Exploring low-resource weather forecasting with echo state network-based architectures and satellite data

Contents lists available at ScienceDirect Knowledge-Based Systems journal homepage: www.elsevier.com/locate/knosys Exploring low-resource weather forecasting with echo state network-based architectures and satellite data E. López Ortiza,∗,1, M. Jiménez b,1, L.M. Soria-Morillo b,2, J.A. Álvarez-García b,2, J.J. Vegas-Olmosc,2 aDepartment of Computer Science and Artificial Intelligence (Universidad de Sevilla), Avenida Reina Mercedes, SN, Sevilla, 41012, Spain bDepartment of Languages and Computer Systems (Universidad de Sevilla), Avenida Reina Mercedes, SN, Sevilla, 41012, Spain cNVIDIA Corporation, Ltd., Hermon Building, Yokneam, 20692, Israel A R T I C L E I N F O Keywords: Echo state networks CloudCast Weather forecasting Internet of Things A B S T R A C T Cloud forecasting plays a crucial role in various fields such as agriculture, energy systems, and air travel. An accurate forecasting system can offer significant benefits by improving decision-making efficiency in these areas. This study investigates the use of Echo State Network (ESN)-based architectures for weather forecasting, focusing on cloud prediction across Central Europe using the CloudCast benchmark, which integrates data from Meteosat satellites and the European Centre for Medium-Range Weather Forecasts (ECMWF) model. Two novel techniques are included in this study, evaluated in two different phases. First, the MultiReservoir Weighted ESN (MWESN) architecture is proposed, featuring optimised inter-reservoir connections that enhance both the effectiveness and adaptability of the model. This model is evaluated along with advanced ESN architectures, including Multi-Reservoir ESN, Deep ESN among others. Second, the Error-Guided Regional Training (ERT) method is introduced to minimise the computational resources required for forecasting at the pixel level while maintaining high accuracy. Combined, MWESN and ERT demonstrate a 1.41% improvement in accuracy, effectively capturing complex spatio-temporal dynamics while significantly reducing computational demands compared to existing state-of-the-art methods. Additionally, models are tested on low-resource devices such as Raspberry Pi units, illustrating their feasibility for real-world meteorological applications. 1. Introduction Weather forecasting plays a crucial role in various domains, including agriculture, transportation, energy management, and disaster preparedness. Accurate predictions of weather conditions, including specific cloud types and clear weather periods, are essential for informed decision-making processes and mitigating potential risks associated with extreme weather events. Identifying cloud patterns and clear skies is also increasingly important for home automation systems, as these systems, can use detailed weather forecasts to make decisions, such as turning off solar panels during storms to prevent damage or delaying washing machine programmes to allow laundry to dry during daylight hours. This integration improves energy efficiency, protects household appliances, and contributes to a smarter and more responsive living environment. ∗Corresponding author. E-mail addresses: [email protected] (E.L. Ortiz), [email protected] (M. Jiménez), [email protected] (L.M. Soria-Morillo), [email protected] (J.A. Álvarez-García), [email protected] (J.J. Vegas-Olmos). URL: https://www.nvidia.com (J.J. Vegas-Olmos). 1Researcher 2Co-ordinator For this purpose, the CloudCast dataset [1] was proposed as a large-scale unified benchmark for the cloud forecasting. This dataset, integrates high-resolution satellite imagery from Meteosat and numerical weather predictions from the ECMWF to enhance the cloud prediction. Traditional numerical weather prediction (NWP) models, while sophisticated, often face challenges in accurately capturing the complex dynamics of weather systems, particularly at the local level and for short-term forecasts. In recent years, machine learning techniques have emerged as promising tools for improving the accuracy and efficiency of weather forecasting models [2–7]. Among these techniques, Echo State Networks (ESNs) have attracted significant attention for their ability to model dynamic, nonlinear systems with temporal dependencies. https://doi.org/10.1016/j.knosys.2025.113692 Received 21 November 2024; Received in revised form 22 April 2025; Accepted 2 May 2025 Knowledge-Based Systems 323 (2025) 113692 Available online 17 May 2025 0950-7051/© 2025 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ ). E.L. Ortiz et al. Originally proposed by Jaeger and Haas [8], ESNs are a type of recurrent neural network (RNN) characterised by a large reservoir of interconnected nodes and a readout layer for making predictions. While ESNs have shown promise in various applications, including time series prediction and signal processing, they are relatively underexplored in weather forecasting tasks. This research builds on our previous work [9,10]. In it, we evaluated various ESN-based architectures in image segmentation tasks, specifically using the MNIST and FashionMNIST datasets. We also investigated the viability of deploying ESN-based models in resource-constrained devices for cloud classification using satellite images. These studies demonstrated the potential of ESNs in handling tasks that involve complex spatial and temporal relationships. In this work, we employ ESN-based models for local weather prediction tasks. We ensure that these models can be trained on low-resource devices while also evaluating their performance against traditional NWP models and other machine learning approaches. Through extensive experimentation and analysis, our objective is to demonstrate the effectiveness of MWESNs in weather forecasting tasks and highlight their potential for real-world applications in various fields, including home automation. This work introduces two key innovations: the Multi-Reservoir Weighted ESN (MWESN) and the Error-Guided Regional Training (ERT). The MWESN enhances the performance of previous ESN-based models by incorporating tunable weights between reservoirs, which improves the model’s accuracy and adaptability to new scenarios. Meanwhile, ERT is a novel pixel-level inference technique designed to extrapolate pixel-level image forecasts from models trained on a set of representative pixels. The remainder of this paper is organised as follows. In Section 2, we provide a comprehensive review of related work in weather forecasting and machine learning techniques. Section 3 introduces the methodology used in this study, including the architecture of MWESNs, the ERT algorithm, and the experimental setup. Section 4 presents the experimental results and analysis, followed by a discussion of the findings in Section 5. Finally, Section 6 concludes the paper and outlines future research directions. 