In the first step of the selection process, a title-based screening was applied to the studies, where they were assessed based on their titles. Shortlisted research articles explicitly referred to techniques related to energy load forecasting, electricity demand prediction, time series modeling, ML, and DL. Also, studies with vague, overly general, or unrelated titles were immediately excluded to retain only relevant literature focused on forecasting within energy systems.

After the title screening, the abstracts of the shortlisted papers were carefully reviewed to determine their relevance. If the study focused on ML or DL techniques specifically applied to energy load forecasting, then the study was included. It also prioritized papers discussing applications in smart grids, utility demand prediction, renewable energy integration, and real-time load management. Suitable for further review were abstracts that provided technical insights into model architectures, datasets used, and performance evaluation metrics. At this phase, studies that lacked technical depth, focused on unrelated domains, or did not employ data-driven forecasting methods were excluded.

Full-text review of the remaining studies completed the last stage of the selection process. This was an important step to ensure that the selected papers clearly described their methodology, experimental setup, and analytical results. Articles were included if they provided quantitative performance evaluation in the form of metrics such as root mean squared error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), R-squared (R²), or computational efficiency. Additionally, prioritized were studies that discussed challenges, limitations, and future research directions in the context of energy load forecasting. To improve the credibility and reliability of the reviewed literature, only articles published in high-impact journals or peer-reviewed conferences were considered. To ensure that only high-quality, methodologically sound, and impactful studies were included, papers with complete methodologies but lacking experimental validation, or those using outdated forecasting techniques, were excluded.

One of the simplest models for energy load forecasting is linear regression with the assumption that a relationship with input variables (e.g., past energy consumption, temperature) and output variable (future energy demand) is linear (Figure 4). For example, Sarker et al.¹⁷ utilized linear regression combined with inverse matrix analysis to forecast energy demand in remote areas of Bangladesh, demonstrating its efficacy in regions with limited data availability. On the other hand, Mahmud¹⁸ employed linear regression analysis to predict electricity loads in isolated areas lacking historical data, underscoring the model’s practicality in diverse settings. The model is represented as:

where Y is the predicted energy load, Xi are input features, βi are coefficients, and ε represents error terms. While LR is computationally efficient, its main limitation is its inability to model complex, nonlinear relationships in energy demand.

As DTs partition the dataset based on feature importances, DTs become suitable for capturing nonlinear dependencies in energy load data (Figure 5). DTs are good with categorical as well as numeric features, but are prone to overfitting, more so for deep tree structure. Likewise, Hambali et al.¹⁹ evaluated various DT algorithms for electric power load forecasting and found that the REPTree technique outperformed others, highlighting its effectiveness in handling nonlinear relationships in load data. Likewise, Jahan et al.²⁰ designed a DT model using weather and power load data as inputs for short-term demand forecasting, demonstrating the model’s capability to capture complex dependencies in energy consumption patterns.

SVMs are effective for short-term load forecasting as they find an optimal hyperplane for classification or regression (Figure 6). Furthermore, Tian and Noore²¹ proposed an SVM-based approach for short-term load forecasting, demonstrating improved generalization and lower prediction error compared to neural network methods. On the other side, Li and Fang²² applied SVMs to power system load forecasting, effectively enhancing forecasting accuracy. The model is based on:

subject to constraints ensuring that predictions fall within an acceptable error margin. However, SVMs can be computationally expensive for large datasets.

RF is an ensemble of DTs that serves the purposes of improving forecasting accuracy and reducing overfitting (Figure 7). It merges the outputs from multiple trees, effectively improving robustness, and is a good candidate for energy load forecasting in dynamic ecosystems. Some researchers work on it like Dudek,²³ who applied RF to short-term electricity load forecasting, demonstrating its ability to handle nonstationary and seasonal time series data effectively. Meanwhile, Gao et al.²⁴ proposed an improved RF regression algorithm for ultra-short-term electricity load forecasting, achieving higher accuracy compared to traditional methods (Table 4).

ANNs consist of multiple layers of neurons that learn energy consumption patterns from historical data (Figure 8). Numerous researchers work on this model, including, Oreshkin et al.²⁵ who introduced the N-BEATS neural network architecture, which demonstrated superior performance in mid-term electricity load forecasting across various European datasets. Similarly, Gao et al.²⁶ proposed an ensemble deep random vector functional link (edRVFL) network, which achieved high accuracy in short-term load forecasting tasks by leveraging deep representation learning and ensemble strategies. The weight updates are as follows:

where w_ij are weights, η is the learning rate, and E is the error function. ANNs perform well for medium- to long-term load forecasting but require large datasets and high computational power.

