Forecasting of residential unit’s heat demands: a comparison of machine learning techniques in a real-world case study

The energy transition (the replacement of the use of fossil energy sources with an ecological, sustainable energy supply) is one of the most important environmental, economic, and sociological challenges this decade.

In addition to expanding renewable energies, increasing energy efficiency and reducing overall energy consumption are essential objectives. In particular, the building and private housing sectors have a high potential for energy savings. Therefore, the goal in the residential sector must be a reduction in heat and primary energy demand. In the future, buildings’ heating requirements must be covered entirely by solar, biomass, or geothermal energy. Accordingly, energy management concepts are being developed to ensure efficient and safe renewable energy use while fulfilling the thermal requirements of residents. However, these concepts necessitate methods for forecasting both the generation and the energy load [1]. Furthermore, they always presuppose individual boundary conditions, i.e., for private housing, the thermal comfort of the occupants must be ensured. So, developing accurate models to forecast the actual heat demand is essential.

For accurate heat demand prediction, the potential of data-driven methods has become apparent in recent years [2‐4]. Unlike traditional engineering and physical methods, these techniques do not require detailed building data or extensive expertise to apply elaborate technical procedures, which is a significant advantage. Data-driven methods learn from real-time or historical data.

Using historical data, statistical models can be trained in a stationary learning environment. Batch learning techniques, known as (supervised) offline machine learning methods, and time series models are used to learn the best predictor from training data.

However, in many use cases, historical data is unavailable from the beginning of a system’s life. Moreover, the prediction of energy demand should be considered a non-stationary problem since unforeseen changes may occur over time, e.g., degradation of insulation, occupant changes, or general usage patterns. Generally, these issues are combined in the term concept drift [5]. To cope with these problems, models must be able to learn and evolve dynamically in an uncertain environment. In this work, the familiar issue of sensor drifts is, however, largely insignificant. The sensors capturing heat usage are calibrated for long-term use and regularly maintained or replaced after the guaranteed runtime. Whereas third-party weather data could theoretically suffer from sensor drifts, this is also unlikely to become a significant problem as those sensors are typically built for long-term stability.

A typical approach for handling (initially) low data availability and concept drift is the usage of online machine learning methods where the data is fed into the model sequentially whenever it becomes available (rather than at fixed timestamps—potentially even a single one before the first deployment—like in offline machine learning) to update its parameters and—hopefully—lead to the best possible predictor at each step.

In this work, we investigate the potential application of a large variety of different model producing methods in a newly built real-world residential setting, based on data we gathered from June 2020 to February 2022. These models should accurately forecast the heat demand of all units within the small complex. We make both the data gathered in this field study, as well as all of our results publicly available.

Regardless of the specific model type, this application domain—as it ensures the thermal comfort of occupants—requires its models to be well understandable for the engineers in the companies responsible. More significant issues could quickly terminate contracts and destroy business models, which in turn makes the application of more complex models less likely. Therefore, we discuss the employed models not only on their merits regarding predictive performance but also on their presumed transparency and explainability of decisions.

Moreover, heat supply is a critical task that must be ensured in any extreme or unusual situation (especially sub-zero temperatures). Therefore, we also examine how well the models predict heat consumption for data outliers.

In Sect. 2, we reintroduce the task of heat consumption forecasting. Section 3 gives a more detailed overview of the aims of this specific work with Sect. 5 introducing the data set we first gathered and then investigated the forecasting methods on. This field’s state-of-the-art and other recent approaches are summarized in Sect. 4. Section 6 gives an overview of the employed methods and their potential merits, whereas Sect. 7 introduces our experimental approach at evaluating these methods in relation to our field study’s data. The results are first presented in Sect. 8 and then discussed in detail (especially regarding the predictive errors, the usage in embedded systems, and the explainability of models) in Sect. 9. In our data, we found some outliers that were quite hard to predict correctly. These and the models’ results are discussed in Sect. 10. Section 11 concludes this paper and gives an overview of our results and an outlook on the next steps within this field study.

