In the literature, it is well known that there is a bidirectional causality between economic growth and energy consumption. This is why it is crucial to forecast energy consumption. In this study, four deep learning models, i.e., Long Short-Term Memory (LSTM), stacked LSTM, bidirectional LSTM, and Gated Recurrent Unit (GRU), were used to forecast energy consumption in Brazil, Canada, and France. After a training test period, the performance evaluation criterion, i.e., R2, mean square error, root mean square error, mean absolute error, and mean absolute percentage error, was performed for the performance measure. It showed that GRU is the best model for Canada and France, while LSTM is the best model for Brazil. Therefore, the energy consumption prediction was made for the 12 months of the year 2017 using LSTM for Brazil and GRU for Canada and France. Based on the selected model, it was projected that the energy consumption in Brazil was 38 597.14–38 092.88, 63 900–4 800 000 GWh in Canada, and 50 999.72–32 747.01 GWh in France in 2017. The projected consumption in Canada was very high due to the country’s higher industrialization. The results obtained in this study confirmed that the nature of energy production will impact the complexity of the deep learning model.

Energy is the backbone of any country’s economic development, and there are various sources through which it can be generated. Some of the sources through which energy can be generated include liquid fuels, coal, natural gas, nuclear, and renewables.1 Akorede et al.2 reported in their study that global energy demand would increase by 44% from 2006 to 2030, of which 80% of the total energy generation in 2030 would be from fossil fuels. This source of energy generation not only causes pollution but also raises questions about its affordability and is non-renewable in nature. This has led countries to increase their dependency on renewable energy sources. The prices of fossil fuels, hydrocarbon production to the consumption ratio, and countries’ technological status are a few of the factors that have a significant impact on renewable energy consumption by a country.3 Technological advancement has made renewable energy equally efficient as non-renewable energy, thereby making renewable energy sources able to completely replace non-renewable sources of energy.4 Energy is a must for the economic development of a country. However, the package comes with a disastrous effect on the environment if fossil fuels are considered a source of energy.5 A bi-directional relationship exists between energy consumption by a country and its economic growth.6 As energy plays an essential role in a country’s as well as mankind’s development, henceforth, it is necessary to forecast energy consumption by nations so that they can keep up with the pace at which it is utilized.

Many researchers have attempted to predict energy consumption in various nations. A study reported a significant growth in energy demand to be expected in Haiti, Jamaica, Trinidad, and Tobago until at least 2010 by using a Bayesian Vector Autoregression (BVAR) forecasting model.7 Zahan and Kenett8 developed a prediction model using the time series forecasting system of the Statistical Analysis Software (SAS) statistical software for forecasting energy consumption in the manufacturing industry in South Asian countries. Barak and Sadegh9 forecasted the energy consumption in Iran using the Autoregressive Integrated Moving Average (ARIMA) model, the Adaptive Neuro-Fuzzy Inference System (ANFIS) model, and the AdaBoost (Adaptive Boosting) data diversification model. In the case of Turkey, ARIMA (1, 1, 1) for coal consumption, ARIMA (0, 1, 0) for oil consumption, ARIMA (0, 0, 0) for natural gas consumption, ARIMA (1, 1, 0) for renewable energy consumption, and ARIMA (0, 1, 2) for total energy consumption were found to be the best-suited models for forecasting energy consumption for the next 25 years with data from 1970–2015.10 Zhao and Lifeng11 predicted non-renewable energy consumption in the Asia-Pacific Economic Cooperation by using an adjacent accumulation discrete gray model. Liu and Wu12 applied an adjacent non-homogeneous gray model to predict renewable energy consumption in four central European countries, namely Austria, the Czech Republic, Hungary, and Poland. Raheem et al.13 employed an adjacent accumulation discrete gray model to forecast the non-renewable energy consumption in G20 countries from 2022 to 2026 based on consumption data from 2011 to 2021. Oh et al.16 studied optimal model estimation for hourly fine power consumption prediction using a deep learning model.

In the milieu, the current study focuses on predicting energy consumption in three of the top ten energy-consuming countries in the world, namely Brazil, Canada, and France. This work used various neural network models, i.e., Long Short-Term Memory (LSTM), stacked LSTM, bidirectional LSTM, and gated recurrent unit, for each country under study.

Monthly data on the combined amount of power consumed (GWh) in Brazil, Canada, and France between 2006 and 2017 are considered for our empirical investigation. These data were collected from the International Energy Agency (IEA) Monthly Electricity Statistics report (Monthly Electricity Statistics, 0000).