2. Background and related work 2.1. Weather forecasting models In recent years, machine learning techniques have emerged as promising alternatives in weather forecasting by offering the potential to improve prediction accuracy and efficiency. Deep Learning (DL) models, Support Vector Machines (SVM), and Random Forests (RF) are widely used machine learning models for weather forecasting [2–7]. SVMs are robust in handling high-dimensional data, which is often the case in weather forecasting tasks involving numerous features. SVMs tend to generalise well on new data, which reduces the risk of overfitting, especially when the right kernel is chosen. The use of kernel functions allows SVMs to perform well on nonlinear data by transforming it into a higher-dimensional space, where it is easier to classify. However, SVMs can be less efficient when dealing with very large datasets, as they require significant computational and memory resources. The performance of SVMs is highly sensitive to the choice of hyperparameters and kernel functions, which requires considerable experimentation for optimisation. Understanding and implementing the kernel trick can be complex and may require domain-specific knowledge. In [4], the authors used SVM for wind speed prediction and compared their performance with neural network approaches. The mean daily wind speed data from Medina city, Saudi Arabia, was used to build and test both models. The results suggested that SVMs performed favourably compared to ANN model based on the root mean square errors between the actual and predicted data. In [5] a grey wolf optimizer (GWO) and a SVM were used to ensure the accuracy and stability of the forecasts of the minimum and maximum air temperature for the next day. RFs reduce the risk of overfitting by aggregating the predictions of multiple decision trees, enhancing model robustness. They offer valuable insights into feature importance, aiding in the identification of key factors that influence weather predictions. RFs are also well suited for handling large datasets with high-dimensional feature spaces efficiently. However, the computational demands of training and predicting with numerous trees can be significant, often requiring considerable memory and processing power. Although RFs are more interpretable than ANNs, their complexity can still obscure interpretation compared to single decision trees. Additionally, RFs can encounter issues with the bias–variance trade-off if individual trees are not adequately tuned. A data-driven method based on an enhanced RF model was proposed in [6]. The method leverages attribute selection techniques in ensemble form to optimise the bias–variance trade-off in short-term photovoltaic power forecasting (STPF), thereby enhancing the quality of forecasting results. To improve the accuracy of hail prediction, [7] applies the RF algorithm in hail identification and prediction on the Shandong Peninsula in a range of 0-6 h. The results showed that the model was effective in identifying hail fall areas and capable of forecasting all hail seasons and the time of hail disasters occurrence. DL models are highly effective at capturing nonlinear and complex relationships within data, which is essential for accurately forecasting weather patterns that involve multiple interacting variables. They can improve their accuracy as more data becomes available, which is beneficial for weather forecasting, where vast amounts of historical data can be used for training. In addition, they can be adapted for both regression and classification tasks, making them versatile tools for different types of weather prediction scenarios. However, training large neural networks requires significant computational resources, including time and hardware capabilities. They are prone to overfitting, especially with limited data, which can reduce their generalisation ability on new or unseen data. The complex structure of ANNs makes them less interpretable compared to simpler models, making it challenging to understand how predictions are made. The U-Net architecture [11] was used by Berthomier et al. [12] for intraday binary cloud forecasting over France. This involved a lead time of up to 90 min and a time step of 15 min. Their study demonstrated the superiority of U-Net cloud forecasts over those generated by the NWP AROME model [13,14]. Furthermore, the U-Net approach exhibited favourable performance compared to various neural network models, including recurrent neural networks (RNNs) and other Convolutional Neural Networks (CNN). Berthomier et al. [12] conducted training and validation of algorithms for the binary cloudiness prediction task (clouds versus no clouds), using the cloud classification data from the second-generation Meteosat (MSG) satellite. In [2], the authors designed three artificial neural networks using temperature, wind speed and precipitation as inputs and tested these on different datasets, yielding favourable results. Atmospheric conditions were utilised as inputs in [3] to train a convolutional neural network (CNN) and predict wind power at the kilometre scale. Among these techniques, ESNs have garnered attention for their ability to model dynamic, nonlinear systems with temporal dependencies. Originally proposed by Jaeger and Haas [8], ESNs are a type of RNN characterised by a large reservoir of interconnected nodes and a readout layer for making predictions. Despite