Energy load data are captured with temporal dependencies by LSTM networks, a type of recurrent neural network (RNN). However, due to vanishing gradients in traditional RNNs, they overcome vanishing gradients through memory cells that store information for long periods (Figure 9). However, the DA-LSTM framework introduced by Bayram et al.²⁷ is a dynamic drift-adaptive learning model designed for interval load forecasting. This approach enhances forecasting accuracy by adapting to changes in consumption patterns without requiring predefined drift thresholds. Meanwhile, a hybrid LSTM model was developed by Lu et al.²⁸ incorporating online correction mechanisms. Their model integrates temporal and nontemporal features and employs an online correction strategy to adjust to real-time data distribution shifts, thereby improving day-ahead load forecasting accuracy. The cell state update is given by:

where C_t is the cell state, C_t is the forget gate, and i_t is the input gate. LSTMs are highly effective for energy load forecasting due to their ability to recognize seasonality and trends.

The main difference between GRUs and LSTMs is that the former has a simpler architecture and therefore computational complexity (Figure 10). The short-term dependency between the periods is balanced with the long-term dependency and therefore, it is a decent indication for real-time energy load forecasting. For example, Emshagin et al.²⁹ developed customized LSTM and GRU models for short-term household electricity consumption prediction. Their study found that while both models effectively captured consumption patterns, LSTM slightly outperformed GRU in forecasting accuracy. Likewise, Dong and Grumbach³⁰ introduced a hybrid long-term load forecasting method utilizing both LSTM and GRU networks. Their approach successfully integrated top-down, bottom-up, and sequential information, demonstrating the practicality of GRUs in capturing temporal dependencies in energy consumption data (Table 5).

Boosting methods, such as gradient boosting machines (GBMs), XGBoost, and AdaBoost, iteratively improve weak learners by focusing on difficult-to-predict instances (Figure 11). A bagging model named XASXG proposed by, Ding et al.³¹ which integrates autoregressive integrated moving average (ARIMA), support vector regression (SVR), and XGBoost. This model effectively captures the nonstationary and nonlinear characteristics of electricity load time series, resulting in superior forecasting accuracy across various Chinese cities. Similarly, Rubattu et al.³² developed a predictive model utilizing probabilistic LightGBM combined with temporal hierarchies and advanced feature engineering. Their approach achieved high accuracy in the BigDeal Challenge 2022, demonstrating the efficacy of boosting methods in load and peak forecasting tasks. The loss function for boosting is:

where Fm (x) is the current model, hm (x) is the new weak learner, and γ is a learning rate. These methods enhance accuracy but may suffer from overfitting if not carefully tuned.

To reduce variance and improve stability, bagging techniques such as RF and bootstrap aggregation perform a number of versions of the training dataset (Figure 12). Thus, these models are good at handling fluctuating energy demand patterns. A cluster-based bootstrapping method was introduced by Dube et al.³³ for interval prediction of electricity demand. Their approach utilizes residual bootstrapping combined with unsupervised clustering to generate accurate interval forecasts, particularly beneficial in microgrid settings with high demand variability. Additionally, the BaggingSHAP model, which was proposed by Olumba et al.,³⁴ combines bagging combines bagging with SHapley Additive exPlanations (SHAP) for enhanced interpretability in energy demand forecasting. The model achieved an R² score of 0.9947, indicating superior predictive performance.

Traditional forecasting techniques are combined with the DL approaches using hybrid models to optimize the forecasting performance (Figure 13). As an example, RF and LSTM can be used together by an RF-LSTM model to select features with RF, apply LSTM to temporal pattern recognition while remaining both interpretable and accurate. Meanwhile, Zhang et al.³⁵ proposed a hybrid model combining RF and LSTM to improve short-term electricity load forecasting, demonstrating reduced prediction errors compared to standalone models. Similarly, Ma et al.³⁶ developed a hybrid RF-LSTM approach that leveraged RF for selecting the most relevant input features and LSTM for modeling sequential dependencies, achieving superior results in multistep energy load forecasting tasks (Table 6).

Ensemble methods provide a robust solution for energy load forecasting, particularly when dealing with fluctuating consumption patterns and large-scale smart grid data. They enhance forecasting accuracy by reducing bias and variance while leveraging the strengths of multiple models.

MSE measures the average squared difference between predicted and actual values, with a focus on penalizing larger errors more than smaller ones. According to, Chai and Draxler³⁷ MSE is a commonly preferred metric in regression tasks due to its mathematical simplicity and sensitivity to large deviations. Likewise, Willmott and Matsuura³⁸ compared MSE with MAE, emphasizing MSE’s utility when highlighting significant prediction errors is crucial in model evaluation. It is calculated as:

̂

where yi is the actual value, ŷi is the predicted value, and n is the total number of data points. MSE is sensitive to outliers, as it squares the error terms, which can lead to a disproportionate influence of large errors.

RMSE is the square root of the MSE and provides a more interpretable error metric in the original units of the data. As highlighted by, Hyndman and Koehler³⁹ RMSE is particularly useful when large prediction errors are undesirable, offering a balance between interpretability and sensitivity. Meanwhile, Hong et al.⁴⁰ emphasized the importance of RMSE in energy forecasting competitions due to its ability to reflect forecasting accuracy effectively across different models and datasets. It is calculated as:

̂

RMSE is widely used in energy load forecasting because it reflects the magnitude of the error in a way that is more understandable to practitioners. However, like MSE, it is also sensitive to large errors.

