**1. Introduction**

Cities around the globe are growing rapidly, following the rising population. According to the United Nations [1], approx. 55% of the world population currently lives in urban areas, and it is foreseen to double the number of residents by 2050 [2]. Further cities development is causing a rising negative impact on the natural environment. Thus, it is necessary to manage cities effectively, heading towards urban sustainability. In general, modern urban development should promote energy-efficient cities which respect the natural environment and provide high-quality life conditions for residents [3]. The above mentioned is valid for both existing and new urban areas; present cities should be managed in a better, more effective way, while new ones should be correctly designed [4]. Urban modelling is a comprehensive subject, including three main areas: land use and transportation model, Urban Energy System Modelling (UESM) [5] and Urban Building Energy Modelling (UBEM). The UBEM is a concept allowing us to validate possible scenarios of cities development towards their sustainability.

Nowadays, building energy analyses are performed using computational software, allowing for comprehensive studies of a single building. Out of numerous available tools [6], the *Energy Plus* is one of the most universal and popular software for various energy-related studies of a singular building [7]. A study focused on the energy behavior of a single building is called Building Energy Modelling (BEM). It is a well-known issue, already performed by academics all over the world; the overview of some popular BEM codes can be found in [8]. On the other hand, the UBEM allows aggregating the energyrelated results of singular buildings to the urban scale, including some complex phenomena

**Citation:** Zygmunt, M.; Gawin, D. Application of Artificial Neural Networks in the Urban Building Energy Modelling of Polish Residential Building Stock. *Energies* **2021**, *14*, 8285. https://doi.org/ 10.3390/en14248285

Academic Editors: Jaroslaw Krzywanski, Marcin Kami ´nski and Angel A. Juan

Received: 22 November 2021 Accepted: 7 December 2021 Published: 9 December 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

occurring in urban environments. Therefore, energy-related analyses of city districts should be performed using specialized UBEM software. According to [9], those tools are the most appropriate approach for analyzing building stocks at a large scale. Each of the UBEM tools has specific fields of applications, as well as they were developed with different assumptions and constraints. Presently, the most popular UBEM software are *CitySim* [10], *Urban Modelling Interface*—UMI [11], *City Building Energy Saver*—CityBES [12] and *City Energy Analyst*—CEA [13]; the capabilities of some UBEM tools are overviewed in [14]. Some interesting analyses can be found in [15–21], where various issues of the UBEM were examined, i.e., city-scale energy planning, renewable energy sources (RES) application, Building Energy Cluster (BEC) modelling or Urban Heat Island (UHI) impact.

The UBEM model can be focused on buildings modelling at an urban scale with different scopes. Some UBEM tools were developed in order to deal with a single and specific aspect, e.g., to optimize daylighting [22] or to provide energy savings derived by buildings [23], while others are more complex in order to examine more comprehensive issues. The UBEM can be categorized into two main approaches (see Figure 1), accordingly top-down and bottom-up methods [14,24]. Generally speaking, the top-down approach is based on the estimation of energy consumption from data of a larger scale (e.g., residential sector), while the bottom-up approach uses calculated energy consumption of individual or group of buildings to aggregate then the results to the urban scale. Out of the literature review, the bottom-up approach is presently a much more popular method of the UBEM.

**Figure 1.** Schematic of the UBEM techniques [25].

The top-down approach assumes the group of buildings as an energy sink, without investigating individual end-uses, based on widely available aggregated data and historic records. Two types of top-down approaches are specified, accordingly econometric or technological. The popularity of the applications of the top-down methods increases whenever the global crisis occurs, such as the one at the end of the 1970s. Some exemplary UBEM analyses using the top-down approach can be found in [26–29].

The bottom-up approach uses data from a small scale (i.e., a single building) for examining the energy consumption at a larger scale (i.e., for a whole region). Usually, the input data for the bottom-up models include parameters such as building geometry and envelope structure, equipment and appliances, exterior and interior climate conditions, occupancy and working schedules. Those detailed parameters are then furtherly used to analyze a whole residential area—it is the biggest advantage of the bottom-up approach. There are two types of bottom-up approaches, accordingly statistical and engineering studies [30]. The statistical approach can be focusing on regression [31,32], conditional demand analysis (CDA) [33,34] or Artificial Neural Network (ANN) approaches [35,36]. On the other hand, the engineering approach might be specified using population distribution [37,38], archetypes [39,40] or sample [41] techniques. The state-of-the-art review on the available bottom-up approaches of the UBEM can be found in [42,43].

Despite the fact, that UBEM became a popular trend for engineers and researchers all over the world, there is no such software available to analyze Polish residential building stock. Therefore, a multi-criteria computer analytic tool called TEAC (*Tool for Energy Efficiency Analyses of an Energy Cluster*), which allows to perform energy, environmental and economic analyses of the Polish household sector was developed. The TEAC software uses a hybrid approach of the UBEM, combining both top-down and bottom-up techniques. The goal of this work is to present the mathematical approaches defining the TEAC software. In this paper, an overview of the method applied for the ANN training process is discussed. Moreover, most of the applied dependencies, expressing considered phenomena of urbanscale areas, are presented. The ANNs application was proven to be useful and efficient for various UBEM analyses, in particular as a main part of the TEAC software. The TEAC software is comprehensively described in [25], while some of its' applications can be found in [44–46]. The analyses described in this paper present exemplary results for a simple neighborhood, considered as BEC. The results are based on the overall energy demand of the cluster, allowing for some further analyses, e.g., the environmental impact of the examined neighborhood or economic profitability of the proposed modernizations. Due to the application of the ANN (and the TEAC software in general), it is possible to perform such comprehensive analyses without the time consuming detailed energy modelling of individual buildings.