Most data-driven models require large and diverse sets of training data for accurate heat consumption prediction. These datasets often contain data from several years to represent seasonal patterns and trends. However, for more specialized use cases, such as individual neighborhoods, these data sets are mostly unavailable. Usually, when new energy systems are commissioned, no training data has been gathered, even if energy management systems had been in place before. Even during the active operation of modern systems, the data sets grow slowly. Additionally, the data can not initially reflect any long-term seasonality or trends. The forecast quality drops significantly when an unfamiliar situation occurs, e.g., the first summer/winter or some concept drift.

The heat consumption can be described by a continuous function that models the relationship between the heat consumption \(y \in {\mathbb {R}}\) and a set of k variables \(x \in {\mathbb {R}}^{k}\) for a time t:The heat consumption is modeled as a sequence of data points over time for time series analysis models. The time series is decomposed into the deterministic trend \({m_t}\), seasonal components \({s_t}\) and a random, stationary component (error) \({\epsilon _t}\).

This research aims to evaluate models predicting heat requirements for an energy management system, which regulates a central heating system and distributes heat to multiple residential units. The models have to achieve good predictive performance despite limited training data (cf. Sect. 5), a situation typically encountered in new energy management systems or newly built or renovated units. If a new and unknown situation occurs, the investigated models must generalize well, i.e., make stable predictions with a small error value. Based on the models’ forecasts, a schedule spanning the next 48 to 72 h is created for the energy management systems. Subsequently, the schedule gets updated every 24 h as more up-to-date (weather) data is available. In line with our field study’s requirements, the duration of the schedules is chosen to ensure that the power systems can continue to run automatically in the event of internet failures. The field of application is the load and storage management, respectively, energy management systems, for buildings and quarters. Specifically, the results of this research will later be used in the area of a cloud application with distributed edge devices. It is analyzed whether the model computations can be performed directly on the embedded systems, which often have low computational and memory performance, or should be outsourced to an external server. In addition, the models are examined to determine whether the model’s predictions can be explained and understood by (non-specialist) persons responsible for the systems and the heat supply.

In recent years, many studies on energy load forecasting have been published. The data-driven approaches can be classified into statistical and machine learning (ML)-based methods.

Time series models are widely used in statistical methods. For these methods, the consumption is modeled as a time series. In general, the forecast horizon for load forecasts for heat (or electricity) is divided into short-term and long-term, where short-term forecasts give a minutely or hourly forecast in a horizon is up to 24 h, whereas long-term predictions refer to load forecasts for, typically, 1 week but also up to one or more years. The goal of short-term horizons is to optimize the day-to-day operation of energy systems while long-term model can be used for the planning of energy systems. In this study, we aim at making short-term predictions, although, the following models after frequently used in both settings. Particularly frequently studied time series models are ARIMA [6‐9] and its improvement SARIMA [10], and Exponential Smoothing [11‐14]. The development of the BATS models (Box-Cox transformation, ARMA residuals, trend, and seasonality) and the TBATS models (trigonometric seasonal BATS) was a significant advance in the field of time series forecasting techniques. BATS and TBATS can be used to model time series with multiple complex seasonalities [15, 16]. The TBATS model has excellent forecast accuracy and offers a possibility for long-term load forecasting [17‐19]. An alternative, based on grey system theory and Markov chains rather than ARMA, are Grey-Markov models (GM) [20‐22]. Studies that have compared GM models with ARIMA models have concluded that the predictive performance of both models is comparable, with ARIMA being slightly better than GM [23] or vice versa [24]. However, GM’s predictions often undershoot, which is detrimental to supplying sufficient heat, while ARIMA tends to overshoot [24]. Also, GM is somewhat more computationally intensive [24]. Another basic statistical analysis method is to model the load forecasts linearly, as with Linear Regression (LR) [25, 26], Recursive Least Squares (RLS) [27‐29], fuzzy LR methods [30] or Polynomial Regression [31].

