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21 pages, 3235 KB  
Article
Machine Learning-Driven Optimization for Predicting Biochar Adsorption Performance Toward Pb(II) and Cd(II)
by Pengcheng Yu, Zixi Huang and Wuming Xie
Water 2026, 18(12), 1416; https://doi.org/10.3390/w18121416 (registering DOI) - 10 Jun 2026
Abstract
With the increasing levels of toxic heavy metals such as Pb(II) and Cd(II), their discharge poses serious threats to environmental safety and human health, necessitating efficient remediation technologies. Biochar has emerged as a promising eco-friendly adsorbent; however, its adsorption performance is constrained by [...] Read more.
With the increasing levels of toxic heavy metals such as Pb(II) and Cd(II), their discharge poses serious threats to environmental safety and human health, necessitating efficient remediation technologies. Biochar has emerged as a promising eco-friendly adsorbent; however, its adsorption performance is constrained by interactions among material properties, environmental conditions, and ion specificity. Conventional machine learning (ML) models are typically built on single-metal-ion datasets, limiting their ability to leverage shared information across related adsorption scenarios. To address this limitation, this study proposes a descriptor-based ML framework for Pb(II)–Cd(II) adsorption prediction, in which ion-related physicochemical descriptors, such as electronegativity and hydrated ionic radius, are incorporated in place of discrete ion labels to enable ion-specific modeling. An Optuna-optimized CatBoost model achieved high predictive accuracy (R2 = 0.952, RMSE = 9.80) and demonstrated improved performance on both Pb and Cd subsets compared with single-ion models. SHAP analysis reveals the model is consistent with known adsorption-related factors. Uncertainty quantification was incorporated to constrain predictions and enhance robustness. Ultimately, this study provides a robust data-driven baseline for heavy metal adsorption modeling, offering mechanistic insights into biochar–metal interactions and demonstrating a physicochemical descriptor approach that supports future extensions to broader multi-ion systems. Full article
(This article belongs to the Section Wastewater Treatment and Reuse)
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27 pages, 908 KB  
Article
Oil-Price Volatility and Renewable-Energy Transition in the Gulf Cooperation Council Countries: Does Financial Development Mitigate Energy Transition Risk?
by Noura Ben Mbarek
Energies 2026, 19(12), 2780; https://doi.org/10.3390/en19122780 (registering DOI) - 10 Jun 2026
Abstract
Oil-price volatility represents a major challenge for hydrocarbon-dependent economies pursuing renewable-energy transition. In GCC countries, fluctuations in global oil markets may influence renewable-energy deployment through their effects on fiscal revenues, investment conditions, and long-term energy planning. While previous studies have largely examined the [...] Read more.
Oil-price volatility represents a major challenge for hydrocarbon-dependent economies pursuing renewable-energy transition. In GCC countries, fluctuations in global oil markets may influence renewable-energy deployment through their effects on fiscal revenues, investment conditions, and long-term energy planning. While previous studies have largely examined the direct effects of oil prices, renewable energy, and financial development separately, limited evidence exists on whether financial development can mitigate the adverse implications of oil-market uncertainty for renewable-energy transition in GCC economies. Using annual data for six GCC countries over the period 1990–2024, this study investigates the links among oil-price volatility, financial development, and renewable-energy transition within a second-generation panel econometric framework that accounts for cross-sectional dependence and heterogeneity. The analysis employs Pesaran cross-sectional dependence tests, CIPS unit-root tests, Westerlund cointegration, common correlated effects mean group (CCE-MG), augmented mean group (AMG), and error-correction modeling. The results support the existence of a stable long-run relationship among the variables. Oil-price volatility is negatively associated with renewable-energy consumption, with a long-run coefficient of approximately −0.21. Financial development exhibits a positive association with renewable-energy transition, while the interaction between oil-price volatility and financial development remains positive and statistically significant. This finding suggests that stronger financial systems may partially reduce the adverse effects of oil-market instability. The short-run estimates also support the presence of a stable adjustment process toward long-run equilibrium. Robustness checks based on alternative financial-development proxies, lagged regressors, Driscoll–Kraay estimations, leave-one-out country analysis, and alternative volatility measures confirm the stability of the main findings. The findings suggest that financial development may strengthen the resilience of renewable-energy transition strategies in GCC economies exposed to volatile energy-market conditions. Full article
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27 pages, 757 KB  
Article
Robust Substrate Control for a Microbial Electrolysis Cell System
by René Alejandro Flores-Estrella, José de Jesús Colin Robles, Ixbalank Torres-Zúñiga, Fernando López-Caamal and Victor Alcaraz-Gonzalez
Processes 2026, 14(12), 1876; https://doi.org/10.3390/pr14121876 (registering DOI) - 9 Jun 2026
Abstract
This paper presents a control design framework that systematically translates nonlinear equilibrium operability analysis into frequency-domain robust synthesis for continuous microbial electrolysis cells (MEC). Since MEC operation is threatened by washout and highly variable influent conditions, analytical local conditions for the existence and [...] Read more.