To understand LSTM, we must first understand recurrent neural networks (RNNs). The connections between devices in recurrent neural networks (RNNs), a type of artificial neural network, form a directed graph along a series.

A recurrent neural network (RNN) is a type of artificial neural network that contains circular connections between its nodes. As a result, the network can exhibit time-varying dynamic behavior. RNNs, unlike feed forward neural networks, can handle any given input sequence using their input memory. Iterative neural networks are strongly dependent on sequential data to function. Regarding machine learning, recurrent neural networks excel in several applications, including speech recognition, natural language processing, and signal processing. When the output of the neuron at time t − 1 is mixed with the subsequent input to feed the neuron at time t, RNNs explicitly manage temporal data dependencies more than convolutional neural networks. Figure 1 shows a schematic representation of a typical neural RNN. Most individuals are familiar with the RNN models of Gated Recurrent Unit (GRU) and Long-Short Term Memory (LSTM). The main difference between the two is the complexity of their learning curves. When the hidden state is the same size as the GRU unit, the LSTM model contains more parameters. We attempt to provide and explore the equations that describe the internal behavior of the LSTM. The symbols for the sigmoid and the hyperbolic tangent functions are σ and tanh, whereas the character * denotes element-wise multiplication.

FIG. 1.

Framework recurrent neural network.

FIG. 1.

Framework recurrent neural network.

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A set of variables (x1, x2, …, xt) are input to an RNN unit, where each element (xt) is a vector and t is the appropriate timestamp.

Long-term memory was developed by Hochreiter and Schmidhuber14 as a special type of RNN approach for modeling sequential data. Generally, in the RNN approach, each piece of information in the input data is examined iteratively, considering the value of the previous output. Although it is claimed that this architecture performs learning that considers the information from previous time periods, it has been stated that this is not possible due to the gradient disappearance/explosion problem. To overcome this problem, the LSTM architecture, which can remember long-term information, has been developed. It is currently used frequently and performs admirably on a few issues.

A formal description of the LSTM problem can be presented by the below equations [Eqs. (1)(6)]:
ft=σ(Wfxxt+Wfhht1+bf),
(1)
it=σ(Wixxt+Wihht1+bi),
(2)
yt=tanh(Wyxxt+Wyhht1+by),
(3)
ct=ityt+ftct1,
(4)
ot=σ(Woxxt+Wohht1+bo),
(5)
ht=ottanh(ct).
(6)
The ct memory and the ht hidden state are the two cell states that make up the LSTM set. Three different gates intervene in the control of the flow of information: the input (it), the forget (ft), and the output (ot). Each of the three gateways combines the current value (xt) with the secret value (ht−1) of the previous timestamp (Fig. 2). The gates also have two crucial purposes: (i) controlling how much information is forgotten or remembered during the process, and (ii) resolving the problem of gradient disappearance or bursting. The gates are clearly implemented using a sigmoid. The values returned by this method are between 0 and 1. The current input is resized thanks to the transient cell state used by the LSTM module. This current cell is used to apply a hyperbolic tangent function with values between −1 and 1. Each function is expressed as the tangent of a sigmoid or hyperbolic curve. It sets the amount of information to keep (ityt), while ft indicates how much memory should be kept in the current step (ftct−1). An RNN takes a series of any time series variables (say, x1, x2, …, xn) as input that represents a generic element for a feature vector xt and t is a timestamp. Last but not least, it affects the newly concealed state, which in turn controls how much data from the present memory are sent to the output. Parameters in model building include the various matrices, W, and bias coefficients, b. Next, we pass on the memory ct and the hidden state ht, respectively.15 The total analysis was carried out on the Python (Jupyter) platform with the TensorFlow (https://www.tensorflow.org) and Keras (https://keras.io) packages. Total methodologies for data processing are indicated in Fig. 3.
FIG. 2.

Framework of LSTM.

FIG. 2.

Framework of LSTM.

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FIG. 3.

Abstract of the research.

FIG. 3.

Abstract of the research.

Close modal

The primary goal of the current study is to predict energy consumption (GWh) in Brazil, Canada, and France. This analysis is based on monthly data on energy consumption gathered from three countries that are considered to be energy consuming. In the present study, secondary data on energy consumed (GWh) in three countries—Brazil, Canada, and France—was considered for the period of 1 June 2006 to 1 December 2016. To better comprehend our dataset and to summarize and identify the essential features, an exploratory data analysis was conducted as described in Table I.