their apparent simplicity, these networks have proven to be very efficient in time series analysis. Several studies have explored the application of ESN-based models in weather forecasting tasks. [15] demonstrated ESNs’ effectiveness for horizontal wind velocity field forecasting, by achieving results comparable to those of traditional methods. Similarly, [16] used ESNs to predict the direction and speed of the wind, which led to improvements Knowledge-Based Systems 323 (2025) 113692 2 E.L. Ortiz et al. in the wind farm efficiency. ESNs have been widely used in the field of wind speed and energy prediction [17–19]. In [20], an ESN was used to predict photovoltaic power generated at a power plant using temperature and solar irradiance as input. Similarly, [21] used the day’s weather type as an input to forecast electricity production at a plant. In [22], atmospheric pressure was used as an input for an ESN to predict ENSO for rainfall prediction. While these approaches have achieved success in capturing the complex dynamics of weather systems, accurately modelling the complex spatio-temporal relationships inherent in weather data remains challenging. Traditional ESN architectures may struggle to capture the diverse patterns and interactions present in complex systems like weather. 2.2. ESN-based models In the past, combinations with other architectures and modifications have been proposed for the standard ESN architecture [23], and models based on these enhanced networks have shown improved performance in specific scenarios. Gallicchio et al. [24] investigated the benefits of deep layering in reservoir computing (RC) models, particularly in terms of temporal representation diversification and dynamic richness. The study highlighted that deep reservoir architectures effectively capture multiple time-scales and improve short-term memory capacity, thereby offering significant advantages for complex temporal tasks such as weather forecasting. [25] underscored the difficulty of achieving high performance in image recognition with raw image data, necessitating a large-scale reservoir with a substantial number of neurons. To address this limitation, they proposed a novel method that combines RC with untrained CNN. In a similar vein, [26] employed a Reservoir Computing Network (RCN) comprising multiple stacked ESNs, showcasing the potential of RC in image recognition tasks. Additionally, [27] conducted a comparative study between ESNs and LSTMs, further illustrating the promise of RC in this domain. [28] presented a DeepESN model optimised using Bayesian Optimisation to predict non-stationary time series data. The model shows improved prediction accuracy and computational efficiency compared to traditional methods. In their 2021 study, Hemin et al. [29] used a grouped-ESN [24], a variation of the Recurrent Neural Network (RNN), and applied Principal Component Analysis (PCA) to address the high dimensionality of outputs from reservoir layers. This advanced architecture was applied to Speech Emotion Recognition, evaluated using the SAVEE dataset and FAU Aibo Emotion Corpus, and demonstrated superior performance compared to contemporary state-of-the-art models. Similarly, [30] employed a grouped deep ESN for emotion recognition using electroencephalogram (EEG) signals, highlighting the versatility and efficacy of grouped-ESN architectures. Furthermore, [31] proposed an ESN-based approach with multidimensional bilinear filter for human emotion recognition, further confirming the suitability of reservoir computing models for processing complex temporal data. In this investigation, we draw on previous studies concerning ESN and our own earlier research [9,10], where we developed a modified version of a grouped-ESN [24] called Multi-Reservoir ESN (MRESN) specifically tailored for classification purposes. Our objective is to expand on and scrutinise the applicability of ESN-based models in the domain of weather forecasting, using satellite imagery as the primary input. We examine the capacity of ESN-based models to discern spatial and temporal patterns within weather data and compare its efficacy with conventional methodologies. By conducting a thorough experimentation and analysis, our aim is to substantiate the efficacy of ESN-based models in improving the precision and computational efficiency of weather prediction models. 3. Methodology In this section, the main contribution of the work is detailed. Firstly, as the contribution is based on ESN, the basics and the background theory on this type of network is explained. Then, the Multi-Reservoir weighted ESN motivation and main components are explained. 3.1. ESN The architecture of ESNs encompasses three primary components: the input layer (𝑊𝑖𝑛 ∈R𝑁𝑥𝐾 , with 𝑁 being the number of neurons in the reservoir and 𝐾 being the size of the input), the reservoir layer (𝑊∈R𝑁𝑥𝑁 ), and the output layer (𝑊𝑜𝑢𝑡 ∈R𝑂𝑥(𝐾+𝑁+1), with 𝑂 being the size of the output). The input layer receives external stimuli (𝑢∈R𝐾), typically in the form of time series data or patterns, which are then projected onto the reservoir layer. The reservoir layer consists of a large number of recurrently connected neurons with random weights, forming a dynamic reservoir of information. These neurons possess non-linear activation functions and the recurrent connections within them allow the reservoir to exhibit a rich internal dynamics, which is crucial for its computational capability. These properties allow the network to capture complex temporal dependencies within the input data. Finally, the output units receive signals from the reservoir layer and produce the response of the network. Unlike traditional feedforward neural networks, where weights are trained directly between input, hidden, and output layers, in ESNs, only the connections between the reservoir and output layer are trained, while the reservoir connections remain fixed. This architecture simplifies training, as it reduces the number of parameters needing adjustment and facilitates efficient learning even with limited training data. Fig. 1 shows this architecture. In addition, to determine the weights of the final layer in