This paper presents a control design framework that systematically translates nonlinear equilibrium operability analysis into frequency-domain robust synthesis for continuous microbial electrolysis cells (MEC). Since MEC operation is threatened by washout and highly variable influent conditions, analytical local conditions for the existence and local stability of normal operating conditions (NOC) and washout equilibria are first established. Departing from these nonlinear properties, the model is linearized within the locally validated NOC region, and a parametric sensitivity screening is used to identify dominant uncertainty sources (α, μmax, Kd). These are embedded into an unstructured multiplicative uncertainty weight, enabling the synthesis of nominal and robust H controllers that explicitly account for actuator effort, disturbance rejection, and measurement noise. Controller order reduction via balanced truncation is performed while preserving closed-loop local robustness properties. As a benchmark, an internal model control proportional–integral (IMC-PI) controller is derived, and its single tuning parameter is selected by solving a univariate multi-objective optimization that balances integral absolute error and maximum control effort, yielding a Pareto-optimal compromise. Numerical simulations under simultaneous inlet disturbances, parametric variations, measurement noise, and actuator saturation show that the reduced-order robust H controller outperforms the optimized IMC-PI in the tracking–effort trade-off, while the nominal H controller satisfies an a posteriori robust stability test for the linearized dynamics. The proposed framework provides a systematic path from nonlinear operability analysis to implementable robust control, demonstrating that high-order H designs can be reduced to low-order transfer functions suitable for standard industrial control hardware while preserving local stability properties against realistic process perturbations. Full article
(This article belongs to the Section Process Control, Modeling and Optimization)
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33 pages, 2919 KB  
Article
Optimal Reordering Strategy for Three-Echelon Spare-Parts Inventory Systems Under Disruption-Dependent Lead-Time Uncertainty: Application to Wind Energy Systems
by Anik Mazumder and Bhaba R. Sarker
Logistics 2026, 10(6), 131; https://doi.org/10.3390/logistics10060131 (registering DOI) - 9 Jun 2026
Abstract
Background: The rapid expansion of wind energy systems has increased the need for reliable and cost-effective maintenance logistics, where the availability of critical spare parts is essential for sustaining turbine performance and reducing downtime. From this background, this study develops a three-echelon [...] Read more.