A wide range of different approaches to ML has been pursued. Often evaluated ML models are Support Vector Regression (SVR) [32‐34], respectively Support Vector Machines [35‐37], Random Forest Regression (RFR) [38, 39], or Kernel Ridge Regression (KRR) [40]. The comprehensive literature review on energy demand forecasting by Ghalehkhondabi et al. [41] shows that artificial neural network (ANN) models perform very well in this domain. This conclusion is also confirmed by later studies that have investigated ANNs [42‐45], Long Short-Term Memory (LSTM) networks [34, 46‐48] or Convolutional Neural Networks (CNNs) [49, 50].

Different ML methods are combined to improve the prediction quality of ML models to reduce their respective drawbacks. In short-term load forecasting, SVR is often combined with other ML methods [51‐53]. Another option is to combine LSTMs with CNNs [54‐57]. The conventional LSTM neural network is extended by a preprocessing phase using a CNN.

Beyond the already presented methods, authors recently took a variety of different approaches towards predicting energy demand: [58] combines ANNs with metaheuristic algorithms, including artificial bee colony optimization, particle swarm optimization, an imperialist competitive algorithm, and a genetic algorithm. In [59], further development of CNNs for limited data is presented. Kannari et al. [60] combine physics-based modeling and ML to forecast the energy consumption of buildings. Potočnik et al. [61] investigate a multi-stage ML-based approach for short-term heat demand forecasting. The approach includes feature extraction and different ML models for forecasting. A similar approach is taken by Golmohamadi [62]. In [63] and [64], probabilistic approaches are presented and combined with ML models. Recently, studies have been published that take a similar approach to our present study. Kurek et al. [65] investigate various regression models, deep neural networks, and models using fuzzy logic for heat demand forecasting for the Warsaw district heating network, which supplies heat for domestic and heating purposes. They divide the year into summer, winter, and intermediate seasons and evaluate the models for each season for a 72-h horizon.

The data was gathered in a newly built residential quarter (completion 2019) in southern Germany near Munich. The quarter contains 66 residential units, and the heat meter is located behind a heat accumulator and records the domestic hot water supply and the space heating demand. A controller keeps the flow after the heat accumulator at a constant temperature of 48\(^\circ \)C. While in the original data, the heat demand of all 66 apartments was recorded individually for billing reasons, we want to stress that in this study we aim at predicting the load at the central heating system. The controller of said system distributes heat to the apartments individually but only the overall required heat is relevant for planning purposes. From a data science perspective, this also has the advantage that we can better compensate for any erroneous data or data failures from individual apartments, therefore also adjusting for noise. The heat demand is examined in a 60-minute interval and measured in watt-hours [Wh]. Thus, it is not the behavior of the residents that is predicted, but the required output of the heating system in 1 h. The scaled heat consumption is shown in Fig. 1. The hydraulic diagram of individual housing stations where a heat meter is installed can be found in the supplementary information’s¹ Sect. 1.

The data was collected in a period from 01. June 2020 to 28. February 2022. The limits of the period are set by the commissioning of the monitoring system and the first draft of this paper. In total, 15,228 data points were collected during this period.

Eight parameters are available as input for the models: Month of the year, day of the week,² the hour of the day, outside temperature, solar radiation, heat consumption 24 h ago, average heat consumption over the last 24 h, and the degree hour. The degree hour is the difference between the target inside and the measured outside temperatures. It is only calculated for days whose average outside temperature is below a heating limit. A target inside temperature of 21\(^\circ \)C and a heating limit of 15\(^\circ \)C is assumed. Outside temperature and solar radiation were retrieved from the weather API Weatherbit.³ Sect. 2 of the supplementary information contains Fig. 1’s corresponding parameters temperature, solar radiation, heat consumption 24 h ago, average heat consumption over the last 24 h, and degree hour.

In this section, we introduce the various forecasting concepts from traditional statistics and modern machine learning (ML) that were used in this work. While none of them are new, this section improves the self-containedness of the paper and hopefully allows readers from a civil engineering background to better understand and follow this work and maybe reapply it to their own data.

In general, forecasting techniques can be divided into two main types: simple statistical or parametric models, and ML-based models.

Classical models, such as (S)ARIMA, Exponential Smoothing, and LR, use historical data for mathematical combinations to forecast heat consumption. Their advantage is that the estimations of the parameters are easily interpretable.

