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Keywords = complex-valued neural networks

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37 pages, 24514 KB  
Article
Prediction and Reliability Analysis of the Pressuremeter Modulus of the Deep Overburden in Hydraulic Engineering Based on Machine Learning and Physical Mechanisms
by Hanyu Guo, Deshan Cui, Qingchun Li, Qiong Chen and Lin Lai
Appl. Sci. 2025, 15(19), 10643; https://doi.org/10.3390/app151910643 - 1 Oct 2025
Abstract
In the process of large-scale water conservancy and hydropower station construction in the southwest region of China, obtaining the deep overburden pressuremeter modulus Em is of great significance for the calculation of foundation bearing capacity and dam foundation settlement. However, due to [...] Read more.
In the process of large-scale water conservancy and hydropower station construction in the southwest region of China, obtaining the deep overburden pressuremeter modulus Em is of great significance for the calculation of foundation bearing capacity and dam foundation settlement. However, due to the complex nature of the soil properties in deep overburden layers, conducting deep-hole pressuremeter tests is challenging, time-consuming, and costly. In order to efficiently and accurately obtain the pressuremeter modulus of deep overburden, this paper takes the deep overburden in the river valley where a large hydropower station dam is located in the southwest region as the research object. It proposes a method based on data-driven prediction of the pressuremeter modulus and combines it with the physical mechanism to carry out the reliability analysis of the prediction results. By constructing a database of soil physical and mechanical parameters, including the pressuremeter modulus, the prediction performance of Random Forest (RF), Support Vector Regression (SVR), and BP Neural Network on the pressure modulus was evaluated. The Particle Swarm Optimization (PSO) was utilized for hyperparameter optimization to enhance the reliability of prediction results. The results indicate that the RF and PSO-RF models exhibit a comprehensive advantage for accurately predicting the pressuremeter modulus. The prediction results of the model for new data have a strong correlation with the results calculated by the Menard formula, which demonstrates the reliability of the model. Therefore, establishing the relationship between the conventional physical and mechanical parameters of deep overburden and the pressuremeter modulus, and predicting the pressuremeter modulus based on data-driven methods, has significant engineering value for obtaining the pressuremeter modulus of deep overburden efficiently, economically, and reliably. It also holds significant importance for the extended application of machine learning in the field of soil parameter prediction. Full article
(This article belongs to the Section Civil Engineering)
37 pages, 1458 KB  
Article
Ensemble-IDS: An Ensemble Learning Framework for Enhancing AI-Based Network Intrusion Detection Tasks
by Ismail Bibers, Osvaldo Arreche, Walaa Alayed and Mustafa Abdallah
Appl. Sci. 2025, 15(19), 10579; https://doi.org/10.3390/app151910579 - 30 Sep 2025
Abstract
Modern cybersecurity threats continue to evolve in both complexity and prevalence, demanding advanced solutions for intrusion detection. Traditional AI-based detection systems face significant challenges in model selection, as performance varies considerably across different network environments and attack scenarios. To overcome these limitations, we [...] Read more.