Background: The rapid expansion of wind energy systems has increased the need for reliable and cost-effective maintenance logistics, where the availability of critical spare parts is essential for sustaining turbine performance and reducing downtime. From this background, this study develops a three-echelon spare-parts inventory optimization model for wind-energy maintenance systems under disruption-dependent lead-time uncertainty. The model considers a hierarchical supply structure, consisting of a central warehouse, regional hub, and local maintenance base, where replenishment lead times are represented as a mixture of normal operating conditions and disruption-induced delays. Method: A total average cost function is formulated by incorporating ordering, holding, shortage, disruption penalty, and downtime costs, and a hybrid Nested Enumeration–Bisection Algorithm is developed as a method to determine the optimal order quantity, reorder points, and shipment multipliers. Results: Numerical experiments based on wind-turbine maintenance scenarios show that disrupted-condition lead-time distributions substantially affect total system cost. More variable disruption distributions increase total average cost, whereas more stable distributions produce lower-cost and more balanced inventory policies. Conclusions: The findings indicate that explicitly modeling disruption-sensitive lead times can improve spare-parts planning and provide decision support for enhancing cost efficiency and reliability in multi-echelon wind-energy maintenance logistics. Full article
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30 pages, 18338 KB  
Article
Spatially Constrained Machine Learning for PRISMA-Based Lithological Mapping of Phosphate Mine Waste Rocks
by Abdelhak El Mansour, Jamal-Eddine Ouzemou, Abdellatif Elghali, Malak Elmeknassi, Rachid Hakkou, Mostafa Benzaazoua and Ahmed Laamrani
Minerals 2026, 16(6), 619; https://doi.org/10.3390/min16060619 (registering DOI) - 9 Jun 2026
Abstract
Phosphate waste rock piles (PWRPs) generated by open-pit phosphate mining are highly heterogeneous and difficult to characterize using conventional point sampling alone, which limits representative resource assessment, selective recovery, and rehabilitation planning. This study develops an integrated framework combining PRISMA spaceborne hyperspectral imagery, [...] Read more.
Phosphate waste rock piles (PWRPs) generated by open-pit phosphate mining are highly heterogeneous and difficult to characterize using conventional point sampling alone, which limits representative resource assessment, selective recovery, and rehabilitation planning. This study develops an integrated framework combining PRISMA spaceborne hyperspectral imagery, ground-based mineralogical analyses, and spatially constrained machine learning to map lithological heterogeneity at the Benguerir phosphate mining site, Morocco. A three-stage spectral optimization workflow, including atmospheric band masking, Savitzky–Golay filtering, and analysis of variance (ANOVA)-based feature selection, was applied to identify the most discriminative Short-Wave Infrared (SWIR) bands for lithological classification. After removing redundant observations located within shared PRISMA pixel footprints, 127 spatially independent samples were retained for model development. Five supervised classifiers (Random Forest, Extra Trees, XGBoost, Support Vector Machine, and K-Nearest Neighbors) were evaluated under a spatially constrained cross-validation framework aligned with the 30 m native PRISMA pixel size. Ensemble-based models, especially Extra Trees and Random Forest, provided the most stable performance, with balanced accuracies of 0.56–0.69 and area under the receiver operating characteristic curve (AUC) values exceeding 0.95 for carbonate-dominated lithologies. Lower discrimination between phosphate and siliceous facies reflects intrinsic mineralogical mixing and spectral overlap at the sensor scale. Entropy-based uncertainty and posterior probability mapping revealed spatially structured prediction ambiguity concentrated along lithological boundaries and transitional zones, consistent with petrographic evidence of compositional heterogeneity. These results indicate that moderate but stable accuracies likely represent realistic performance limits for spaceborne hyperspectral mapping of complex mining environments under spatial constraints. The proposed framework provides a transferable and uncertainty-aware basis for lithological mapping, selective recovery assessment, and sustainable phosphate waste management. Full article
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35 pages, 36080 KB  
Article
A Dual-Ensemble Machine Learning Framework for Coconut Yield Projection Under CMIP6 Climate Scenarios in the Andaman and Nicobar Islands
by Abhilash, Hemareddy Thimmareddy, Iyyappan Jaisankar, Arkadeb Mukhopadhyay and Gurunath Raddy
Climate 2026, 14(6), 123; https://doi.org/10.3390/cli14060123 (registering DOI) - 9 Jun 2026
Abstract
Climate change directly affects agricultural productivity, particularly in small island systems where ecosystems and livelihoods are highly exposed to climate variability. This study presents a comprehensive analysis of climate variability for the three districts North and Middle Andaman, South Andaman, and Nicobar, using [...] Read more.
