Search Results (59)

The fractional Whitham–Broer–Kaup model governs nonlinear wave propagation in memory-dependent media, including porous structures, viscoelastic fluids, and irregular seabeds, yet the full dynamical spectrum from quasi-periodicity to deterministic chaos, the role of stochastic forcing, and reliable identification from noisy data remains insufficiently explored, particularly how the fractional order $\beta$ influences these regimes. This study addresses these gaps through a comprehensive, multi-method dynamical analysis of a representative nonlinear oscillator embodying key FWBK features. Three-dimensional attractor visualizations, return maps, and surrogate data tests demonstrate a transition from quasi-periodic toroidal attractors to fully developed chaos via torus breakdown, confirming that observed complexity originates from deterministic nonlinearity. Poincaré sections reveal multistability and KAM-type structures, where coexisting attractors depend on initial conditions, while increasing noise progressively disrupts coherent dynamics. The OGY control method effectively stabilizes unstable periodic orbits across chaotic regimes with minimal perturbation, and Lyapunov analysis indicates that stochastic forcing attenuates chaos while enhancing dissipation. The Fokker–Planck framework shows that noise reshapes probability landscapes, driving transitions from unimodal to bimodal distributions. Comparative analysis of SINDy, JMAP and VBA highlights trade-offs in interpretability, computational efficiency, and uncertainty quantification, while an integrated Bayesian–PCE–Sobol approach quantifies parametric uncertainty and reveals time-dependent sensitivity variations. Additionally, the overlapping of soliton solutions extracted via the enhanced modified Sardar sub-equation method reveals structural relationships among soliton families and their stability under interaction. Soliton branches that maintain high overlap under noise correspond to stable regimes, while those losing coherence indicate the onset of chaos. Furthermore, while the reduced dynamics in $\eta$-space are independent of $\beta$, the fractional order controls spatial compression and temporal scaling in physical coordinates, directly influencing observable wave localization. These results imply that fractional effects can modify chaos transitions, support controllability through OGY, and influence noise–instability interactions depending on $\beta$. This framework provides a robust, transferable methodology for analyzing and controlling nonlinear oscillatory systems under deterministic and stochastic conditions, with direct applications to FWBK-based models in coastal engineering, fiber optics, and quantum interference systems. Full article

Artificial intelligence (AI) is increasingly influencing nanopharmaceutical development by supporting the transition from empirical formulation screening toward predictive, data-driven, and translationally oriented design. Nanocarrier-based therapeutics are governed by nonlinear relationships among material composition, physicochemical attributes, manufacturing parameters, biological identity, pharmacokinetics, toxicity, and therapeutic performance. In this review, we examine how AI can contribute to nanopharmaceutical development from predictive formulation design to clinical translation. We synthesize current applications of machine learning, deep learning, physics-informed modeling, hybrid mechanistic–AI approaches, and automated optimization workflows, with emphasis on critical quality attribute modeling, multi-objective optimization, design of experiments, quality-by-design, process analytical technology, digital twins, and continuous manufacturing. We also discuss applications involving nano–bio interactions, pharmacokinetics, toxicity, immunogenicity, and precision nanomedicine. AI-based approaches can support rational nanocarrier design, identify nonlinear formulation–property relationships, guide optimization, improve process understanding, and integrate heterogeneous experimental, biological, and manufacturing datasets across diverse nanopharmaceutical platforms. These methods are particularly relevant for modeling protein corona formation, cellular uptake, intracellular trafficking, biodistribution, pharmacokinetics, toxicity, immunogenicity, and patient-specific responses. However, translational implementation remains limited by fragmented datasets, inconsistent reporting standards, limited interpretability, insufficient external validation, uncertain predictions, poorly defined applicability domains, and evolving regulatory expectations for adaptive computational models. Overall, AI should be viewed not only as an optimization tool, but also as a translational framework connecting formulation science, biological prediction, manufacturing control, and clinical implementation. Future progress will depend on standardized data infrastructures, explainable and externally validated models, uncertainty quantification, applicability-domain definition, hybrid mechanistic–AI frameworks, regulatory-ready documentation, and clinically relevant case studies. Full article

