable energy sources such as wind and solar power [2]. An important sector for providing this energy efficiency and flexibility is the building sector. As of 2016, buildings accounted for 40% of total primary energy consumption worldwide and around 55% of total electricity consumption in the EU [3]. With these numbers expected to rise over the years, efficient control of building energy consumption will play a crucial role in the energy transition process.

Significant research has been carried out in the context of control algorithms for energy management in buildings, ranging from simple Rule-based Controllers to advanced controllers like Model Predictive Control (MPC) and Reinforcement Learning (RL) [4]. In MPC, a physical model of the system is used to anticipate the future behavior of the system and optimize its performance [5]. This enables MPC-based controllers to be sample efficient and produce interpretable control decisions. However, the accuracy of MPC is closely related to the fidelity of the model, which is often difficult to obtain for real-world scenarios [6]. Contrary to this, data-driven controllers like RL, work directly with past interactions between the system, without the need for explicit physics knowledge. Although these RL-based controllers have shown promising results, they present a black-box solution that requires large amounts of training data. Additionally, in previous work such as [7], RL controller was trained using a physics model-based simulator to ensure that training data obtained was sufficiently diverse and to avoid taking harmful exploration actions.

This makes obtaining accurate building models a crucial requirement for developing better control algorithms. A variety of modeling techniques have been studied previously and are broadly classified into physics models (white box, gray box) and data-driven models (black box) [8]. The physics models involve solving a system of partial differential equations based on the underlying physical laws, commonly achieved using numeric solvers such as EnergyPlus, Modelica, as presented in, e.g., [9], [10]. The use of such models however has been limited in the control domain, primarily due to the high computational cost associated with solving the underlying system of partial differential equations [9]. Alternatively, a lumped parameter model using resistive and capacitive networks is used for control-oriented modeling. With this framework, different thermal components in a building are modeled using an RC network and simplified to obtain a lower order model that is easier to solve. However, even with these approximations, the models obtained are highly specific and require significant modeling effort as demonstrated in [11].

Data-driven models circumvent these modeling challenges by relying completely on obtained data. Previously, techniques such as ARIMA, Genetic Algorithms, Neural Networks, etc., have been studied and have shown good modeling capabilities [8], [12]. Yet, as discussed in [8], these techniques have their own challenges in the form of huge training data requirement and lack of interpretability.

To get the best of both these worlds, we propose to incorporate self-learning, physics guided models with model-based reinforcement learning algorithms to develop interpretable control agents in a data-driven manner. As a first building block, we propose to work with Physics Informed Neural Network architectures to learn physically relevant control-oriented models of real-world systems. This is achieved by explicitly providing information related to the underlying physics of the system to a deep neural network during the training procedure.

The main contributions of this paper can be summarized as:

• We propose two new variants of physics informed neural network architectures (Section 3) for control-oriented modeling of thermal behavior of a building and validate their accuracy using simulated data (Section 5.1).

• Based on real-world cold storage data (Section 4) we show that these physics informed neural networks perform better than conventional, non-physics informed neural networks at predictions for longer time horizons (Section 5.3).

• We further show that training these physics informed neural network architectures is a data-efficient process, requiring less training data than conventional, non-physics informed neural networks (Section 5.2).

While we acknowledge that the general concept of using physics informed neural networks models in itself is not new (as indicated through the literature review in the subsequent Section 2), the specific physics informed neural network model we have designed (incorporating basic constraints based on a simple RC model) is. Through aforementioned experiments we demonstrate our model’s feasibility and practical applicability, based on experiments using real-world data.