Climate change directly affects agricultural productivity, particularly in small island systems where ecosystems and livelihoods are highly exposed to climate variability. This study presents a comprehensive analysis of climate variability for the three districts North and Middle Andaman, South Andaman, and Nicobar, using a six-model CMIP6 ensemble under four SSP scenarios (SSP126, SSP245, SSP370, and SSP585), coupled with ensemble tree-based machine learning algorithms to project coconut yield responses. The historical data was analysed from 1981 to 2025 and the projection was from 2026 to 2100. Observed rainfall reveals a persistent north-to-south gradient, with South Andaman recording the highest mean annual rainfall (3408.40 mm) and Nicobar recording the lowest (2442.13 mm), alongside pronounced inter-annual variability and a discernible drying tendency post-2015. Nicobar consistently records the warmest mean Tmax (30.89 °C) and Tmin (24.11 °C), while North and Middle Andaman exhibit the greatest inter-annual temperature variability. Future projections indicate a robust and statistically significant warming across all districts and scenarios, with end-of-century Tmax increases reaching up to 4.05 °C (Nicobar, SSP585) and Tmin increases up to 3.73 °C (North and Middle Andaman, SSP585), accompanied by a progressive compression of the diurnal temperature range. Precipitation projections show modest wetting in the Andaman districts under most scenarios, while Nicobar exhibits a muted response, with SSP370 uniquely projecting a decline of approximately 69 mm below the observed baseline. Among the ten evaluated CMIP6 models, six (ACCESS-CM2, CMCC-ESM2, CNRM-ESM2-1, EC-Earth3-Veg-LR, GFDL-ESM4, and NorESM2-MM) were selected based on composite skill scores across rainfall, Tmax, and Tmin. Model selection was optimized independently for each district via Leave-One-Year-Out cross-validation with hyperparameter tuning, yielding district-specific best performers: GradientBoost for North and Middle Andaman (R2 = 0.471), RandomForest for South Andaman (R2 = 0.609), and ExtraTrees for Nicobar (R2 = 0.289). K-Nearest Neighbours demonstrated competitive predictive skill in all three districts, confirming that instance-based learning can capture non-linear climate–yield relationships, though tree-based ensembles were preferred for their robustness and interpretability. Ensemble tree-based ML models and instance-based learning consistently outperformed all linear and kernel-based approaches, confirming the non-linear nature of climate–yield relationships in this setting. Coconut yield projections indicate above-baseline productivity gains of 3.4–21.5% in North and Middle Andaman and 24.6–36.8% in South Andaman, driven by favourable warming and precipitation trends, while Nicobar yields plateau at 7.7–13.7% above baseline, indicating thermal saturation of the climate yield response under already near-optimal thermal conditions. Notably, Nicobar exhibits a reversed yield–emission relationship wherein lower-emission pathways marginally outperform high-emission scenarios, likely reflecting avoidance of thermal stress thresholds. Inter-CMIP6-model uncertainty emerges as the dominant source of projection spread, exceeding scenario uncertainty across most districts, underscoring the critical importance of multi-model ensemble frameworks for robust agricultural climate impact assessments in data-sparse tropical island environments. Full article
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37 pages, 1307 KB  
Systematic Review
Safety-Oriented Model Predictive Control for Autonomous Vehicles: A Systematic Review
by Ali Mahmood and Róbert Szabolcsi
Automation 2026, 7(3), 88; https://doi.org/10.3390/automation7030088 (registering DOI) - 9 Jun 2026
Abstract
Ensuring safety in autonomous vehicles (AVs) requires predictive control methods that can handle dynamic constraints, uncertain interactions, and real-time decision making. This review examines safety-oriented model predictive control (MPC) for AVs using a PRISMA-guided screening process. From 363 records published between January 2015 [...] Read more.