Modern cybersecurity threats continue to evolve in both complexity and prevalence, demanding advanced solutions for intrusion detection. Traditional AI-based detection systems face significant challenges in model selection, as performance varies considerably across different network environments and attack scenarios. To overcome these limitations, we propose a comprehensive ensemble learning approach that systematically integrates feature selection, model optimization, and rigorous evaluation components. Our framework evaluates fourteen distinct machine learning approaches, ranging from individual classifiers to sophisticated ensemble methods including bagging, boosting, and hybrid stacking/blending architectures. These techniques are applied to multiple base algorithms such as neural networks and tree-based models. Extensive testing was conducted on two complementary benchmark datasets (RoEduNet-SIMARGL2021 and CICIDS-2017) to assess detection capabilities across varied threat landscapes. Our experimental results revealed several key findings. Ensemble techniques universally surpass standalone models in detection accuracy, with random forest achieving the best performance on RoEduNet-SIMARGL2021, while the blending and bagging methods approach yielded perfect scores (F1 > 0.996) on CICIDS-2017. Feature selection via information gain demonstrated particular value, reducing model training times by 94% while maintaining detection accuracy. Among ensemble methods, XGBoost showed exceptional computational efficiency, whereas stacking and blending architectures delivered maximum accuracy at the expense of greater resource requirements. This research provides practical guidance for security professionals in model selection based on specific operational constraints and threat profiles. To support community advancement, we have made our complete framework publicly available, facilitating reproducibility and future innovation in intrusion detection systems. Full article
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21 pages, 831 KB  
Article
TSAD: Transformer-Based Semi-Supervised Anomaly Detection for Dynamic Graphs
by Jin Zhang and Ke Feng
Mathematics 2025, 13(19), 3123; https://doi.org/10.3390/math13193123 - 30 Sep 2025
Abstract
Anomaly detection aims to identify abnormal instances that significantly deviate from normal samples. With the natural connectivity between instances in the real world, graph neural networks have become increasingly important in solving anomaly detection problems. However, existing research mainly focuses on static graphs, [...] Read more.
Anomaly detection aims to identify abnormal instances that significantly deviate from normal samples. With the natural connectivity between instances in the real world, graph neural networks have become increasingly important in solving anomaly detection problems. However, existing research mainly focuses on static graphs, while there is less research on mining anomaly patterns in dynamic graphs, which has important application value. This paper proposes a Transformer-based semi-supervised anomaly detection framework for dynamic graphs. The framework adopts the Transformer architecture as the core encoder, which can effectively capture long-range dependencies and complex temporal patterns between nodes in dynamic graphs. By introducing time-aware attention mechanisms, the model can adaptively focus on important information at different time steps, thereby better understanding the evolution process of graph structures. The multi-head attention mechanism of Transformer enables the model to simultaneously learn structural and temporal features of nodes, while positional encoding helps the model understand periodic patterns in time series. Comprehensive experiments on three real datasets show that TSAD significantly outperforms existing methods in anomaly detection accuracy, particularly demonstrating excellent performance in label-scarce scenarios. Full article
(This article belongs to the Special Issue New Advances in Graph Neural Networks (GNNs) and Applications)
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18 pages, 9355 KB  
Article
Two-Dimensional Image Lempel–Ziv Complexity Calculation Method and Its Application in Defect Detection
by Jiancheng Yin, Wentao Sui, Xuye Zhuang, Yunlong Sheng and Yongbo Li
Entropy 2025, 27(10), 1014; https://doi.org/10.3390/e27101014 - 27 Sep 2025
Abstract
Although Lempel–Ziv complexity (LZC) can reflect changes in object characteristics by measuring changes in independent patterns in the signal, it can only be applied to one-dimensional time series and cannot be directly applied to two-dimensional images. To address this issue, this paper proposed [...] Read more.
Although Lempel–Ziv complexity (LZC) can reflect changes in object characteristics by measuring changes in independent patterns in the signal, it can only be applied to one-dimensional time series and cannot be directly applied to two-dimensional images. To address this issue, this paper proposed a two-dimensional Lempel–Ziv complexity by combining the concept of local receptive field in convolutional neural networks. This extends the application scenario of LZC from one-dimensional time series to two-dimensional images, further broadening the scope of application of LZC. First, the pixels and size of the image were normalized. Then, the image was encoded according to the sorting of normalized values within the 4 × 4 region. Next, the encoding result of the image was rearranged into a vector by row. Finally, the Lempel–Ziv complexity of the image could be obtained based on the rearranged vector. The proposed method was further used for defect detection in conjunction with the dilation operator and Sobel operator, and validated by two practical cases. The results showed that the proposed method can effectively identify independent pattern changes in images and can be used for defect detection. The accuracy rate of defect detection can reach 100%. Full article
(This article belongs to the Special Issue Complexity and Synchronization in Time Series)
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16 pages, 25234 KB  
Article
Real-Time Observer and Neuronal Identification of an Erbium-Doped Fiber Laser
by Daniel Alejandro Magallón-García, Didier López-Mancilla, Rider Jaimes-Reátegui, Juan Hugo García-López, Guillermo Huerta-Cuellar and Luis Javier Ontañon-García
Photonics 2025, 12(10), 955; https://doi.org/10.3390/photonics12100955 - 26 Sep 2025
Abstract
This paper presents the implementation of a real-time nonlinear state observer applied to an erbium-doped fiber laser system. The observer is designed to estimate population inversion, a state variable that cannot be measured directly due to the physical limitations of measurement devices. Taking [...] Read more.