an ESN, linear regression is used, offering a computationally efficient alternative to the backpropagation algorithm commonly used in ANNs. Linear regression leverages the fixed, random weights of the reservoir layer to map the reservoir states to the desired output, simplifying the training process. This approach significantly reduces computational costs and training time, as it involves solving a linear system of equations rather than iteratively adjusting weights through multiple layers. Consequently, linear regression facilitates faster and more efficient training of ESNs, making them particularly advantageous for applications with limited computational resources or time constraints. Typically, linear regression with Tikhonov regularisation, also known as ridge regression, is used to find these output weights. This regularisation technique adds a penalty term to the linear regression objective, which helps prevent overfitting and enhances the generalisation capability of the model. See Eq. (1). 𝑊𝑜𝑢𝑡 = (𝐻′𝐻+𝛽𝐼)−1𝐻′𝑌(1) There are two main components in this equation: first, the matrix 𝐻∈R𝑇 𝑥(𝑁+𝐾+1), with 𝑇 being the training steps. The matrix 𝐻 contains the various states produced by the network during training. Secondly, we have the matrix or vector 𝑌∈R𝐿𝑥𝑂, which represents the expected result, that is, the target vector. 𝛽 is used to express the regularisation coefficient, which is a small number that is multiplied by an identity matrix. 𝐻′ is used to express the transpose of 𝐻. Due to the randomness in the generation of the input layer and the reservoir, the network develops its unique way of responding to the input data, thereby generating states. In ESNs, the objective is to find weights for the output layer that can interpret the network’s reactions to the input to produce the expected output. Concerning state generation, the classical formula was proposed by [32] and is known as Leaking Integration (see Formula (2)). 𝑥𝑡= (1 − 𝛼)𝑥𝑡−1 +𝛼𝑆(𝑊𝑖𝑛 ⋅𝑢𝑡+𝑊⋅𝑥𝑡−1)(2) Knowledge-Based Systems 323 (2025) 113692 3 E.L. Ortiz et al. Fig. 1. Vanilla ESN architecture. Symbol is used to express vector concatenation and ⨂ to express matrix multiplication. Only the weights of the output layer (𝑊 𝑜𝑢𝑡) needs to be trained, the rest of weights are generated randomly and remain fixed during training. 𝜆 is used to express the function to calculate the new state and 𝑥’ is usually the previous step of the time series (𝑥𝑡−1). Fig. 2. Vanilla-ESN for classification. Symbol is used to express vector concatenation and ⨂ to express matrix multiplication. In this formula, the parameter 𝛼 is known as the leaking rate and is used to regulate the amount of information from the previous state that remains in the newly generated state. 𝑥𝑡∈R𝑁 represents the state of the network at time 𝑡, and 𝑆 is a sigmoid function, which is typically the hyperbolic tangent. In prior research, we have successfully adapted several advanced variations of ESNs for classification tasks, specifically a DeepESN, a deep-IA ESN, and a grouped-ESN [24], the latter of which we term as a Multi-Reservoir ESN (MRESN). This adaptation for classification involves incorporating an output layer designed with multiple outputs, each corresponding to a distinct class. Additionally, a final argmax layer processes these output probabilities to identify and return the class with the highest probability. Despite these differences, the method for calculating the states of an MRESN is identical to that of the original architecture, with the distinction that in MRESNs, the vector 𝑥𝑡 is constructed from multiple reservoirs instead of just one. In the MRESN, each reservoir independently contributes its state to the vector. Collectively, they build a final-state vector that encapsulates the response to the input from each of these reservoirs. Fig. 2 depicts this modification for the basic architecture, and Fig. 3 depicts the MRESN architecture. Another distinction is the multiple outputs provided by the MRESN output layer. As mentioned above, in this architecture, the output layer produces multiple outputs, each representing the probability of belonging to one of the possible classes. However, despite the multiplicity of outputs, it is not necessary to retrain the network for each class. Instead, we obtain these probabilities by comparing the states stored in the matrix 𝐻 with different target vectors, one for each class. These target vectors have only two possible values: 1 if the example belongs to the class, and 0 otherwise. Thus, to compute the weights of the output layer, we use the same matrix 𝐻, but confront it with different vectors 𝑌 (one for each class). See Eq. (3). 𝑊𝑐 𝑜𝑢𝑡 = (𝐻𝑇𝐻+𝛽𝐼)−1𝐻𝑇𝑌𝑐, 𝑐 ∈ [1,2,…, 𝑞](3) In the above equation, 𝑞 represents the number of classes, with 𝑐 denoting each of the possible classes. The values at each position of the target vectors 𝑌𝑐 belong to the discrete interval [0,1]. Consequently, each column of 𝑊𝑜𝑢𝑡 corresponds to weights specifically trained to determine whether an example belongs to a particular class or not. 3.2. Multi-reservoir weighted ESN Understanding what is happening inside a reservoir in an ESN is challenging because the reservoir consists of a large, randomly connected, and fixed set of nodes, where the state of each node is influenced by the complex and nonlinear dynamics of the entire network. The interactions between the nodes create a high-dimensional space, where the transient responses of the system to inputs are difficult to interpret. These internal states capture intricate patterns, but the randomness and recurrence make it hard to disentangle and explain how specific features or temporal dependencies are encoded, leading to the ‘‘black-box’’ nature of reservoir computing. This is why, to date, we are not aware of any effective method for improving training by modifying the connection weights of the reservoir nodes, which limits the potential for enhancing the basic ESN architecture. In architectures with multiple reservoirs, we still have some room for improvement. One possible improvement is to modify the connections weight between the reservoirs. In most variations of ESN, except for the basic ESN