However, as the complexity of the forecast data increases, these methods become less reliable. A transition from linear to nonlinear models is necessary. ML-based methods are generally adaptive and robust to noisy data due to their ability to generalize from observed patterns. Often used ML methods in load forecasting are ANNs, SVR and RFR. Within the family of ANNs, different architectures are common: The traditional fully connected network, as well as CNNs, LSTMs, or combinations of these.

If the training data \(D=\{(x_1,y_1),...,(x_t,y_t)\}\) is available in sequential order, a model to predict the next time step \(t+1\) can be learned via online learning. Online learning updates the predictor in real-time, always incorporating the newest available data, which can protect against the influences of data drifts but might struggle with strong seasonalities in the data.

In our work, we incorporate a variety of online learners: RLS, Stochastic Gradient Descent trained linear models (SGD), and three types of ANNs. As fully connected ANNs have some limitations in an online learning environment, two additional concepts are investigated: an ANN combined with an Experience Replay (ER)–like buffer and the online framework based on Hedge Backpropagation (HBP) presented by [66].

The following is a brief outline of the methods examined. We sort them from time series over offline ML to online ML, and within their respective category by model complexity:

Exponential Smoothing is a powerful time series forecasting method for univariate data that is often used as an alternative to the autoregressive approach. Exponential Smoothing combines the advantages of flexibility, reliability of predictions, and low cost. Holt-Winter Smoothing (HWS) [67, 68] is an extension of simple exponential smoothing for trends and seasonal patterns.

Autoregressive Integrated Moving Average (ARIMA) is a statistical model for non-stationary time series. Seasonal ARIMA (SARIMA) takes the non-seasonal components of the ARIMA and adds a seasonal term. The seasonal term is very similar to the non-seasonal components of the model, but it includes a backward shift by a seasonal period [69].

ARIMA and exponential smoothing use complementary approaches to predict time series. Exponential smoothing models describe the trend and seasonality in the data, while ARIMA models describe the autocorrelation in the data [69].

Linear Regression (LR) is the simplest approach to model the relationship between a set of independent variables \({x^T = (x_1, x_2,..,x_p})\) and a dependent variable y. This is in contrast to the aforementioned time series approaches, where predictions on y were made based on previous values for y, assuming that there is a sequential order. Fitting a linear model to a given data set requires the estimation of regression coefficients, typically by minimizing the squared error terms.

When a learning task can not be modeled using a linear function, a kernel can be used to transform the data into a higher dimensional space, called kernel space, where the data can be modeled linearly. A fundamental algorithm to be kernelized is Ridge Regression, which attempts to solve the frequent problems of multicollinearity and high variance in LR by including shrinkage methods and L2 regularization in the updates. Kernel Ridge Regression (KRR) combines Ridge Regression with a kernel.

Support Vector Regression (SVR) is a generalization of traditional support vector machines for classification and supports both linear and nonlinear regressions. SVR formulates the function approximation itself as a linear function, where the data is mapped into kernel space for a nonlinear function to achieve lower errors.

A fully connected layer is a way to arrange neurons in an ANN where all neurons of a layer are connected to all neurons of the next layer (with individual weights). A sufficiently large network (having multiple fully connected layers in sequence) is commonly referred to as a deep neural network (DNN). Although this term nowadays often refers to networks with a wide variety of layers (as long as they are numerous), we stick to the original sense of multiple fully connected layers for this work.

Convolutional Neural Networks (CNNs) comprise three types of layers: convolutional Layers, pooling Layers, and fully connected layers. Parameters of the convolutional layer focus on the use of filter operations. A discrete convolution calculates the activation of the neurons, instead of matrix multiplication as in other ANNs. A pooling layer gradually reduces the dimensionality of the representation, thus reducing the number of parameters and computational complexity of the model.

ANNs have limitations in solving sequential data problems, such as time series. Long Short-Term Memory (LSTM) is a recurrent network using a chain-like structure of repeating cells. These cells store important information from previous training steps, enabling the learning of long-term dependencies, and use a feedback loop to accept a sequence of inputs.