Aerobiology, the science that studies atmospheric biological particles (including pollen, fungal spores, bacteria, and viruses), has undergone a profound transformation from a descriptive, observational discipline into a predictive, data-driven field, thanks to advances in statistical methods and environmental sensing technologies. Early research, based on classical statistical methods such as descriptive analysis, correlation analysis, and linear regression, established a fundamental understanding of seasonal dynamics and environmental relationships. However, the inherent complexity of aerosol biological systems—characterized by nonlinear interactions, spatiotemporal variability, and multiscale processes—has spurred the adoption of modern statistical techniques. These techniques include time-series analysis, generalized linear and additive models, spatial statistics, Bayesian inference, machine learning, and data assimilation, often combined with high-resolution environmental monitoring and sensor networks. In recent years, hybrid modeling approaches have emerged, combining mechanistic understanding of atmospheric transport and biological emissions processes with data-driven learning to improve the accuracy, robustness, and interpretability of predictions. This review comprehensively compares classical, modern, and hybrid statistical methods in air biology, exploring their theoretical foundations, practical applications, and inherent limitations. Furthermore, this review highlights emerging paradigms such as uncertainty quantification, causal inference, digital twins, and AI-driven real-time prediction systems. It also discusses challenges, including data heterogeneity, model interpretability, and cross-regional portability. By treating aerobiology as a complex adaptive environmental–biological system, this study highlights statistical methods that link observations to mechanisms and advance scalable, reliable, systems-oriented prediction frameworks for future research and applications. Full article

This study presents the results from a comparison of measurement quantification methods of methane emissions from two onshore liquefied natural gas (LNG) export terminals, comparing site-level measurements, made using an in situ airborne technique, and estimates based on emission factors (EFs) derived from measurements using a remote sensing, ground-based, differential absorption LIDAR (DIAL) technique. The methane emissions from each site were quantified at an approximately one-year interval for each of the two techniques. DIAL was used to measure emissions at the sub-site, functional element (FE) level and calculate EFs for each FE using the specific FE activity data (AD). The total site methane emissions during the airborne measurements were estimated for each site using these EFs and the AD at the time. The results show the estimated methane emissions and the airborne measurements are close to agreement when considering the average of all the flight curtains (down to a 7% difference between uncertainty limits), whilst individual curtains were potentially significantly different. These results highlight the importance of fully characterising the methodology and uncertainty of both approaches. Using up-to-date, site-specific EFs or comparing over a statistically large sample size should improve agreement by reducing unknown emission uncertainties associated with site changes affecting the emission profile. Understanding each FE emission profile across a range of AD is critical to address potential differences due to non-linearity. It is important that accurate, specific and up-to-date AD is obtained to give a reliable estimate of emissions. The potential of the concept to estimate methane emissions from the FE EFs is demonstrated. Full article

Longitudinal data, characterized by repeated measurements on the same subjects over time, are ubiquitous in biomedical sciences, economics, social sciences, and engineering. Analyzing such data presents unique statistical and computational challenges, including within-subject correlation, time-varying covariates, irregular observation times, informative dropout, and high dimensionality. While traditional statistical methods, such as linear mixed-effects models and generalized estimating equations, remain foundational, they often struggle with complex nonlinear dynamics, ultra-high-dimensional feature spaces, and very large sample sizes. Over the past two decades, machine learning (ML) and artificial intelligence (AI) methods have emerged as powerful complementary approaches to address these limitations. This review provides a comprehensive survey of mathematical and computational methods for longitudinal data analysis. We cover classical statistical models, penalized regression techniques, tree-based ensemble methods, kernel machines, Bayesian hierarchical models, and modern deep learning architectures, including recurrent neural networks, temporal convolutional networks, attention-based Transformers, neural ordinary differential equations, and generative models. We propose a unified taxonomy that organizes existing methods along two primary axes: the underlying mathematical framework and the analytical objective. For each category, we present detailed mathematical formulations, discuss key theoretical properties, examine computational considerations, and summarize representative reported applications drawn from the published literature. To increase the practical value of this review, we provide a cross-cutting comparison of method families against five key challenges (within-subject correlation, irregular sampling, missing data, high dimensionality, and scalability) and offer concrete guidance on method selection according to sample size, dimensionality, and analytical objective. Finally, we critically evaluate the strengths and limitations of these approaches, with particular emphasis on interpretability, scalability, handling of missing data, robustness to covariance misspecification, and uncertainty quantification. Full article