architecture and the MRESN architecture, direct connections between the different reservoirs are used. That is, the state received by a reservoir located in an intermediate layer corresponds to the unchanged state of the previous-layer reservoir or reservoirs. In other words, the edges that connect the reservoirs have a weight of 1. Based on this idea, a Multi-Reservoir Weighted ESN (MWESN) architecture is proposed to explore optimal weights for the connections between reservoirs. The architecture consist on a series of fully connected multi-reservoir layers, where the edges between the reservoirs of each layer are learnable weights in the range [−1,1]. Knowledge-Based Systems 323 (2025) 113692 4 E.L. Ortiz et al. Fig. 3. MRESN architecture. Symbol is used to express vector concatenation and ⨂ to express matrix multiplication. Fig. 4. Multi-reservoir Weighted ESN (MWESN). Example of MWESN with a layer of 5 reservoirs and a second layer with 2 reservoirs. The dotted lines represent the connections between reservoirs and are trainable parameters whose values fall in the range [−1,1]. During experimentation, various configurations of input are tested, sometimes directing it only to the reservoirs in the first layer, while at other times selecting specific reservoirs to receive the original input. Fig. 4 shows an example of this kind of network. To determine the edge weights, we employed a particle swarm optimisation (PSO) algorithm [33], although alternative search methods, such as gradient descent or genetic algorithms, could also be applied. The necessity for search-based optimisation arises from the inherent characteristics of the architecture. In MWESN, reservoirs are generated through random initialisation, following the conventional approach in Echo State Networks. These reservoirs, by design, exhibit blackbox behaviour due to their recurrent connectivity and the internal generation of echo states, which is a fundamental trait of ESN-based models. The objective of MWESN is to introduce an additional layer of optimisation by assigning weights to the edges that interconnect the reservoirs. Importantly, these weights are not solely dictated by the architectural topology — meaning that two MWESN networks with identical configurations, in terms of the number of layers and reservoirs per layer, trained on the same task, may nonetheless exhibit different sets of inter-reservoir weights. This variability is primarily driven by the random internal structures of the reservoirs formed during the initialisation phase. Table 1 Characteristics of the models used in PSO algorithm. 𝐿𝑖𝑛 is used to express the layers that receive the original input beside the states of the reservoirs of previous Layer if any. 𝐿𝑜𝑢𝑡 is used to express the layers that contribute to generating the final state, only the state of the reservoirs in these layers will be used to perform training. Edges is used to express the size of the vector we are searching with the PSO in each execution; this corresponds to the number of edges in the network. A graphical representation of the model used in Run 1 can be seen in Fig. 4. Run 1 Run 2 Run 3 Run 4 Layer 1 (𝑅⋅𝑛) 5 ⋅ 200 5 ⋅ 500 10 ⋅ 150 10 ⋅ 100 Layer 2 (𝑅⋅𝑛) 2 ⋅ 300 3 ⋅ 500 3 ⋅ 500 3 ⋅ 300 Layer 3 (𝑅⋅𝑛) – 2 ⋅ 300 – – Edges 10 21 30 30 𝐿𝑖𝑛 𝐿1, 𝐿2𝐿1, 𝐿3𝐿1𝐿1, 𝐿2 𝐿𝑜𝑢𝑡 𝐿2𝐿3𝐿2𝐿2 Table 2 PSO parameters for all runs. Population Iterations C1 C2 w Target 20 20 1.5 1.2 0.5 ℎ4 Given this dependency, defining optimal edge weights analytically or a priori is not feasible, thereby necessitating the use of heuristic search methods such as PSO. The characteristics of each model are shown in Table 1, while the parameters used for the PSO are listed in Table 2. Different techniques such as Gradient Descent (GD), Genetic Algorithm (GA) or Particle Swarm Optimisation (PSO) can be used to find the weights of a MWESN. In this work we have used a PSO algorithm whose parameters are shown in Table 2. 3.3. Error-guided regional training Pixel-level video prediction is a computationally intensive task that often requires specialised clusters with graphic processing units (GPUs) to generate forecasts quickly enough during inference. This challenge grows with increasing image quality, making it nearly impossible for satellites with lower resolution to handle. Additionally, when factoring in the time required to fit and update the model, the problem becomes even more significant. To address this issue, the Error-Guided Regional Training (ERT) method has been proposed, based on the following hypothesis: Hypothesis 1. A model trained on a specific representative pixel can be extrapolated to similar areas. According to this hypothesis, a multi-classifier methodology is proposed. Each individual model is trained using its respective representative pixels and can then be applied to the entire image. Based on this approach, the following algorithm is proposed in Algorithm 1. Knowledge-Based Systems 323 (2025) 113692 5 E.L. Ortiz et al. Table 3 Characteristics of the devices used in this work. BlueField 2.0 Raspberry Pi 5 Server Desktop PC CPU ARMv8 A72 ARM Cortex A76 AMD Ryzen 7 5800X intel Core i7 12700 Cores 8 4 16 20 GPU – – GeForce RTX 4090 GeForce RTX 4060 RAM 16 GB 8 GB 64 GB 32 GB OS Ubuntu 20.04 Raspberry OS Ubuntu 20.04 Ubuntu 22.04 kW / h 6.4 5 – – Algorithm 1 Error-guided Regional Training algorithm. 1: Input: Image 𝐼, stopping criterion 𝜖 2: Initialize: Set of representative pixels 𝑆= ∅ 3: Initialize: Set of representative models 𝑀= ∅ 4: Initialize: Set of assignations 𝐷=𝑀←←→ [] 5: 6: Select an initial pixel 𝑝 from the image 𝐼 7: Add pixel 𝑝 to the set of representative pixels 𝑆 8: 9: while stopping criterion is not met do 10: Initialize and train a model 𝑚 on pixel 𝑝 11: Extrapolate model 𝑚 across the entire image 𝐼 12: Compute the error across the image 13: Update D: Assign the best 𝑚 to each 𝑝𝑖∈𝐼 14: Identify the pixel 𝑝max with the largest error 15: Add 𝑝max to the set of representative pixels 𝑆 16: Add 𝑚 to the set of representative models 𝑀 17: Assign the pixel 𝑝 to 𝑝max 18: end while 19: 20: Output: Set of assignations 𝐷, Set of trained models 𝑀, set of representative pixels 𝑆 It is important to note that this approach significantly reduces the memory required both for input and to store the model, as the model is simplified to its minimum form. Furthermore, the process can be easily parallelised, drastically reducing training and inference time by several orders of magnitude. An application of this method, comparing state-ofthe-art approaches with an ESN-based model utilising ERT, is presented in Section 5.2. 