Recursive Least Squares (RLS) is an extension of the Least Squares method, with a recursive algorithm to design an adaptive filter where the parameters are updated iteratively, enabling this method to optimize a linear function in an online learning setting.

The straightforward approach to transferring the training process of a fully connected network to an online learning environment is to apply the backpropagation algorithm to a single instance rather than batches or mini-batches of data. We refer to this as Online Deep Learning (ODL).

Experience Replay (ER) is a technique designed to resolve the problem of catastrophic forgetting in ANNs, where subsequent updates of the model lead to a forgetting of previously learned information. This problem is especially big when using very small online updates rather than shuffled mini-batches and can lead to the loss of seasonal information. In this paper, we employ an ER-like technique to a DNN (ODL-ER), where we add new training data to a fixed length FIFO buffer from which we randomly sample data points and merge them with the newest data points into a mini-batch to perform model updates using backpropagation.

ODL, as described above, has some critical limitations. The main challenge is to choose the network’s ideal architecture (complexity) in advance of the training. If the model is too complex, the learning process converges too slow, breaking an essential requirement property of online learning. However, if the model is too simple, complex patterns cannot be learned. In traditional model selection, this problem would be solved using validation data, which is unavailable in an online environment. Sahoo et al. [66] present a framework that attempts to solve these challenges by developing an ANN that is adaptive in complexity. The framework was initially developed for classification problems but is applied to the continuous regression problem of heat load forecasting in this work.

The existing ANN architecture is adapted by connecting each hidden layer to an output layer. Instead of the standard backpropagation, Hedge Backpropagation (HBP) is used, which evaluates the performance of the output layers in each online round and extends the backpropagation to train the ANN online. The outputs of the different depths are optimally utilized by the hedge algorithm [70]. This allows training an ANN with adaptive capacities to simultaneously share knowledge between shallow and deep networks. The architecture of multiple depths makes the learning process robust to vanishing gradients and decreasing feature reuse.

The basic design of experiments is the same for all methods examined and outlined below. However, the evaluation of prediction quality distinguishes between time series models, offline ML methods, and online ML methods. On the one hand, from an algorithmic perspective, the heat demand is modeled according to the different approaches of taking data between the models. More importantly, the application options differ between the three approaches. Time series models do not require additional features beyond the raw consumption, whereas offline and online ML methods use additional features (as outlined in Sect. 5). If such data is available both approaches are theoretically viable. However, offline models would be employed in settings with low concept or sensor drifts for which plenty of historical data is available, whereas online models would be used when strong drifts occur or data has not (yet) been gathered sufficiently.

An overview of the main software libraries used can be found in the supplementary information’s Sect. 3.

In this section, we present the results of the experiments for the different methods, grouped by the three families of algorithms, producing different scenarios of a deployed prediction system (cf. Sect. 7).

In preliminary investigations, we could show that the quality of 24-h and 48-h forecasts hardly differ. Therefore, the 24-h forecast, which is the—at the moment—typical application in a real-world scenario, is presented here in more detail. A detailed comparison of the metrics for a 24-h and 48-h prediction for the offline and online ML models can be found in the supplementary information’s Sect. 5. In the future, the 48-h forecast might become more important. Therefore, we want to stress that the following findings do transfer.

For all models examined, the RMSE value is lower in the summer months than in the winter months, as can be seen in Tables 1, 3, and 6. This is in no way surprising, as heat consumption is lower in the summer months than in winter (cf. Fig. 1, as there is no need for space heating. However, the relative deviation of the forecast from the actual consumption is higher in summer.

The time series models, the LSTM, and the SGD have the highest RMSE values among all the examined models and do not seem to be competitively performing options (even within their respective scenarios) (Table 2).

This section discusses the experimental results and the advantages and disadvantages of the methods for the specific real-world use case.

In our use case, as well as many similar ones, the most commonly used controller is the single-board computer PhyBOARD-Regor from Phytec Messtechnik GmbH.⁴ Here, a phyCORE-AM335x is used as the processor and 512 MB NAND Flash and 512 MB DDR RAM are integrated as memory modules. The controllers have limited computational and memory power, which is a critical limitation for the direct use of the models in embedded systems. Keep in mind that besides doing statistical inference using the trained models (and maybe even model training), these controllers also need to do their original task allocating substantial shares of their available resources.