This paper presents the implementation of a real-time nonlinear state observer applied to an erbium-doped fiber laser system. The observer is designed to estimate population inversion, a state variable that cannot be measured directly due to the physical limitations of measurement devices. Taking advantage of the fact that the laser intensity can be measured in real time, an observer was developed to reconstruct the dynamics of population inversion from this measurable variable. To validate and strengthen the estimate obtained by the observer, a Recurrent Wavelet First-Order Neural Network (RWFONN) was implemented and trained to identify both state variables: the laser intensity and the population inversion. This network efficiently captures the system’s nonlinear dynamic properties and complements the observer’s performance. Two metrics were applied to evaluate the accuracy and reliability of the results: the Euclidean distance and the mean square error (MSE), both of which confirm the consistency between the estimated and expected values. The ultimate goal of this research is to develop a neural control architecture that combines the estimation capabilities of state observers with the generalization and modeling power of artificial neural networks. This hybrid approach opens up the possibility of developing more robust and adaptive control systems for highly dynamic, complex laser systems. Full article
(This article belongs to the Special Issue Lasers and Complex System Dynamics)
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39 pages, 10748 KB  
Article
Modeling the Dynamics of the Jebel Zaghouan Karst Aquifer Using Artificial Neural Networks: Toward Improved Management of Vulnerable Water Resources
by Emna Gargouri-Ellouze, Tegawende Arnaud Ouedraogo, Fairouz Slama, Jean-Denis Taupin, Nicolas Patris and Rachida Bouhlila
Hydrology 2025, 12(10), 250; https://doi.org/10.3390/hydrology12100250 - 26 Sep 2025
Abstract
Karst aquifers are critical yet vulnerable water resources in semi-arid Mediterranean regions, where structural complexity, nonlinearity, and delayed hydrological responses pose significant modeling challenges under increasing climatic and anthropogenic pressures. This study examines the Jebel Zaghouan aquifer in northeastern Tunisia, aiming to simulate [...] Read more.
Karst aquifers are critical yet vulnerable water resources in semi-arid Mediterranean regions, where structural complexity, nonlinearity, and delayed hydrological responses pose significant modeling challenges under increasing climatic and anthropogenic pressures. This study examines the Jebel Zaghouan aquifer in northeastern Tunisia, aiming to simulate its natural discharge dynamics prior to intensive exploitation (1915–1944). Given the fragmented nature of historical datasets, meteorological inputs (rainfall, temperature, and pressure) were reconstructed using a data recovery process combining linear interpolation and statistical distribution fitting. The hyperparameters of the artificial neural network (ANN) model were optimized through a Bayesian search. Three deep learning architectures—Multi-Layer Perceptron (MLP), Convolutional Neural Network (CNN), and Long Short-Term Memory (LSTM)—were trained to model spring discharge. Model performance was evaluated using Kling–Gupta Efficiency (KGE′), Nash–Sutcliffe Efficiency (NSE), and R2 metrics. Hydrodynamic characterization revealed moderate variability and delayed discharge response, while isotopic analyses (δ18O, δ2H, 3H, 14C) confirmed a dual recharge regime from both modern and older waters. LSTM outperformed other models at the weekly scale (KGE′ = 0.62; NSE = 0.48; R2 = 0.68), effectively capturing memory effects. This study demonstrates the value of combining historical data rescue, ANN modeling, and hydrogeological insight to support sustainable groundwater management in data-scarce karst systems. Full article
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23 pages, 3115 KB  
Article
Deep Learning-Based Prediction of Multi-Species Leaf Pigment Content Using Hyperspectral Reflectance
by Ziyu Wang and Duanyang Xu
Remote Sens. 2025, 17(19), 3293; https://doi.org/10.3390/rs17193293 - 25 Sep 2025
Abstract
Leaf pigment composition and concentration are crucial indicators of plant physiological status, photosynthetic capacity, and overall ecosystem health. While spectroscopy techniques show promise for monitoring vegetation growth, phenology, and stress, accurately estimating leaf pigments remains challenging due to the complex reflectance properties across [...] Read more.