4. Experimental setup This section outlines the key components used in the experimentation process of this work. Section 4.1 provides an overview of the devices used to measure model performance. Section 4.2 presents the dataset and its main characteristics. Section 4.3 lists the models used for comparison. Section 4.4 define the metrics employed during the evaluation, while Section 4.5. Finally, Section 4.6 describes the hyperparameter tuning process to achieve optimal configuration. 4.1. Hardware Due to the dependence of training times on the hardware used, the specific configurations used in this study are detailed below. One of the key purposes of this study is to demonstrate that these models can be effectively trained on small consumer devices such as Raspberry Pi units. Consequently, we have incorporated the characteristics of such devices into our configuration. The hardware specifications, which cover various components required for efficient processing and analysis of our models and datasets, are described in the Table 3. 4.2. Datasets In the initial phase of our study, we will use the CloudCast dataset to perform several experiments, using the entire region of central Europe as a benchmark. 4.2.1. CloudCast The CloudCast dataset is a satellite-based resource designed to enhance cloud forecasting models. It comprises 70,080 high-resolution images, each annotated at the pixel level to identify 10 different types of clouds and 5 types of no-clouds. These images have a spatial resolution of 928 × 1530 pixels (equivalent to 3 × 3 km per pixel) and are captured at 15 min intervals across Europe, spanning January 1, 2017, to December 31, 2018. When working with this dataset, the ultimate goal is: Given a target pixel and its neighbourhood, and a historical sequence of cloud types in them, predict the cloud type in the target pixel for the next 4 time steps. Each pixel of the dataset contains a value between 0 and 14, indicating the class to which the pixel belongs at that time. These values correspond to the following classes: 0. Cloud-free land 1. Cloud-free sea 2. Snow over land 3. Sea ice 4. No clouds or missing data 5. Very loud clouds 6. Low clouds 7. Mid-level clouds 8. High opaque clouds 9. Very high opaque clouds 10. Fractional clouds 11. High semitransparent thin clouds 12. High semitransparent moderately thick clouds 13. High semitransparent thick clouds 14. High semitransparent above low or medium clouds The first four classes correspond to cloud-free land, cloud-free sea, snow over land, and sea ice. Although colours can be assigned to the images for visualisation purposes, as illustrated in Fig. 5, it is essential to note that these four classes are removed during preprocessing of the dataset. Consequently, the final dataset only comprises classes ranging from 4 to 14. Therefore, we are not working with three-channel images but with matrices whose values fall within the discrete interval [4-14]. See Fig. 6. During the comparative phase of ESN-based models, we use exclusively the first 50,000 instances of the dataset, of which the first 49,000 are allocated for training the models presented in Section 5.1, and the subsequent 1000 instances are used for testing. The MWESN model, which will be discussed later, requires an additional validation set to optimise the parameters of the PSO algorithm. For this purpose, we select a subset from the training data, resulting in the following distribution for MWESN: 48,000 instances for training, 1000 for validation, and 1000 for testing, ensuring that all models make predictions over the same time period. Subsequently, for the comparison with state-of-the-art models, we use the complete dataset, that is, 52,416 instances for training and Knowledge-Based Systems 323 (2025) 113692 6 E.L. Ortiz et al. Fig. 5. CloudCast sample. Fig. 6. CloudCast 128 × 128 dataset sample after preprocess. 17,664 for testing, so that all models are evaluated under the same conditions. A particular aspect of this phase is that the original cloud classes from CloudCast are grouped into four superclasses. Since CloudCast is based on real meteorological measurements, class imbalance is inherent to the dataset. Some categories, such as specific cloud types or certain weather conditions, are naturally underrepresented due to their low frequency in the historical records. This uneven distribution presents an additional challenge, as models must be capable of achieving good overall performance without compromising their ability to correctly predict the less frequent classes. To mitigate this issue, when evaluating the models used in [1] with this dataset, the original 11 classes were grouped into 4 superclasses, which significantly reduces the class imbalance, although it does not eliminate it completely. The distribution of these classes after grouping is shown in Table 4. The authors also offer a downscaled version of this dataset with a spatial resolution of 128 × 128 pixels (equivalent to 15 × 15 km per pixel), which is the version employed in this work. The CloudCast dataset aims to improve the accuracy of weather predictions by providing detailed and comprehensive cloud coverage data. It is stored in the Network Common Data Form (NetCDF) format, making it accessible and compatible with a wide range of data analysis tools and frameworks. This dataset is applied across diverse research areas and applications, including weather forecasting, climate modelling, environmental monitoring, energy management, agricultural planning, disaster preparedness, and resource allocation optimisation in cloud computing infrastructures. Table 4 Class distribution in the Cloudcast dataset. Class Training Test Total Day Night Ungrouped 4 (Clear sky) 26.5% 32.1% 27.9% 29.5% 26.5% 5 (Low clouds) 12.8% 13.5% 13.0% 13.5% 12.3% 6 (Low clouds) 12.4% 11.2% 12.1% 12.6% 11.7% 7 (Medium clouds) 12.0% 9.0% 11.2% 10.7% 11.8% 8 (High clouds) 9.6% 9.6% 9.6% 9.4% 9.7% 9 (High clouds) 0.8% 0.7% 0.8% 0.8% 0.8% 10 (Low clouds) 7.8% 7.9% 7.8% 8.4% 7.1% 11 (High clouds) 3.5% 3.5% 3.5% 3.7% 3.2% 12 (High clouds) 6.4% 6.2% 6.4% 3.4% 9.6% 13 (High clouds) 5.6% 4.0% 5.2% 3.8% 6.8% 14 (High clouds) 2.6% 2.3% 2.5% 4.4% 0.4% Grouped 0 Clear sky 26.5% 32.1% 27.9% 29.5% 26.5% 1 Low clouds 33.0% 32.6% 32.9% 34.4% 31.1% 2 Medium clouds 12.0% 9.0% 11.3% 10.7% 11.8% 3 High clouds 28.5% 26.3% 27.9% 25.4% 30.6% Fig. 7. ESN. Fig. 8. MRESN. 