TABLE I.

Descriptive statistics for energy consumed in GWh.

StandardStandardConfidence
CountryMeanerrorMediandeviationKurtosisSkewnessMinimumMaximumRangelevel (95.0%)
Brazil 35 626.00 289.70 36 344.5 3251.88 −1.22 −0.26 29 114 41 653 12 539 573.35 
Canada 47 676.70 521.83 46 102.5 5857.55 1.72 −0.14 21 954 59 563 37 609 1032.77 
France 40 562.94 656.45 38 642 7368.60 −0.75 0.43 21 954 58 898 36 944 1299.19 
StandardStandardConfidence
CountryMeanerrorMediandeviationKurtosisSkewnessMinimumMaximumRangelevel (95.0%)
Brazil 35 626.00 289.70 36 344.5 3251.88 −1.22 −0.26 29 114 41 653 12 539 573.35 
Canada 47 676.70 521.83 46 102.5 5857.55 1.72 −0.14 21 954 59 563 37 609 1032.77 
France 40 562.94 656.45 38 642 7368.60 −0.75 0.43 21 954 58 898 36 944 1299.19 

It is clear from Table I that the mean and median of energy consumption for each country are quite close to each other, and skewness nearly equals zero, reflecting that datasets are almost normally distributed. Additionally, we can see the kurtosis of energy consumption in Canada and Brazil is more than 1 (leptokurtic), and in France, it is less than 1 (platykurtic). Skewness involves the third moment, while kurtosis involves the fourth moment of data distribution. The outliers in a sample, consequently, have even more effect on the kurtosis than on the skewness. Therefore, the energy consumption of Brazil, Canada, and France is supposed to possess outlier values, which is also clear from the maximum and minimum values of the dataset, where the difference between minimum and maximum is quite large. Additionally, the standard deviation of energy consumption for all three countries is relatively high. They show how significantly varied the electricity consumption patterns of each country are from one another. Keeping these points on note, we have tried different deep learning models, i.e., LSTM, stacked LSTM, Bidirectional LSTM (BiLSTM), and GRU, where independent variables are their own time series lag values. Due to data-driven concepts, these gated architectures operate without making any assumptions about the distribution of the underlying dataset.

The whole dataset of energy consumption for each country is divided into a training as well as a testing section, where 100 data points were kept in the training dataset from January 2007 to April 2015, while the rest 20 were used to test the model performance from May 2015 to December 2016 (Table II).

TABLE II.

Details of the train_test split.

CountryYearMonthTotal data pointsTraining data pointsTesting data points
Brazil 2007–2016 12 120 100 20 
Canada 2007–2016 12 120 100 20 
France 2007–2016 12 120 100 20 
Forecasting period January 2017 to December 2017 
CountryYearMonthTotal data pointsTraining data pointsTesting data points
Brazil 2007–2016 12 120 100 20 
Canada 2007–2016 12 120 100 20 
France 2007–2016 12 120 100 20 
Forecasting period January 2017 to December 2017 

The predicting abilities of various neural network architectures for time series forecasting of energy consumption, i.e., LSTM, stacked LSTM, bidirectional LSTM, and GRU, were compared for each country. Those models were initially trained from January 2007 to April 2015, and then these architectures were further used to access their performance on unseen test datasets, i.e., from May 2015 to December 2016. The model architectures of LSTM, stacked LSTM, bidirectional LSTM, and GRU for each country were carefully chosen based on their performance on the testing dataset.

Performance evaluation metrics R2, mean square error (MSE), root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) values have been calculated based on the testing data for deep learning architectures, i.e., LSTM, stacked LSTM, BiLSTM, and GRU, as summarized in Table III. It can be seen that LSTM, having one hidden layer, performed better in terms of MSE, RMSE, and MAE than other neural network architectures for predicting the energy consumption of Brazil. This might be due to two reasons: first, fewer data points in the training dataset, and second, more computational parameters involving the mentioned stacked LSTM and BiLSTM as compared to simple LSTM.15,17 Additionally, GRU, which is the simplest architecture among all, surpassed other models for predicting the energy consumption of Canada and France, and this again indicates that a model with minimum computational parameters is more suitable for a dataset with fewer data points.

TABLE III.

Evaluation of four deep learning architectures on testing data on energy consumption (GWh).