Leaf pigment composition and concentration are crucial indicators of plant physiological status, photosynthetic capacity, and overall ecosystem health. While spectroscopy techniques show promise for monitoring vegetation growth, phenology, and stress, accurately estimating leaf pigments remains challenging due to the complex reflectance properties across diverse tree species. This study introduces a novel approach using a two-dimensional convolutional neural network (2D-CNN) coupled with a genetic algorithm (GA) to predict leaf pigment content, including chlorophyll a and b content (Cab), carotenoid content (Car), and anthocyanin content (Canth). Leaf reflectance and biochemical content measurements taken from 28 tree species were used in this study. The reflectance spectra ranging from 400 nm to 800 nm were encoded as 2D matrices with different sizes to train the 2D-CNN and compared with the one-dimensional convolutional neural network (1D-CNN). The results show that the 2D-CNN model (nRMSE = 11.71–31.58%) achieved higher accuracy than the 1D-CNN model (nRMSE = 12.79–55.34%) in predicting leaf pigment contents. For the 2D-CNN models, Cab achieved the best estimation accuracy with an nRMSE value of 11.71% (R2 = 0.92, RMSE = 6.10 µg/cm2), followed by Car (R2 = 0.84, RMSE = 1.03 µg/cm2, nRMSE = 12.29%) and Canth (R2 = 0.89, RMSE = 0.35 µg/cm2, nRMSE = 31.58%). Both 1D-CNN and 2D-CNN models coupled with GA using a subset of the spectrum produced higher prediction accuracy in all pigments than those using the full spectrum. Additionally, the generalization of 2D-CNN is higher than that of 1D-CNN. This study highlights the potential of 2D-CNN approaches for accurate prediction of leaf pigment content from spectral reflectance data, offering a promising tool for advanced vegetation monitoring. Full article
(This article belongs to the Section Forest Remote Sensing)
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15 pages, 3510 KB  
Article
Real-Time Vehicle Emergency Braking Detection with Moving Average Method Based on Accelerometer and Gyroscope Data
by Hadi Pranoto, Abdi Wahab, Yoppy Yoppy, Muhammad Imam Sudrajat, Dwi Mandaris, Ihsan Supono, Adindra Vickar Ega, Tyas Ari Wahyu Wijanarko and Hutomo Wahyu Nugroho
Vehicles 2025, 7(4), 106; https://doi.org/10.3390/vehicles7040106 - 25 Sep 2025
Abstract
Emergency braking detection plays a vital role in enhancing road safety by identifying potentially hazardous driving behaviors. While existing methods rely heavily on artificial intelligence and computationally intensive algorithms, this paper proposes a lightweight, real-time algorithm for distinguishing emergency braking from non-emergency events [...] Read more.