4.3. Model comparison This subsection outlines the various models utilised in the subsequent analysis, each tailored to classification tasks with modifications to the output layer as described above. The comparison is divided into two phases. Firstly, a comprehensive selection of ESNs architectures spanning a wide spectrum are compared against the architecture proposed in Section 5.3. During the first phase, the models are evaluated on specific representative pixels. Secondly, the best performing model from the first phase is compared with the state-of-the-art models found in the literature. During the second phase, the ERT technique is applied to extrapolate the information learned by the model to the entire region studied. In both steps, the models included here were carefully selected to investigate their efficacy within the problem domain. Regarding the first phase, the models studied are the following ones: Vanilla-ESN: The foundational architecture of ESN, using a single reservoir. This model serves as a reference point against which the performance of more complex architectures is evaluated. Fig. 7. Multi-Reservoir ESN (MRESN): It integrates multiple reservoirs in one single layer, each independent of the others. The inclusion of parallel reservoirs encourages richer representations of the input data. Fig. 8. Deep ESN (DESN): Leveraging the concept of depth in neural network architectures, the deep ESN extends the traditional ESN framework by incorporating multiple layers of reservoirs. This hierarchical arrangement enables the network to capture intricate temporal dependencies across varying time scales, facilitating more nuanced pattern recognition and prediction. Fig. 9. Deep ESN with Input-to-All (DESNIA): As an extension of the deep ESN paradigm, deep input-to-all ESN extends the connectivity between layers by establishing direct connections between the input and Knowledge-Based Systems 323 (2025) 113692 7 E.L. Ortiz et al. Fig. 9. DESN. Fig. 10. DESNIA. Fig. 11. DWESN. the reservoirs of each layer. This comprehensive input dissemination mechanism aims to promote the flow of information throughout the network, thereby enhancing its learning capability. Fig. 10. Deep-Wide-ESN (DWESN): This architecture consists of launching a series of deepESN-type architectures in parallel. The weights of the output layer are calculated using the final states of each of them. Fig. 11. DWESN with Input-to-all (DWESNIA): This architecture is similar to the DWESN architecture. The difference is that in this architecture the input data is used as input to the intermediate layers, enriching the information that reaches the hidden reservoirs. Fig. 12. Deep-MRESN (DMRESN): In this architecture, a number of MRESNtype layers are combined. In each layer, the reservoirs operate independently of their layer partners, but the layers are connected in a fully-connected fashion. Fig. 13. Deep-MRESN with Input-to-all (DMRESNIA): This architecture is a modification of the DMRESN architecture. As in the DWESNIA architecture, the input data is used as input for the intermediate layers, enriching the information that reaches the hidden reservoirs. Fig. 14. Each of these models has a unique architectural configuration and has been adapted for classification tasks by incorporating the output layer modification described above. In Section 5, we will analyse their performance in relation to the research objectives. During the second phase the ESN-based architectures are compared against state-of-the-art video prediction methods studied in [1]. In this work, the authors used the CloudCast dataset to test the performance of various models. Since these models are fed exclusively from this dataset and do not use additional information such as humidity and temperature data, which is often included in similar tasks, comparing our models with this work will provide a fair assessment of model performance. The tested models were: Fig. 12. DWESNIA. Fig. 13. DMRESN. •Optical Flow Algorithm (TV-L1) •Autoencoder ConvLSTM (AE-ConvLSTM) •Multi-Stage Dynamic Generative Adversarial Networks (MD-GAN) 4.4. Evaluation Our task focuses on classifying the target pixel into one of the 11 or 4 possible classes, depending on the experimentation phase performed. In the first phase, the evaluation is conducted across all classes available in the dataset to assess performance on the more complex task. Subsequently, in the second phase, the evaluation is aligned with the original CloudCast study to enable a direct comparison of results. To ensure a rigorous evaluation of the models, the dataset is divided into training and test sets. For the ESN models presented in Section 5.1, from the total dataset of 70,080 instances, 49,000 are used for training and 1000 for testing. The MWESN model requires a validation set to optimise the PSO parameters; therefore, the training set is further split, reserving the last 1000 instances for validation. Consequently, for MWESN, we use 48,000 instances for training, 1000 for testing, and 1000 for final validation, ensuring that all models perform predictions over the same period. In the final stage of our experiments, where the ERT method is applied, we adopt the same conditions as those specified for models in the CloudCast study, using 52,416 instances for training and 17,664 for testing. In order to provide a comprehensive evaluation of model performance, we employ a set of standard classification metrics derived from the confusion matrix: accuracy, precision, recall, and