Ensuring safety in autonomous vehicles (AVs) requires predictive control methods that can handle dynamic constraints, uncertain interactions, and real-time decision making. This review examines safety-oriented model predictive control (MPC) for AVs using a PRISMA-guided screening process. From 363 records published between January 2015 and March 2026, 101 peer-reviewed studies were selected for qualitative synthesis. The literature is organized into three domains: collision avoidance and risk mitigation, trajectory tracking and path following, and intersection and coordination tasks. Across these domains, MPC has evolved from nominal tracking and geometric avoidance toward risk-aware, robust, hierarchical, and learning-enhanced formulations. Unlike broader reviews on autonomous driving control, this review focuses specifically on safety-oriented MPC and compares the reviewed literature in terms of safety mechanisms, uncertainty treatment, validation practice, computational feasibility, and deployment limitations. The review shows that MPC remains one of the most versatile frameworks for AV safety, but the evidence base is weakened by heavy reliance on simulation, inconsistent safety metrics, limited validation under uncertainty, and uneven treatment of computational feasibility. The most promising directions are hybrid architectures that combine model-based safety guarantees with uncertainty-aware prediction, learning-assisted adaptation, and scalable coordination mechanisms. Full article
(This article belongs to the Section Smart Transportation and Autonomous Vehicles)
31 pages, 13937 KB  
Article
Distributionally Robust Bi-Level Optimization of Distribution Network and Charging Stations for Sustainable Operation Under Climate–Charging Load Uncertainty
by Deyu Ma, Ximin Cao, Yanchi Zhang and Suhong Chen
Sustainability 2026, 18(12), 5903; https://doi.org/10.3390/su18125903 (registering DOI) - 9 Jun 2026
Abstract
With the large-scale integration of electric vehicles (EVs), charging demand exhibits significant spatiotemporal variability, further intensified by climatic factors, which makes it difficult for existing uncertainty models to capture underlying dependency structures. To address this issue, this paper proposes a Copula–Wasserstein-based distributionally robust [...] Read more.
With the large-scale integration of electric vehicles (EVs), charging demand exhibits significant spatiotemporal variability, further intensified by climatic factors, which makes it difficult for existing uncertainty models to capture underlying dependency structures. To address this issue, this paper proposes a Copula–Wasserstein-based distributionally robust optimization (C-WDRO) framework for the coordinated operation of distribution networks and charging stations. A climate-sensitive physical mapping model of electric vehicle energy consumption is first developed to establish a coupled climate–energy–load mechanism. Copula functions are then used to characterize dependencies among temperature, precipitation, and charging demand, and are incorporated into a bi-level optimization formulation. The model is solved using Karush–Kuhn–Tucker (KKT) conditions and a column-and-constraint generation (C&CG) algorithm. Case studies on the IEEE 33-bus system show that the proposed method reduces total operating cost by 4.26% compared with robust optimization (RO), while maintaining economic efficiency, and reduces the load shedding rate by 0.14 percentage points compared with Wasserstein distributionally robust optimization (WDRO), while keeping voltage security. These results demonstrate that explicitly modeling dependency structures can enhance operational efficiency and support more sustainable and reliable power–transportation system operation under uncertainty. Full article
(This article belongs to the Section Energy Sustainability)
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27 pages, 2321 KB  
Article
A Machine Learning Ensemble Framework for Carbon Price Prediction and Decision Support Under Information Structure Heterogeneity in Regional Carbon Markets in China
by Yingyue Xing, Siyuan Zou and Guohua Liu
Entropy 2026, 28(6), 656; https://doi.org/10.3390/e28060656 (registering DOI) - 9 Jun 2026
Abstract
Reliable prediction of carbon allowance prices plays a crucial role in emissions trading systems, particularly for market participation, regulatory compliance, and long-term cost planning. In China, regional carbon markets differ markedly in trading activity, price formation mechanisms, and responsiveness to external signals, which [...] Read more.