Emergency braking detection plays a vital role in enhancing road safety by identifying potentially hazardous driving behaviors. While existing methods rely heavily on artificial intelligence and computationally intensive algorithms, this paper proposes a lightweight, real-time algorithm for distinguishing emergency braking from non-emergency events using accelerometer and gyroscope signals. The proposed approach applies magnitude calculations and a moving average filters algorithm to preprocess inertial data collected from a six-axis IMU sensor. By analyzing peak values of acceleration and angular velocity, the algorithm successfully separates emergency braking from other events such as regular braking, passing over speed bumps, or traversing damaged roads. The results demonstrate that emergency braking exhibits a unique short-pulse pattern in acceleration and low angular velocity, distinguishing it from other high-oscillation disturbances. Furthermore, varying the window length of the moving average impacts classification accuracy and computational cost. The proposed method avoids the complexity of neural networks while retaining high detection accuracy, making it suitable for embedded and real-time vehicular systems, such as early warning applications for fleet management. Full article
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26 pages, 7282 KB  
Article
Simulation of Urban Sprawl Factors in Medium-Scale Metropolitan Areas Using a Cellular Automata-Based Model: The Case of Erzurum, Turkey
by Şennur Arınç Akkuş, Ahmet Tortum and Dilan Kılıç
Appl. Sci. 2025, 15(19), 10377; https://doi.org/10.3390/app151910377 - 24 Sep 2025
Viewed by 34
Abstract
Urban development is the planned growth of cities that takes into account ecological issues, the needs of urban life, social and technical equipment standards, and quality of life. However, as a result of policies implemented by decision-makers and users, both planned and unplanned, [...] Read more.
Urban development is the planned growth of cities that takes into account ecological issues, the needs of urban life, social and technical equipment standards, and quality of life. However, as a result of policies implemented by decision-makers and users, both planned and unplanned, urban space is expanding spatially outwards from the city, while also experiencing densification in vacant areas within the city and functional transformations in land use. This process, known as urban sprawl, has been intensely debated over the past century. Making the negative effects of urban sprawl measurable and understandable from a scientific perspective is critically important for sustainable urban planning and management. Transportation surfaces hold a significant share in the land use patterns of expanding cities in physical space, and accessibility is one of the main driving forces behind land use change. Therefore, the most significant consequence of urban sprawl is the increase in urban mobility, which is shaped by the needs of urban residents to access urban functions. This increase poses risk factors for the planning period in terms of time, cost, and especially environmental impact. Urban space has a dynamic and complex structure. Planning is based on being able to guess how this structure will change over time. At first, geometric models were used to study cities, but as time went on and the network of relationships became more complicated, more modern and technological methods were needed. Artificial Neural Networks, Support Vector Machines, Agent-Based Models, Markov Chain Models, and Cellular Automata, developed using computer-aided design technologies, can be cited as examples of these approaches. In this study, the temporal change in urban sprawl and its relationship with influencing factors will be revealed using the SLEUTH model, which is one of the cellular automata-based urban simulation models. Erzurum, one of the medium-sized metropolitan cities that gained importance after the conversion of provincial borders into municipal borders with the Metropolitan Law No. 6360, has been selected as the case study area for this research. The urban sprawl process and determining factors of Erzurum will be analyzed using the SLEUTH model. By creating a simulation model of the current situation within the specified time periods and generating future scenarios, the aim is to develop planning decisions with sustainable, ecological, and optimal size and density values. Full article
(This article belongs to the Section Civil Engineering)
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15 pages, 678 KB  
Article
Comparing PINN and Symbolic Transform Methods in Modeling the Nonlinear Dynamics of Complex Systems: A Case Study of the Troesch Problem
by Rafał Brociek, Mariusz Pleszczyński, Jakub Błaszczyk, Maciej Czaicki, Christian Napoli and Giacomo Capizzi
Mathematics 2025, 13(18), 3045; https://doi.org/10.3390/math13183045 - 22 Sep 2025
Viewed by 203
Abstract
Nonlinear complex systems exhibit emergent behavior, sensitivity to initial conditions, and rich dynamics arising from interactions among their components. A classical example of such a system is the Troesch problem—a nonlinear boundary value problem with wide applications in physics and engineering. In this [...] Read more.