A critical constraint is the prediction of peak demand. Accurate forecasting of peaks is essential for safe and reliable scheduling of heat supply at peak times to ensure the thermal needs of residents are met.

For all methods and models, the deviation of the prediction for the summer months is higher than the deviation in the winter months. This is particularly well shown by the MASE values of the offline ML methods for the summer and winter months. MASE values are higher in the summer months with an average of 0.67 than in the winter months with 0.53.

The prediction errors are lower in the summer months than in the winter months, but if the low consumption in the summer months is taken into account, the prediction is inaccurate. This is because the heat demand in the summer months consists mainly of hot water demand and the drawing patterns vary considerably. Due to the low number of apartments and residents, water consumption deviating from the norm strongly influences the summer months’ heat demand. The domestic hot water demand is difficult to predict because single deviations strongly influence existing patterns. While hot water shows inconsistent trends all year, summer vacations additionally disrupt general everyday patterns for occupants. A high variation of the prediction for the summer months cannot be avoided in this use case. The additional space heating demand—related to the outside temperature—in the winter months compensates for those irregularities.

In addition to the main experiment, we investigated how well the offline and online ML methods can predict anomalies in consumption. An anomaly is a data point significantly different from the other observations. Predicting anomalous data, such as sudden cold snaps, is essential for a critical task such as predicting heating demand, as an adequate heat supply to the occupants must be guaranteed and not interrupted due to an incorrect model prediction. This could, in turn, also lead to legal consequences for the heating system operator. A model cannot make reliable predictions if it cannot deal with anomalous consumption. One possible scenario would be for a model to fail to respond to a cold snap. The heat consumption increases dramatically, and the model predicts too low heat consumption so that the heat supply to the residents can no longer be guaranteed.

The paper investigated simple time series analysis methods and offline and online machine learning (ML) methods for predicting the heat demand of residential units in a specific scenario for which hardware specifications and also first data were available. The possibility of application in this real-world use case influenced the selection of methods. The new quarter we selected as a case study is comparatively small with only 66 units connected to the centralized heating system, and data has been available for 1.75 years. The results of this study will soon be used in the field in the form of a cloud application with distributed edge devices to enable remote training.

We found that, for this use case, a comparably high deviation of forecast and consumption in the summer months, where heat demand is fully based on hot water usage, is unavoidable with the available features due to erratic usage patterns among the limited number of occupants. The methods cannot model domestic hot water demand well and are therefore not perfectly suited for summer. Although, we want to stress that they do outperform a naive model. If the number of residents was higher, individual deviations in consumption patterns would not affect the hot water demand as much, making the methods more suitable. However, the additional space heating demand in the winter months is predictable as it is dependent on features such as daytime and outside weather. Interestingly, models trained and evaluated only on one seasonal subset do not outperform models trained on all data but evaluated on the same subset.

Additionally, we investigated whether there is a significant difference between a 24 and a 48 h forecasting window, finding that all methods performed comparably on the longer forecasting window.

In general, we investigated three families of methods:

Time Series models (Holt-Winter Smoothing and Seasonal ARIMA) were unable to convincingly perform on the data available and did not even beat a naive model, which takes as a prediction the heat consumption of 24 h ago.

Offline ML models performed the best out of the three. Interestingly, the more complex deep learning methods were outperformed by much simpler kernel-based (kernel ridge regression (KRR) and support vector regression) and ensemble-based (random forest regression) approaches. This might be due to the limited data availability or simply because underlying patterns between available features and heat demand are not so complex that they would warrant those methods. Given the remaining prediction errors, we can, however, suspect that the features that were gathered over the selected time period are not sufficient to describe all usage. Based on civil engineering knowledge, we are unaware of specific features that might have improved this other than more weather data and better forecasting thereof.