F1-score. These metrics provide complementary insights into the predictive capabilities of the models. A successful classification occurs when the predicted class matches the expected output, whereas any deviation constitutes an error. Accuracy measures the overall correctness of the model and is defined as the proportion of correctly classified instances out of the total number of instances, as shown in Eq. (4). Knowledge-Based Systems 323 (2025) 113692 8 E.L. Ortiz et al. Fig. 14. DMRESNIA. Accuracy =Number of Correct Predictions Total Number of Predictions (4) To further analyse performance, we also compute precision, recall, and F1-score for each class and report the macro-averaged values. Precision (Eq. (5)) quantifies the proportion of correct positive predictions among all positive predictions made by the model. Recall (Eq. (6)) measures the ability of the model to correctly identify all actual positive cases. The F1-score (Eq. (7)), which is the harmonic mean of precision and recall, provides a balanced metric that accounts for both false positives and false negatives. Precision =True Positives True Positives +False Positives (5) Recall =True Positives True Positives +False Negatives (6) F1-score = 2 × Precision ×Recall Precision +Recall (7) The use of these metrics ensures a thorough evaluation of the models, particularly in scenarios involving class imbalance, and allows for a deeper understanding of the strengths and weaknesses of each approach. 4.5. Model training An important consideration is that while some experiments apply the trained model to all pixels in the image to perform full scene prediction, the training process itself focuses on a specific target pixel and teaches the network to understand the influence of neighbouring pixels on that target. First, a target pixel is selected from the CloudCast dataset. Next, a radius of pixels around this target is determined. For our experiments, we have chosen three different target pixels (Fig. 15): 1. Pixel (30,30): A region in North Sea. 2. Pixel (70,105): A region in the Alps. 3. Pixel (113,13): A region in the Cantabrean Sea. We use a radius of 3 pixels around the targets, which results in a 7 × 7 pixel window representing the neighbourhood of the target pixel. This gives us a time series with 49 new values, the value of each pixel of our window, at each time point t. Some of these values have a direct influence on the target pixel at time t+1, but the influence of others on the target pixel is not so direct and takes a few more steps to arrive or may not have any influence on the target at all. What we want is that the network learns the relationship between these input values at the target pixel over time. Fig. 16 illustrates this concept. At each time step, the trained models give us the prediction of the next four steps, which we will refer to as ℎ1, ℎ2, ℎ3 and ℎ4. As the time resolution of CloudCast is 15 min, this gives us a prediction horizon of 1 h in ℎ4, which allows us to make comparisons with other models used with this dataset. Fig. 15. Target pixels from the CloudCast dataset used for training. Pixel marked as 1 corresponds to the North Sea, pixel marked as 2 corresponds to the Alps and pixel marked as 3 corresponds to Cantabrian Sea. Fig. 16. Example of influence of the neighbouring pixels on the target pixel (green cell). The pixel marked ‘‘1’’ needs only 1 time step for its information to reach the target, the pixel marked ‘‘2’’ needs 5 time steps. 4.6. Hyperparameter selection The selection of hyperparameters in ESNs has a crucial impact on their performance. Hyperparameters determine the dynamics and ability of the network to model complex temporal patterns. Proper tuning of these parameters ensures that the network can effectively capture the underlying relationships in the data, balancing between model complexity and computational efficiency. 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López Ortiz received a degree in computer engineering from the University of Seville (Spain) in September 2019 and a master’s degree in logic, computation and artificial intelligence in October 2020. Since June 2020, he has been a researcher at the University of Seville (Spain) in the field of multi-agent systems and neural networks. He has been working on different projects at the University of Seville since 2019, and is currently a Ph.D. student at the same university. Manuel Jiménez received a degree in Software Engineering from the University of Seville (Spain) in 2018 and a Ph.D. degree in Computer Engineering from the University of Seville (Spain) in 2022, and has been a researcher at the same university since December 2023. He is an Assistant Professor at the Department of Languages and Computer Systems at the University of Seville (Spain). Knowledge-Based Systems 323 (2025) 113692 16 E.L. Ortiz et al. Luis Miguel Soria Morillo received a degree in Computer Engineering and a Ph.D. degree in Computer Engineering from the University of Seville (Spain) in 2009 and 2011 respectively. He is an Assistant Professor at the Department of Languages and Computer Systems at the University of Seville. His research focuses on Activity Recognition and Ubiquitous Computing. Juan A. Álvarez-García holds a Computer Engineering degree from the University of Seville (Spain). He is an Associate Professor at the Department of Languages and Computer Systems at the University of Seville. His research focuses on Human Behaviour Analysis and Activity Recognition using wearable/mobile devices or computer vision from CCTV cameras. J.J. Vegas Olmos received the B.Sc. and the M.Sc. in Telecommunications and Electronic Engineering, respectively, in 2001 and 2003. He obtained his Ph.D. degree from the Eindhoven University of Technology, The Netherlands, in 2006. He also holds an MA in East Asian Studies, a BEc in Business Administration and an MBA. He was a Research Fellow at Osaka University, Japan, from 2006 to 2008, and a Research Associate at the Central Research Laboratory, Hitachi Ltd, until 2011. He is now the Research Program Coordinator for NVIDIA Corporation in Software Architecture. Knowledge-Based Systems 323 (2025) 113692 17