Nonlinear complex systems exhibit emergent behavior, sensitivity to initial conditions, and rich dynamics arising from interactions among their components. A classical example of such a system is the Troesch problem—a nonlinear boundary value problem with wide applications in physics and engineering. In this work, we investigate and compare two distinct approaches to solving this problem: the Differential Transform Method (DTM), representing an analytical–symbolic technique, and Physics-Informed Neural Networks (PINNs), a neural computation framework inspired by physical system dynamics. The DTM yields a continuous form of the approximate solution, enabling detailed analysis of the system’s dynamics and error control, whereas PINNs, once trained, offer flexible estimation at any point in the domain, embedding the physical model into an adaptive learning process. We evaluate both methods in terms of accuracy, stability, and computational efficiency, with particular focus on their ability to capture key features of nonlinear complex systems. The results demonstrate the potential of combining symbolic and neural approaches in studying emergent dynamics in nonlinear systems. Full article
(This article belongs to the Special Issue Nonlinear Dynamics, 2nd Edition)
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16 pages, 3394 KB  
Communication
Optimized Non-Linear Observer for a PMSM Speed Control System Integrating a Multi-Dimensional Taylor Network and Lyapunov Theory
by Chao Zhang, Ya-Qin Qiu and Zi-Ao Li
Modelling 2025, 6(3), 108; https://doi.org/10.3390/modelling6030108 - 19 Sep 2025
Viewed by 261
Abstract
Within the field of permanent magnet synchronous motor sensorless speed control systems, we present a novel scheme with a Multi-dimensional Taylor Network (MTN)-based nonlinear observer as the core, supplemented by two auxiliary MTN modules to realize closed-loop control: (1) MTN Model Identifier: Provides [...] Read more.
Within the field of permanent magnet synchronous motor sensorless speed control systems, we present a novel scheme with a Multi-dimensional Taylor Network (MTN)-based nonlinear observer as the core, supplemented by two auxiliary MTN modules to realize closed-loop control: (1) MTN Model Identifier: Provides real-time PMSM nonlinear dynamic feedback for the observer; (2) MTN Adaptive Inverse Controller: Compensates for load disturbances using the observer’s estimated states. The study focuses on optimizing the MTN observer to address key limitations of existing methods (high computational complexity, lack of stability guarantees, and low estimation accuracy). Compared with the neural network observer, this MTN-based scheme stands out due to its straightforward structure and significantly reduced approximately 40% computational complexity. Specifically, the intricate calculations and high resource consumption typically associated with neural network observers are circumvented. Subsequently, by leveraging Lyapunov theory, an adaptive learning rule for the MTN weights is meticulously devised, which seamlessly bridges the theoretical proof of the nonlinear observer’s stability. Simulation results demonstrate that the proposed MTN observer achieves rapid convergence of speed and position estimation errors (with steady-state errors within ±0.5% of the rated speed and ±0.02 rad for rotor position) after a transient period of less than 0.2 s. Even when stator resistance is increased by tenfold to simulate parameter variations, the observer maintains high estimation accuracy, with speed and position errors increasing by no more than 1.2% and 0.05 rad, respectively, showcasing strong robustness. These results collectively confirm the efficacy and practical value of the proposed scheme in PMSM sensorless speed control. Full article
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29 pages, 1718 KB  
Review
Bacillus Pectinases as Key Biocatalysts for a Circular Bioeconomy: From Green Extraction to Process Optimization and Industrial Scale-Up
by Fatima Zohra Kaissar, Khelifa Bouacem, Mohammed Lamine Benine, Sondes Mechri, Shubha Rani Sharma, Vishal Kumar Singh, Mahfoud Bakli, Seif El Islam Lebouachera and Giovanni Emiliani
BioTech 2025, 14(3), 74; https://doi.org/10.3390/biotech14030074 - 19 Sep 2025
Viewed by 467
Abstract
Pectins are high-value plant cell-wall polysaccharides with extensive applications in the food, pharmaceutical, textile, paper, and environmental sectors. Traditional extraction and processing methodologies rely heavily on harsh acids, high temperatures, and non-renewable solvents, generating substantial environmental and economic costs. This review consolidates recent [...] Read more.