Reliable prediction of carbon allowance prices plays a crucial role in emissions trading systems, particularly for market participation, regulatory compliance, and long-term cost planning. In China, regional carbon markets differ markedly in trading activity, price formation mechanisms, and responsiveness to external signals, which limits the effectiveness of conventional single-model forecasting approaches. This study develops a unified machine learning framework designed to accommodate such cross-market heterogeneity. The framework incorporates a diverse set of explanatory variables, including historical price-based indicators, trading volume information, inter-market linkage signals, and macroeconomic factors. Three ensemble-based learning algorithms-XGBoost, LightGBM, and Random Forest—are implemented, and their outputs are further integrated using a weighted aggregation scheme to improve generalization across markets. The empirical evaluation across seven pilot markets shows that, while LightGBM consistently performs well as a standalone model, the proposed ensemble framework achieves superior stability and adaptability under varying market conditions. The forecasting accuracy is high across all cases, with coefficients of determination above 0.74 and reaching values greater than 0.92 in most markets. Further investigation through feature ablation highlights the heterogeneous role of external information, indicating that predictor importance varies significantly between markets and that no universal feature combination yields optimal performance. Leveraging the forecast outputs, the study also demonstrates practical applications in decision support, including timing strategies for allowance sales and dynamic cost assessment in offshore wind engineering scenarios. By systematically evaluating the marginal contribution of different information groups to predictive uncertainty, the framework offers a flexible tool for managing information-structure uncertainty in fragmented carbon markets. The proposed framework offers an integrated solution that connects predictive modeling with operational and engineering decision on processes, providing a flexible tool for managing uncertainty in fragmented carbon markets. Full article
30 pages, 4885 KB  
Review
Review of Hydraulic Fracture Diagnostics: Technologies, Interpretation Challenges, and Emerging Advances
by Tianhao Bai, Guan Qin and Mohamed Y. Soliman
Geosciences 2026, 16(6), 231; https://doi.org/10.3390/geosciences16060231 (registering DOI) - 9 Jun 2026
Abstract
Hydraulic fracture diagnostics are essential for characterizing fracture geometry, connectivity, and effectiveness in unconventional reservoirs. However, the diversity of available techniques and fragmented understanding of their physical mechanisms hinder multidisciplinary communication and lead to inconsistent field decisions. This review provides a systematic assessment [...] Read more.
Hydraulic fracture diagnostics are essential for characterizing fracture geometry, connectivity, and effectiveness in unconventional reservoirs. However, the diversity of available techniques and fragmented understanding of their physical mechanisms hinder multidisciplinary communication and lead to inconsistent field decisions. This review provides a systematic assessment of diagnostic methods, focusing on their physical foundations, applicability, and limitations, and proposes a unified reference framework. Direct diagnostics, including microseismic monitoring, fiber-optic sensing (DTS and DAS), and tiltmeter measurements, are evaluated in terms of data characteristics, interpretation challenges, and field applicability. Indirect methods based on pressure, production, and tracer data—such as DFITs, pressure interference tests, and tracer analysis—are examined for their roles in fracture closure evaluation and interwell connectivity. The review further distinguishes between single-well and multi-well applications, providing a structured classification framework. It highlights that individual methods are constrained by non-uniqueness, modeling assumptions, and non-ideal field conditions, especially in complex fracture networks. Therefore, reliable characterization requires integrating multiple diagnostics with physics-based modeling and uncertainty-aware interpretation. Recent advances in AI and machine learning are also briefly discussed as tools to enhance automated analysis and support real-time, predictive diagnostics. Full article
(This article belongs to the Section Geophysics)
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20 pages, 4114 KB  
Article
Automated Storytelling for Neurodiversity: Comparative Evaluation Between Multilayer LSTM, Advanced Embeddings, and Modern Narrative Generation Techniques
by Arnulfo Alanis, Ximena Díaz, Bogart Yail Márquez, Teresa Guarda and J Ascención Guerrero Viramontes
Appl. Sci. 2026, 16(12), 5817; https://doi.org/10.3390/app16125817 (registering DOI) - 9 Jun 2026
Abstract
An important issue to consider is the training time, as it can have a considerable influence on the set of stories generated, due to factors such as uncertainty, diversity, and narrative coherence. This paper presents a systematic analysis of the dynamics of predictive [...] Read more.
An important issue to consider is the training time, as it can have a considerable influence on the set of stories generated, due to factors such as uncertainty, diversity, and narrative coherence. This paper presents a systematic analysis of the dynamics of predictive entropy at different times and random seeds, studying the interaction of entropy with lexical diversity, repetition, semantic consistency, and entity continuity in probabilistic language generation models. A comparative evaluation of recurrent and attention-based architectures is performed using linguistic metrics. Predictive entropy was reduced by 32.4% (LSTM) and 28.7% (Transformer). LexDiv obtained 0.71 ± 0.03 and Self-BLEU obtained 0.42 ± 0.02, suggesting greater confidence in the model. However, it should be noted that a greater reduction in entropy may be associated with lower lexical diversity and higher Self-BLEU scores. This indicates a trade-off between confidence and expressiveness in probabilistic language models. The entropy term encourages smoother probability distributions and reduces premature mode collapse during Adam optimization. Ltotal=LCEλH(p(y|x) aims to improve stability, reduce random initialization, and enable the generation of adaptable narratives, which may be relevant for neurodiversity-oriented narratives. Full article
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19 pages, 337 KB  
Article
Hamilton–Jacobi–Bellman-Based Optimal Effort Allocation for Student Productivity Dynamics
by Wafa Louafi, Houda Tadjer and Yacine Lafifi
AppliedMath 2026, 6(6), 91; https://doi.org/10.3390/appliedmath6060091 (registering DOI) - 9 Jun 2026
Abstract
The adaptive regulation of student productivity remains a challenging problem in technology-enhanced learning environments due to the continuous and uncertain nature of cognitive effort, attention, and behavioral fluctuations. While existing educational intervention models are predominantly based on discrete-time decision frameworks, they often provide [...] Read more.
