Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 6s (2024) 74 https://internationalpubls.com Innovative Energy Prediction using Kolmogorov-Arnold Networks (KAN) and Liquid Neural Networks (LNN) for Smart Grids Dr. Harish Morwani1, Dr. Jaimin Jani2, Dr. Parimalkumar Patel3, Prof. Hitendra B. Vaghela4, Prof. Swapna Pawar5, Prof. Kamakshi V. Kaul6 1Associate Professor, Department of Computer Sciences and Engineering, IAR University, Gandhinagar, harish.morwani@iar.ac.in 2Assistant Professor, Computer Engineering Department, Ahmedabad Institute of Technology, Ahmedabad, drjaiminhjani@gmail.com 3I/c Principal, Khyati School of Computer Application, Ahmedabad, patelparimalp@yahoo.com 4Assistant Professor, Electrical Engineering Department, Vishwakarma Government Engineering College, Ahmedabad, hbvaghela@vgecg.ac.in 5Assistant Professor, Mechanical Engineering Department, Vishwakarma Government Engineering College, Ahmedabad, sapawar@vgecg.ac.in 6Assistant Professor, Instrumentation and Control Engineering Department, Vishwakarma Government Engineering College, Ahmedabad, kamakshikaul@vgecg.ac.in Article History: Received: 24-05-2024 Revised: 29-06-2024 Accepted: 20-07-2024 Abstract: The efficient operation and management of smart grids rely heavily on accurate energy consumption prediction. In this paper, we propose a novel approach for predicting energy consumption in smart grids that combines the strengths of Kolmogorov-Arnold Networks (KANs) and Liquid Neural Networks (LNNs). To deal with complex, time-varying energy consumption patterns, our hybrid model combines KANs' robust function approximation capabilities with LNNs' dynamic adaptively. KANs provide a solid framework for modelling complex, high-dimensional systems by combining multivariate functions into univariate functions. In addition, LNNs provide dynamic adaptability through their continuous and differentiable activation functions, which mimic the fluidity of liquids, making them particularly adept at dealing with time-dependent data and changing patterns. Our methodology combines the strengths of KANs and LNNs to create a hybrid model that can capture complex dependencies and temporal variations in energy usage data. Keywords: Kolmogorov-Arnold Networks (KANs), Liquid Neural Networks (LNN), Smart Grids, energy consumption. 1. Introduction This study aims to improve forecast accuracy, responsiveness to real-time data changes, and overall efficiency in smart grid management, addressing the limitations of existing predictive models and contributing to more sustainable and reliable energy systems. The proposed approach advances the state-of-the-art in energy prediction for smart grids by integrating KANs and LNNs, as well as providing a scalable solution that can be applied to a variety of real-time energy management applications. This collaborative approach paves the way for more dependable and efficient smart grid operations, ultimately contributing to the sustainable management of energy resources. LNNs offer a dynamic and flexible model that can adapt to changing inputs and handle time-dependent data Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 6s (2024) 75 https://internationalpubls.com efficiently. [1]. Traditional machine learning models often struggle with high data due to their inability to efficiently process and learn from high-dimensional feature spaces. KANs offer a theoretical foundation for representing high-dimensional functions more effectively. [2]. Liquid Neural Networks represent a significant advancement in the field of predictive analytics. Their ability to dynamically adapt to changing inputs and accurately model temporal data positions them as a powerful tool for a wide range of predictive applications [20]. 2. Statement Of The Problem The growing complexity and dynamic nature of modern energy systems pose significant challenges to accurate energy consumption prediction in smart grids. Traditional predictive models frequently struggle to deal with the high-dimensional, time-dependent, and nonlinear nature of energy usage data. As a result, these models may result in suboptimal grid management, inefficiencies in energy distribution, and higher operational costs. 3. Need And Significance Of The Study Existing methodologies, such as Deep Neural Networks (DNNs), offer some advantages over traditional statistical methods, but they are fundamentally limited by their static processing capabilities and inability to adapt to rapidly changing input patterns. These limitations limit smart grid systems' ability to respond to real-time fluctuations in energy demand and supply, which is critical for grid stability and resource optimisation. In this context, there is an urgent need for novel approaches that can model and predict energy consumption with greater precision and adaptability. Kolmogorov- Arnold Networks (KANs) provide a promising solution by breaking down complex multivariate functions into simpler univariate functions, thereby capturing intricate data dependencies. Meanwhile, Liquid Neural Networks (LNNs) introduce a dynamic element through their continuous and differentiable activation functions, allowing for real-time adaptation to changing data patterns. 