Pectins are high-value plant cell-wall polysaccharides with extensive applications in the food, pharmaceutical, textile, paper, and environmental sectors. Traditional extraction and processing methodologies rely heavily on harsh acids, high temperatures, and non-renewable solvents, generating substantial environmental and economic costs. This review consolidates recent advances across the entire Bacillus–pectinase value chain, from green pectin extraction and upstream substrate characterization, through process and statistical optimization of enzyme production, to industrial biocatalysis applications. We propose a practical roadmap for developing high-efficiency, low-environmental-footprint enzyme systems that support circular bioeconomy objectives. Critical evaluation of optimization strategies, including submerged versus solid-state fermentation, response surface methodology, artificial neural networks, and design of experiments, is supported by comparative data on strain performance, fermentation parameters, and industrial titers. Sector-specific case studies demonstrate the efficacy of Bacillus pectinases in fruit-juice clarification, textile bio-scouring, paper bio-bleaching, bio-based detergents, coffee and tea processing, oil extraction, animal feed enhancement, wastewater treatment, and plant-virus purification. Remaining challenges, including enzyme stability in complex matrices, techno-economic scale-up, and structure-guided protein engineering, are identified. Future directions are charted toward CRISPR-driven enzyme design and fully integrated circular-economy bioprocessing platforms. Full article
(This article belongs to the Section Industry, Agriculture and Food Biotechnology)
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18 pages, 4570 KB  
Article
MultivariateSystem Identification of Differential Drive Robot: Comparison Between State-Space and LSTM-Based Models
by Diego Guffanti and Wilson Pavon
Sensors 2025, 25(18), 5821; https://doi.org/10.3390/s25185821 - 18 Sep 2025
Viewed by 211
Abstract
Modeling mobile robots is crucial to odometry estimation, control design, and navigation. Classical state-space models (SSMs) have traditionally been used for system identification, while recent advances in deep learning, such as Long Short-Term Memory (LSTM) networks, capture complex nonlinear dependencies. However, few direct [...] Read more.
Modeling mobile robots is crucial to odometry estimation, control design, and navigation. Classical state-space models (SSMs) have traditionally been used for system identification, while recent advances in deep learning, such as Long Short-Term Memory (LSTM) networks, capture complex nonlinear dependencies. However, few direct comparisons exist between these paradigms. This paper compares two multivariate modeling approaches for a differential drive robot: a classical SSM and an LSTM-based recurrent neural network. Both models predict the robot’s linear (v) and angular (ω) velocities using experimental data from a five-minute navigation sequence. Performance is evaluated in terms of prediction accuracy, odometry estimation, and computational efficiency, with ground-truth odometry obtained via a SLAM-based method in ROS2. Each model was tuned for fair comparison: order selection for the SSM and hyperparameter search for the LSTM. Results show that the best SSM is a second-order model, while the LSTM used seven layers, 30 neurons, and 20-sample sliding windows. The LSTM achieved a FIT of 93.10% for v and 90.95% for ω, with an odometry RMSE of 1.09 m and 0.23 rad, whereas the SSM outperformed it with FIT values of 94.70% and 91.71% and lower RMSE (0.85 m, 0.17 rad). The SSM was also more resource-efficient (0.00257 ms and 1.03 bytes per step) compared to the LSTM (0.0342 ms and 20.49 bytes). The results suggest that SSMs remain a strong option for accurate odometry with low computational demand while encouraging the exploration of hybrid models to improve robustness in complex environments. At the same time, LSTM models demonstrated flexibility through hyperparameter tuning, highlighting their potential for further accuracy improvements with refined configurations. Full article
(This article belongs to the Section Environmental Sensing)
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24 pages, 3544 KB  
Article
A Deep Learning Model Integrating EEMD and GRU for Air Quality Index Forecasting
by Mei-Ling Huang, Netnapha Chamnisampan and Yi-Ru Ke
Atmosphere 2025, 16(9), 1095; https://doi.org/10.3390/atmos16091095 - 18 Sep 2025
Viewed by 390
Abstract
Accurate prediction of the air quality index (AQI) is essential for environmental monitoring and sustainable urban planning. With rising pollution from industrialization and urbanization, particularly from fine particulate matter (PM2.5, PM10), nitrogen dioxide (NO2), and ozone (O [...] Read more.