The adaptive regulation of student productivity remains a challenging problem in technology-enhanced learning environments due to the continuous and uncertain nature of cognitive effort, attention, and behavioral fluctuations. While existing educational intervention models are predominantly based on discrete-time decision frameworks, they often provide limited support for the representation of stochastic productivity dynamics and continuous effort adaptation. This paper proposes a continuous-time stochastic optimal control framework for adaptive effort allocation in student productivity regulation. The learner productivity level is modeled as a bounded stochastic diffusion process evolving on the interval ([0, 1]), where the drift and diffusion coefficients depend on both effort allocation and learner-specific psychological characteristics. The control objective is formulated as the maximization of an expected cumulative productivity reward penalized by excessive cognitive effort over a finite study horizon. Using the Hamilton–Jacobi–Bellman (HJB) framework, we derive an optimal state-dependent feedback policy that dynamically adjusts effort allocation according to the current productivity level, the remaining study horizon, and the learner profile. We establish the well-posedness of the controlled stochastic dynamics and show that the productivity state remains invariant within the admissible interval. The resulting HJB equation is solved numerically using a semi-implicit finite-difference approximation combined with iterative feedback updates. Simulation experiments conducted on synthetic learner profiles illustrate the qualitative behavior of the proposed controller under heterogeneous psychological configurations. Compared with constant-effort and threshold-based heuristic strategies, the adaptive feedback policy produces smoother productivity trajectories and more stable effort allocation patterns under stochastic perturbations. The proposed framework provides a mathematically grounded approach for studying adaptive productivity regulation under uncertainty and establishes a foundation for future data-driven calibration and personalized intervention systems. Full article
(This article belongs to the Special Issue Advanced Mathematical Modeling, Dynamics and Applications)
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38 pages, 1491 KB  
Systematic Review
Advances in Hybrid Evolutionary–Fuzzy Systems for Optimization and Intelligent Decision-Making Under Uncertainty: A Systematic Review
by Hugo Martínez Ángeles, Cesar Augusto Navarro Rubio, José Gabriel Ríos Moreno, José Luis Reyes Araiza, Roberto Valentín Carrillo-Serrano, Mariano Garduño Aparicio, Ivan Gonzalez-Garcia and Mario Trejo Perea
Mathematics 2026, 14(12), 2056; https://doi.org/10.3390/math14122056 (registering DOI) - 9 Jun 2026
Abstract
Hybrid Evolutionary–Fuzzy Systems (HEFS) have emerged as a powerful computational paradigm for addressing complex engineering optimization and intelligent decision-making problems under uncertainty. This study presents a systematic review, conducted following the PRISMA 2020 methodology, to analyze advancements in the integration of evolutionary algorithms, [...] Read more.