CountriesEvaluationLSTMStacked LSTMBiLSTMGRU
Brazil R2 0.54 0.00 0.33 0.51 
MSE 531 302.34 1 830 767.86 778 498.13 572 117.09 
RMSE 728.90 1 353.06 882.33 756.38 
MAE 610.01 1 065.04 734.83 636.90 
MAPE 0.02 0.03 0.02 0.02 
Canada R2 0.84 0.81 0.84 0.86 
MSE 4 720 242.95 5 802 229.97 4 929 389.97 4 328 169.01 
RMSE 2 172.61 2 408.78 2 220.22 2 080.43 
MAE 1 860.90 1 980.36 1 888.61 1 688.29 
MAPE 0.04 0.04 0.04 0.04 
France R2 0.80 0.80 0.83 0.84 
MSE 8 721 191.89 8 801 927.35 7 372 900.23 7 181 056.85 
RMSE 2 953.17 2 966.80 2 715.31 2 679.75 
MAE 2 296.80 2 103.13 2 335.67 2 187.29 
MAPE 0.06 0.05 0.06 0.05 
CountriesEvaluationLSTMStacked LSTMBiLSTMGRU
Brazil R2 0.54 0.00 0.33 0.51 
MSE 531 302.34 1 830 767.86 778 498.13 572 117.09 
RMSE 728.90 1 353.06 882.33 756.38 
MAE 610.01 1 065.04 734.83 636.90 
MAPE 0.02 0.03 0.02 0.02 
Canada R2 0.84 0.81 0.84 0.86 
MSE 4 720 242.95 5 802 229.97 4 929 389.97 4 328 169.01 
RMSE 2 172.61 2 408.78 2 220.22 2 080.43 
MAE 1 860.90 1 980.36 1 888.61 1 688.29 
MAPE 0.04 0.04 0.04 0.04 
France R2 0.80 0.80 0.83 0.84 
MSE 8 721 191.89 8 801 927.35 7 372 900.23 7 181 056.85 
RMSE 2 953.17 2 966.80 2 715.31 2 679.75 
MAE 2 296.80 2 103.13 2 335.67 2 187.29 
MAPE 0.06 0.05 0.06 0.05 

Figure 4 reflects that LSTM fits quite well with the training dataset (January 2007 to April 2015) and also shows promising predictions over the testing dataset (May 2015 to December 2016) of energy consumption in Brazil. The architecture has only 2% of mean absolute percentage error (MAPE), as mentioned in Table III, confirming that the model accounts for most of the variability present in the dataset. Additionally, it illustrates that deep learning models can be effective even when the dataset is small.

FIG. 4.

LSTM model fitting on energy consumed (GWh) in Brazil.

FIG. 4.

LSTM model fitting on energy consumed (GWh) in Brazil.

Close modal

The result reflected in Table III confirmed the superiority of GRU over LSTM, stacked LSTM, and BiLSTM. Figure 5 reveals that GRU fit offers a better prediction of energy consumption in Canada in contrast to the other evaluated deep learning architectures having the lowest RMSE of 2080.43% and 4% of MAPE. On the other side, LSTM, stacked LSTM, and BiLSTM deliver comparatively poor prediction accuracy in terms of MSE, RMSE, and MAE. This could be attributed to the absence of sufficient training data required to fully understand the dynamics of energy consumption patterns and computational necessity.

FIG. 5.

GRU model fitting on energy consumed (GWh) in Canada.

FIG. 5.

GRU model fitting on energy consumed (GWh) in Canada.

Close modal

The graph in Fig. 6 demonstrates the superiority of GRU performance in training as well as testing (unseen) datasets by offering strong forecasting capabilities with the least RMSE, MSE, and MAE as described in Table III. The GRU architecture once again outperforms all other deep learning models and generates promising predictions for energy consumption in France. This might be attributed to its capacity to capture time-variant features and meaningful patterns of historical data. Additionally, the remaining architectures fit poorly to the dataset compared to GRU due to the inclusion of more parameters, which require larger data to get a good prediction, while GRU is able to handle the small dataset.

FIG. 6.

GRU model fitting on energy consumed (GWh) in France.

FIG. 6.

GRU model fitting on energy consumed (GWh) in France.

Close modal

After finalizing the model based on their performance on the testing dataset, a forecast of energy consumption in GWh using the best suitable deep learning architecture was generated for the next 12 months of 2017 for Brazil, Canada, and France, as described in Table IV.