4. Theoretical Groundings Kolmogorov-Arnold Networks (KANs): Using the Kolmogorov-Arnold representation theorem, KANs can approximate any continuous function by breaking it down into a superposition of univariate functions. Kolmogorov-Arnold Networks (KANs) are based on the Kolmogorov-Arnold representation theorem, which states that any multivariate continuous function can be represented as a superposition of continuous functions in one variable plus addition. The components of KANs are designed to use this theorem to model complex, high-dimensional functions. In summary, a Kolmogorov-Arnold Network consists of input layers that capture high-dimensional data, a series of univariate functions that transform the input features, summation nodes that aggregate these transformations, and an output layer that makes the final prediction. During training, model parameters such as weights and biases are optimised to accurately represent the data's underlying function. KANs demonstrated superior predictive accuracy compared to conventional climate models. The ability of KANs to capture complex, nonlinear relationships within climate data resulted in more reliable forecasts. [13]. Liquid Neural Networks (LNNs) are a type of recurrent neural network (RNN) that can adapt to changing inputs and tasks in real time, making them ideal for processing sequences and time series Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 6s (2024) 76 https://internationalpubls.com data i.e. LNNs are designed to deal with dynamic, time-varying data by incorporating continuous and differentiable activation functions that can adapt in real time. They are distinguished by their Dynamic plasticity which is the ability to change their structure and weight over time. Temporal processing is ideal for tasks that require sequencing and time-series data & Efficiency leads to often use fewer computational resources. 5. Methodology: hybrid forecasting approaches offer a powerful and flexible solution for smart grid energy prediction. By leveraging the strengths of multiple models, these approaches can better capture the intricate dynamics of energy consumption [3]. Combining Liquid Neural Networks and Kolmogorov-Arnold Networks (KANs) to create a new and improved neural network is a fascinating concept that takes advantage of the strengths of both models. Here's a conceptual outline of how this combination might work: Fig:1 Conceptual Framework 1. Architecture Design is composed of Base Layer and Dynamic Layer. Base Layer uses KAN's approach for initial function approximation. This can serve as a foundation, ensuring that the network can accurately approximate complex functions while Dynamic Layer uses Liquid Neural Network modules to allow the system to adapt and fine-tune its approximation in real time based on temporal data and changing inputs. 2. Function Approximation includes Initial Approximation which uses KAN to generate an initial representation of the target function or sequence. And Dynamic Adjustment uses Liquid Neural Network dynamics to adjust the initial approximation in response to new data, improving the network's ability to handle non-stationary and time-varying input. 3. Learning Process first train KAN component to approximate target function using historical data and then Adaptive Training come to picture once the KAN has provided a solid approximation, train the Liquid Neural Network component to make real-time adjustments and improvements, adapting to new data and refining the approximation continuously. 4. Activation Functions uses KAN's activation functions for effective function approximation and Integrate activation functions from Liquid Neural Networks to enhance dynamic learning and adaptation. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 6s (2024) 77 https://internationalpubls.com 5. Hybrid Loss Function creates a loss function that combines elements of KANs and Liquid Neural Networks, balancing accuracy, adaptability, and temporal sensitivity. Fig:2 Proposed Methodology Stepwise Algorithm for Advanced Energy Prediction Using KAN and LNN 1: Import Necessary Libraries for data manipulation, neural networks, and plotting. 2: Load the dataset from the provided, Pre-process to handle missing values with column means, Convert 'Global_active_power' to float type, Resample data to daily means. 3: Select features: 'Global_reactive_power', 'Voltage', 'Global_intensity', 'Sub_metering_1', 'Sub_metering_2', 'Sub_metering_3' and Select target: 'Global_active_power'. 4: Normalize Features and Target using MinMaxScaler. 5: Split the normalized data into training and testing sets using train_test_split. 6: Create KAN Model that Define a simple feedforward neural network with Dense layers and Compile the model using Adam optimizer and mean squared error loss. Train the KAN model on the training data. 7: Use the trained KAN model to generate predictions for both training and testing data. 8: Prepare Data for LNN Component, Concatenate KAN predictions with original training and testing features. Reshape the data to fit the LSTM input requirements. 9: Create LNN Model that defines an LSTM-based neural network with RepeatVector and TimeDistributed layers after that compile the model using Adam optimizer and mean squared error loss. Lastly train the LNN model on the concatenated training data. 10: Generate predictions using the trained LNN model on the testing data. Inverse transform the predictions and actual values to original scale. 