MAE measures the average magnitude of errors in a set of predictions, without considering their direction. However, Willmott et al.³⁸ emphasized the interpretability and robustness of MAE in environmental and climate modeling contexts, showing its reliability across diverse datasets. However, Hyndman and Koehler³⁹ discussed MAE as a reliable baseline metric in forecast accuracy comparisons, particularly useful when comparing models across datasets with different scales. It is given by:

̂

MAE is less sensitive to outliers compared to MSE and RMSE, making it suitable for applications where large deviations are less critical. It provides a straightforward measure of how far the predictions are from the actual values on average.

MAPE calculates the error as a percentage of the actual value, making it easier to interpret and compare across different datasets. As noted by Makridakis,⁴¹ MAPE remains one of the most commonly used metrics in forecasting competitions due to its intuitive nature and interpretability. However Evans,⁴² also pointed out that MAPE’s sensitivity to low actual values may distort its usefulness, especially in datasets with high variability or occasional zero values. It is calculated as:

̂

MAPE is useful when comparing forecast accuracy across different models and datasets, but it can be problematic when actual values are close to zero, leading to inflated error percentages.

R² measures the proportion of the variance in the dependent variable that is predictable from the independent variables. According to Draper and Smith,⁴³ R² is widely used in regression analysis as it succinctly summarizes the explanatory power of a model. However, as noted by Alexander,⁴⁴ R² alone can be misleading in evaluating model performance, especially in cases of overfitting or when used with nonlinear models, thus warranting the use of adjusted R² or complementary metrics. It is calculated as:

̂

Where y is the mean of the observed values. R² provides a measure of the goodness-of-fit, indicating how well the model explains the variation in the data. A higher R² value indicates a better model fit, though it does not always correlate with improved prediction accuracy, particularly in complex datasets (Table 7).

Popular traditional ML models include linear regression, DTs, SVMs, and RF which are always popular for their interpretability and ease of implementation. These models are best applicable for reasonably simple, short-term forecasting tasks with relatively simpler and easy-to-understand data. But they are not very useful with long-term dependencies or high nonlinearity in the process data. For instance,Hippert et al.⁴⁵ and Wang et al.⁴⁶ demonstrated the effectiveness of linear regression in short-term load forecasting due to its simplicity and speed. DTs, as shown by Liu et al.⁴⁷ and, Singh et al.⁴⁸ are useful for capturing nonlinear relationships in structured energy data. Meanwhile, RF have been proven robust in handling noisy data and enhancing forecasting accuracy, as shown in the works of Lahouar et al.⁴⁹ and, Deb et al.⁵⁰ particularly in short-term electricity demand forecasting (Table 8).

Indeed, energy load forecasting is a good application for DL models, especially LSTM networks, GRU, and even ANN. These models are capable of capturing the time series and the nonlinear patterns within a large amount of data. This type of model is great in finding long-term trends and fine relationships between time series data, which are perfect for predicting purposes when historical consumption data is used as a fundamental in forecasting future energy demand.

LSTM and GRU are structures of rather diverse DL models, being parts of the RNN, which aims to deal more efficiently with sequential data compared to classic feed-forward networks, e.g., ANN. GRUs are known to be not as good as LSTMs at capturing long-term dependencies in time series data; however, GRUs are computationally lighter and more efficient at performing similar tasks as LSTMs. Several studies have validated this: Kuster et al.⁵¹ and Suganthi and Samuel⁵² demonstrated the utility of ANN in modeling complex energy consumption behaviors due to its flexibility and learning capabilities. LSTMs, as applied by Marino et al.⁵³ and, Kong et al.⁵⁴ have shown exceptional performance in capturing long-term dependencies in electricity demand prediction. Meanwhile, GRUs have been successfully employed by Liu et al.⁵⁵ and, Liang et al.⁵⁶ where they offered competitive accuracy with reduced computational overhead compared to LSTMs, making them suitable for real-time forecasting applications (Table 9).

Ensemble methods like boosting (e.g., XGBoost) and bagging (e.g., RF) combine multiple models to improve forecasting accuracy and reduce variance. These methods are highly effective in energy load forecasting, particularly for datasets with noisy or fluctuating patterns. However, several researchers have demonstrated the effectiveness of these ensemble approaches. For boosting, Hong et al.⁵⁷ applied gradient boosted regression trees (GBRTs) to improve short-term load forecasting accuracy in large-scale smart grid applications, while Taieb and Hyndman⁵⁸ evaluated boosting strategies for probabilistic forecasting in energy systems. For bagging, Lahouar and Slama⁵⁹ showed that RFs provided high accuracy and robustness in hourly electricity demand prediction and Zhou et al.⁶⁰ confirmed their efficiency in handling feature-rich energy datasets and capturing nonlinear relationships (Table 10).

Selecting the right ML technique for energy load forecasting depends on the specific characteristics of the dataset and the forecasting horizon. While traditional models are efficient and easy to interpret, DL and ensemble approaches offer superior accuracy in complex scenarios. Performance metrics such as MSE, RMSE, MAE, and R² play a vital role in comparing and selecting the best model for a given task.