Accurate prediction of the air quality index (AQI) is essential for environmental monitoring and sustainable urban planning. With rising pollution from industrialization and urbanization, particularly from fine particulate matter (PM2.5, PM10), nitrogen dioxide (NO2), and ozone (O3), robust forecasting tools are needed to support timely public health interventions. This study proposes a hybrid deep learning framework that combines empirical mode decomposition (EMD) and ensemble empirical mode decomposition (EEMD) with two recurrent neural network architectures: long short-term memory (LSTM) and gated recurrent unit (GRU). A comprehensive dataset from Xitun District, Taichung City—including AQI and 18 pollutant and meteorological variables—was used to train and evaluate the models. Model performance was assessed using root mean square error, mean absolute error, mean absolute percentage error, and the coefficient of determination. Both LSTM and GRU models effectively capture the temporal patterns of air quality data, outperforming traditional methods. Among all configurations, the EEMD-GRU model delivered the highest prediction accuracy, demonstrating strong capability in modeling high-dimensional and nonlinear environmental data. Furthermore, the incorporation of decomposition techniques significantly reduced prediction error across all models. These findings highlight the effectiveness of hybrid deep learning approaches for modeling complex environmental time series. The results further demonstrate their practical value in air quality management and early-warning systems. Full article
(This article belongs to the Section Air Quality)
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18 pages, 6012 KB  
Article
Vision-AQ: Explainable Multi-Modal Deep Learning for Air Pollution Classification in Smart Cities
by Faisal Mehmood, Sajid Ur Rehman and Ahyoung Choi
Mathematics 2025, 13(18), 3017; https://doi.org/10.3390/math13183017 - 18 Sep 2025
Viewed by 409
Abstract
Accurate air quality prediction (AQP) is crucial for safeguarding public health and guiding smart city management. However, reliable assessment remains challenging due to complex emission patterns, meteorological variability, and chemical interactions, compounded by the limited coverage of ground-based monitoring networks. To address this [...] Read more.
Accurate air quality prediction (AQP) is crucial for safeguarding public health and guiding smart city management. However, reliable assessment remains challenging due to complex emission patterns, meteorological variability, and chemical interactions, compounded by the limited coverage of ground-based monitoring networks. To address this gap, we propose Vision-AQ (Visual Integrated Operational Network for Air Quality), a novel multi-modal deep learning framework that classifies Air Quality Index (AQI) levels by integrating environmental imagery with pollutant data. Vision-AQ employs a dual-input neural architecture: (1) a pre-trained ResNet50 convolutional neural network (CNN) that extracts high-level features from city-scale environmental photographs in India and Nepal, capturing haze, smog, and visibility patterns, and (2) a multi-layer perceptron (MLP) that processes tabular sensor data, including PM2.5, PM10, and AQI values. The fused representations are passed to a classifier to predict six AQI categories. Trained on a comprehensive dataset, the model achieves strong predictive performance with high accuracy, precision, recall and F1-score of 99%, with 23.7 million parameters. To ensure interpretability, we use Grad-CAM visualization to highlights the model’s reliance on meaningful atmospheric features, confirming its explainability. The results demonstrate that Vision-AQ is a reliable, scalable, and cost-effective approach for localized AQI classification, offering the potential to augment conventional monitoring networks and enable more granular air quality management in urban South Asia. Full article
(This article belongs to the Special Issue Explainable and Trustworthy AI Models for Data Analytics)
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