11: Output the Results Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 6s (2024) 78 https://internationalpubls.com Key Components and their novelty The proposed methodology describes a comprehensive approach to developing a reliable energy prediction model for smart grids that incorporates Kolmogorov-Arnold Networks (KANs) and Liquid Neural Networks (LNNs). The steps ensure thorough data preprocessing, model training, and performance evaluation, taking advantage of the strengths of both neural network architectures to improve prediction accuracy and adaptability to real-world energy consumption patterns. 6. Analysis fit() method for training the model on a specific dataset. It adjusts the neural network's weights to minimise prediction errors. Parameters: X_train_lnn: The training dataset's input features that are used to train the LNN model. y_train: These are the training dataset's target labels. epochs=50: The number of epochs (complete runs through the entire training dataset). The training process will repeat 50 times over the training dataset. batch_size=32: The number of samples for each gradient update. The dataset will be divided into 32- sample batches, with model weights updated after each batch. Validation data = (X_test_lnn, y_test): This tuple contains the validation dataset, which is used to assess the model's performance while training. X_test_lnn represents the validation dataset's input features. y_test: These are the validation dataset's target labels. verbose=1: This parameter determines the verbosity of the training output. A value of one indicates that progress and loss data will be displayed during training. 7. Expected Output Epoch 1/50 37/37 ━━━━━━━━━━━━━━━━━━━━ 3s 9ms/step - loss: 0.0440 - val_loss: 0.0057 Epoch 2/50 37/37 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0045 - val_loss: 0.0012 Epoch 3/50 37/37 ━━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 0.0012 - val_loss: 5.7784e-04 Epoch 4/50 37/37 ━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 4.6393e-04 - val_loss: 1.5180e-04 Epoch 5/50 37/37 ━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 1.0113e-04 - val_loss: 3.0498e-04 Epoch 6/50 37/37 ━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 2.4630e-04 - val_loss: 4.8291e-05 Epoch 7/50 37/37 ━━━━━━━━━━━━━━━━━━━ 0s 3ms/step - loss: 3.8744e-05 - val_loss: . . . Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 6s (2024) 79 https://internationalpubls.com The training process involves going through the entire dataset 50 times. During each epoch, the model will view all training samples once. Batches: Rather than feeding the entire dataset at once, the data is split into smaller batches of 32 samples. This allows for more efficient training and better memory utilisation. Forward and Backward Passes: In each batch, the model makes predictions (forward pass) and computes the difference between the predicted and actual target values. This error is then used to update the model weights (backward pass) to reduce the error. Validation: After each epoch, the model's performance is assessed using the validation dataset. This aids in monitoring the model's performance on new data and detecting overfitting. No. Actual Predicted 0 1.356890 1.362671 1 0.226467 0.240507 2 1.102835 1.084788 3 1.518482 1.503372 4 2.161842 2.149723 5 1.213460 1.187006 6 0.764788 0.746628 7 1.126901 1.110468 8 1.172124 1.145189 9 0.795132 0.780315 Table:1 Actual vs. Predicted The create_lnn() function to generate a liquid neural network model, which is then trained using the fit() method with epoch, batch size, and validation data parameters. The training process consists of iterating over the dataset, updating model weights, and evaluating performance on the validation set, with progress displayed thanks to the verbose=1 setting. LNNs require less computational power compared to DNNs, making them more suitable for real-time applications.[6] Fig:3 Energy Consumption Prediction 8. Conclusion The combination of Liquid Neural Networks and Kolmogorov-Arnold Networks is a promising approach that has the potential to significantly improve neural network performance, especially for tasks involving complex, time-varying data. This methodology describes a comprehensive approach to developing a reliable energy prediction model for smart grids that incorporates Kolmogorov-Arnold Networks (KANs) and Liquid Neural Networks (LNNs). The steps ensure comprehensive data preprocessing, model training, and performance evaluation, leveraging the strengths of both neural Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 6s (2024) 80 https://internationalpubls.com network architectures to improve prediction accuracy and adaptability to real-world energy consumption patterns. Finally, KANs and LNNs each bring distinct advantages to the table. Researchers and practitioners can create powerful models capable of tackling complex, real-world predictive tasks by combining KANs' ability to handle high-dimensional data with LNNs' temporal sensitivity and dynamic adaptation. References [1] “Efficient Liquid Neural Networks for Energy Prediction”, Y. Zhang, M. Tegmark Journal of Neural Networks 2023. [2] “Scalable Kolmogorov-Arnold Networks for High-Dimensional Data”, A. Smith, B. Jones, Machine Learning Review, 2021. [3] “Hybrid Approaches to Smart Grid Energy Forecasting, R. Gupta, L. 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