TABLE IV.

Forecasting energy consumption in GWh using the best deep learning model.

DateBrazil (LSTM)Canada (GRU)France (GRU)
2017-01-01 38 597.14 63 900 50 999.72 
2017-02-01 38 456.06 61 100 44 717.36 
2017-03-01 38 343.23 74 200 39 973.73 
2017-04-01 38 262.05 78 600 32 500.41 
2017-05-01 38 205.84 113 000 34 532.92 
2017-06-01 38 167.41 149 000 35 606.35 
2017-07-01 38 141.21 254 000 35 246.46 
2017-08-01 38 123.31 405 000 33 933.85 
2017-09-01 38 111.05 770 000 33 335.27 
2017-10-01 38 102.64 1 360 000 32 974.75 
2017-11-01 38 096.86 2 620 000 32 807.17 
2017-12-01 38 092.88 4 800 000 32 747.01 
DateBrazil (LSTM)Canada (GRU)France (GRU)
2017-01-01 38 597.14 63 900 50 999.72 
2017-02-01 38 456.06 61 100 44 717.36 
2017-03-01 38 343.23 74 200 39 973.73 
2017-04-01 38 262.05 78 600 32 500.41 
2017-05-01 38 205.84 113 000 34 532.92 
2017-06-01 38 167.41 149 000 35 606.35 
2017-07-01 38 141.21 254 000 35 246.46 
2017-08-01 38 123.31 405 000 33 933.85 
2017-09-01 38 111.05 770 000 33 335.27 
2017-10-01 38 102.64 1 360 000 32 974.75 
2017-11-01 38 096.86 2 620 000 32 807.17 
2017-12-01 38 092.88 4 800 000 32 747.01 

With the growth of the world population, energy production has become a primary issue. The aim of this paper was to forecast energy consumption in Brazil, Canada, and France using a deep learning framework. To carry out this study, monthly energy consumption data are used from January 2006 to December 2016 for each country.

First, the predicting abilities of LSTM, stacked LSTM, bidirectional LSTM, and GRU were assessed during a training test period for each country. The performance indices indicated that GRU is the best model for forecasting energy consumption in Canada and France, while LSTM is the best model for Brazil. This difference can be explained by the fact that, unlike Canada and France, electricity production in Brazil is strongly based on renewable energies, i.e., greater heterogeneity in production sources. Moreover, these energies are often reputed to have a strong intermittent character in their production. Therefore, a more complex model (LSTM) will be required to represent this type of energy.

The study’s main discovery, which came about as a result of the models’ validation, suggested that deep learning models might replace statistical models in the prediction of energy use. While the GRU model was appropriate for the Canada and France series, the LSTM model was shown to be suitable for predicting energy consumption in the Brazil dataset. The study’s results show great promise and represent a first step toward forecasting energy consumption in the context of the energy transition from fossil fuels to renewable sources. It will be necessary to analyze data from various nations in order to examine how the heterogeneities of renewable energies affect the deep learning models’ complexity and bolster the validity of these models. In addition, it would be interesting to document the findings with hybrid deep learning techniques like ARIMA-LSTM18 and hybrid XGBoost models19 that are used to get precise error accuracy for energy consumption series.

Princess Nourah Bint Abdulrahman University Researchers Supporting Project No. PNURSP2024R120, Princess Nourah Bint Abdulrahman University, Riyadh, Saudi Arabia.

The authors have no conflicts to disclose.

Shikha Yadav: Conceptualization (equal); Investigation (equal); Resources (equal); Supervision (equal); Writing – original draft (equal). Nadjem Bailek: Data curation (equal); Formal analysis (equal); Investigation (equal). Prity Kumari: Visualization (equal); Writing – review & editing (equal). Alina Cristina Nuţă: Conceptualization (equal); Data curation (equal); Supervision (equal). Aynur Yonar: Data curation (equal); Formal analysis (equal). Thomas Plocoste: Conceptualization (equal); Supervision (equal). Soumik Ray: Methodology (equal); Supervision (equal); Writing – original draft (equal); Writing – review & editing (equal). Binita Kumari: Validation (equal); Writing – review & editing (equal). Mostafa Abotaleb: Resources (equal); Validation (equal). Amal H. Alharbi: Resources (equal); Visualization (equal). Doaa Sami Khafaga: Supervision (equal); Visualization (equal). El-Sayed M. El-Kenawy: Formal analysis (equal); Visualization (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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