Hybrid Evolutionary–Fuzzy Systems (HEFS) have emerged as a powerful computational paradigm for addressing complex engineering optimization and intelligent decision-making problems under uncertainty. This study presents a systematic review, conducted following the PRISMA 2020 methodology, to analyze advancements in the integration of evolutionary algorithms, swarm intelligence, fuzzy logic, and Multi-Criteria Decision-Making (MCDM) techniques over the period 2020–2026. The analysis focuses on identifying key algorithmic mechanisms, hybridization strategies, performance metrics, and application domains. The results indicate that HEFSs significantly enhance optimization performance by balancing exploration and exploitation, improving robustness, and enabling adaptive and interpretable decision-making in uncertain and multi-objective environments. In particular, fuzzy systems contribute to effective uncertainty modeling and interpretability, while evolutionary and metaheuristic algorithms provide strong global search capabilities. Despite these advantages, important challenges remain, including high computational complexity, scalability limitations, and the trade-off between accuracy and interpretability. The review also identifies emerging research directions involving Explainable Artificial Intelligence (XAI), deep learning integration, digital twins, and big-data-enabled optimization. However, the reviewed evidence suggests that these technologies should currently be interpreted as promising but still evolving extensions, whose maturity and large-scale validation remain heterogeneous across application domains. Full article
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33 pages, 3812 KB  
Article
Modeling Vocational Preferences in STEM Students Through Explainable and Fuzzy AI to Support Personalized Learning
by Gabriel Marín Díaz
Educ. Sci. 2026, 16(6), 917; https://doi.org/10.3390/educsci16060917 (registering DOI) - 9 Jun 2026
Abstract
Understanding students’ vocational preferences in STEM domains is a complex challenge characterized by uncertainty, subjectivity, and overlapping interests. Traditional profiling approaches often rely on rigid categorizations that fail to capture the hybrid and dynamic nature of learners. This study proposes FAS-XAI, a reproducible [...] Read more.
Understanding students’ vocational preferences in STEM domains is a complex challenge characterized by uncertainty, subjectivity, and overlapping interests. Traditional profiling approaches often rely on rigid categorizations that fail to capture the hybrid and dynamic nature of learners. This study proposes FAS-XAI, a reproducible learning analytics framework that integrates fuzzy logic and explainable artificial intelligence for interpretable profiling of STEM vocational preferences. The methodology combines fuzzy AHP for criterion weighting, Fuzzy C-Means clustering to identify overlapping profiles, and XGBoost for supervised validation, complemented by SHAP and LIME to provide global and local explanations of model behavior. The study is framed as a methodological simulation under controlled conditions, using synthetic data to evaluate the internal coherence, transparency, and transferability of the proposed pipeline. The results show that the framework can generate multidimensional and interpretable learner profiles, with resilience, communication, and commitment emerging as relevant discriminative dimensions within the simulated setting. Overall, the proposed approach provides a reproducible methodological basis for future empirical applications in personalized learning, vocational guidance, and AI-supported educational decision-making. Full article
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22 pages, 456 KB  
Article
Balancing Cost and Service Performance: A Multi Objective Inventory Planning Approach for Multi Echelon Supply Chains
by Joaquim Jorge Vicente
Systems 2026, 14(6), 664; https://doi.org/10.3390/systems14060664 (registering DOI) - 9 Jun 2026
Abstract
This paper presents a decision-support framework for analysing the trade-off between total operational cost and customer service level in multi echelon inventory systems. The model integrates fixed-order-quantity replenishment policies, lead-time dynamics and multi objective optimisation to generate a detailed Pareto frontier of efficient [...] Read more.
This paper presents a decision-support framework for analysing the trade-off between total operational cost and customer service level in multi echelon inventory systems. The model integrates fixed-order-quantity replenishment policies, lead-time dynamics and multi objective optimisation to generate a detailed Pareto frontier of efficient solutions. A real multi echelon distribution network is used to demonstrate the model’s applicability and managerial relevance. The results indicate that raising the service level from 46% to the sector standard of 96% increases total cost by approximately 19%, while achieving full demand satisfaction requires an additional 5% cost increase for only marginal service improvement. This pattern reveals a clear cost–service turning point around the 96% service level, beyond which additional gains exhibit sharply diminishing returns. The framework, therefore, provides a transparent and analytical mechanism for identifying replenishment strategies that balance cost efficiency with service performance. By decomposing total cost into ordering, holding, transport and lost-sales components, the model enhances managerial visibility and supports targeted policy adjustments. The paper also discusses limitations of the current formulation and outlines avenues for future research, including alternative replenishment policies, multi-product extensions and richer uncertainty modelling. Full article
(This article belongs to the Section Supply Chain Management)
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