The kernel-based approaches are not only easier to implement but also to understand for engineers. An easier implementation allows engineers without a strong computer science background to debug and maintain the code base while still getting useful forecasts in return. Moreover, such an interpretable/comprehensible approach allows us to improve the energy management systems (its overall installation) rather than only the prediction system and, overall, gain a better understanding of the relationships between feature characteristics and heat demand needs. The great disadvantage of offline ML models is that they need large amounts of data before they can be first deployed and can, therefore, not go online with the energy management system itself. They are also vulnerable to concept and sensor drifts as they do not prioritize newer information over old data.

Theoretically, this is where online ML models should shine. However, in our data, drifts (besides the obvious seasonalities) seem to not have occurred yet. In general, the online methods did not perform competitively to their offline counterparts in terms of prediction errors and the critical peak demand forecasting. In a more detailed analysis, we found that all of the methods do lack behind in their forecast, while some overcompensate heavily. The best performing methods were the simple recursive least squares (RLS) algorithm and a deep learning approach where we used an experience replay–like buffer to sample mini-batches from for training whenever a new data point became available to the model.

In addition, it should be noted that the data was gathered during the COVID-19 pandemic period. To contain the pandemic, various measures were enacted in Germany, causing people to spend more time at home (e.g., increased work from home, lockdowns, or closed restaurants, bars, and clubs). These non-static restrictions had obvious impacts on the consumption patterns. Therefore, future examinations into how consumption patterns have changed after the enactment of restrictions and whether the models can cope with such strong concept drifts can be important. Likewise, it should be critically investigated to what extent our data can be useful in a post-pandemic world.

Another extreme situation, but not yet represented in the data, is the Russian invasion of Ukraine, which started on 24. February, 2022. Undoubtedly, this will strongly impact usage patterns (and energy supply) in Germany, with many users likely keeping the heating below previous thermal comfort levels to save energy as well as money. Again, the resulting consumption patterns and models need to be re-examined.

Besides the already investigated methods, a wide variety of other approaches is available with many having been explored in other settings in the existing literature. For this specific case study, the effect of other environmental parameters, such as wind speed, cloud cover, or humidity, on the heat demand should be evaluated. A re-examination of time series analysis techniques could be considered when data representing long-term seasonal patterns becomes available in a few years.

Also, the forecast accuracy of the models for a 48 and 72-h period should be analyzed again in more detail. However, our initial findings are that the forecasting horizon does not play a major role. For a safe application in the real world, a 24-h forecast might be too short-term as power plants might exhibit substantially longer lead times. Even if it is just about energy storage needs, e.g., in pumped-storage hydroelectricity plants rather than hydrogen gas or nuclear power plants.

Models that operate according to the divide-and-conquer principle in offline ML can be further investigated. The problem space can be divided into smaller spaces for which individual models, called experts, are trained. Another model or function can be used as a transition. This requires a more detailed data analysis to partition the problem space appropriately. One approach is Mixture of Experts (MoE), which divides the problem space between a few experts monitored by a gating network. Typically, these experts are individual smaller neural networks. This could allow for the more obvious expert models for summer, winter, and transition periods but also for models that are good at forecasting in certain weather settings or after certain usage patterns.

Additional methods can also be evaluated for online ML, e.g., XCSF [74], a highly interpretable rule set learning algorithm, or Online Random Forests [75], an incremental version of the Extreme Random Forest. Another promising approach is an online error correction presented in [76]. ANNs are used for prediction, which is combined with error correction methods.

The immediate next step will be to test selected methods in online applications, for example, starting with RLS, which is then later replaced by KRR. With these models, no data science experts are required for commissioning and maintenance.

Overall, we conclude that in this and similar settings online ML methods should only be used in the beginning and soon be replaced by offline ML approaches. However, engineers should keep the models in semi-regular observation in case of drifts (or directly deploy mechanisms to detect those). In a cloud-based training scenario, the algorithmic complexity is less important, as long as the models can run on the non-allocated hardware. Whether explainability is important needs to be determined on a case-by-case basis, but explainable methods are available and competitive.

The supplementary information for this paper is available at https://​github.​com/​NeeleKemper/​residential-unit-heat-forecast/​tree/​main/​supplementary_​information.