Accurate and trustworthy prediction of lithium-ion battery aging remains challenging due to multi-mechanistic degradation, cell-to-cell variability, and distribution shift between laboratory calibration and deployment. Fractional-order models have been proposed to capture long-memory effects in electrochemical systems; however, it remains unclear when such memory is empirically identifiable and beneficial within the common prognostics abstraction of state-of-health (SOH) versus cycle index. This work develops a fully reproducible computational pipeline for mechanistic battery aging based on a Caputo fractional differential equation (FDE) and evaluates its cross-cell generalization on open NASA cycling data. Parameters are identified using bounded robust nonlinear least squares and validated under a strict transfer protocol: calibration on cells B0005/B0006 and evaluation on held-out cells B0007/B0018 without refitting. The fractional model is benchmarked against a classical ODE surrogate, an ECM-inspired resistance-proxy baseline, and one-step-ahead machine-learning predictors. Uncertainty quantification is performed via parameter bootstrap and subsequently calibrated using conformal correction to target nominal coverage under transfer. Results show that the fractional order tends to collapse toward the integer-order limit (α → 1) in this dataset, indicating limited evidence of additional long-memory at the SOH-versus-cycle level under the considered protocol, while robust identification remains essential for stability. Calibrated prediction intervals achieve near-nominal coverage on held-out cells, highlighting the importance of UQ calibration under cell-to-cell shift. The proposed scripts and environment specifications enable direct replication and facilitate future extensions to stress-aware fractional models and hybrid physics–ML approaches. Full article

Large-scale population datasets are rarely generated via simple random sampling; instead, they reflect complex designs involving stratification, clustering, and unequal inclusion probabilities. While survey weights are provided to recover population-representative estimates, standard Bayesian Kernel Machine Regression (BKMR), a flexible nonlinear model for high-dimensional exposure mixtures, does not explicitly accommodate these design features. We present a simulation-based framework that evaluates performance under complex sampling by comparing two analytic strategies applied to identical survey-like data: (i) a naïve, unweighted BKMR implementation and (ii) a design-aware workflow that can be executed using existing software without modifying the BKMR algorithm itself. Finite populations are generated with correlated exposures and a known nonlinear data-generating function. Stratified two-stage cluster samples are then drawn under both non-informative and exposure-dependent (informative) selection mechanisms, with controlled intra-class correlation (ICC). The design-aware approach incorporates sampling weights through resampling of the dataset while preserving primary sampling unit structure, followed by standard BKMR fitting. Methods are evaluated using bias, interval width, and empirical 95% coverage relative to the known truth. Across simulation scenarios, naïve BKMR exhibits bias and systematic under-coverage under informative sampling, with empirical 95% coverage often dropping to approximately 0–40%, whereas the design-aware workflow improves coverage to approximately 40–60%, moving results closer to nominal levels. These findings provide a practical, implementation-ready strategy for integrating survey design considerations into BKMR analyses and delineate conditions under which accounting for sampling design affects inference. While the proposed approach improves inferential performance relative to naïve BKMR, it does not fully achieve nominal coverage, indicating that further methodological development is required for fully valid uncertainty quantification under complex survey designs. Full article

Quantitative trading systems require predictive models that simultaneously deliver accurate forecasts, calibrated uncertainty quantification, and actionable risk measures. This paper proposes an information-theoretic semiparametric regression framework combining a convolutional neural network–Transformer (CNN–Transformer) network for nonlinear temporal dependencies with a Gaussian process (GP) prior for residual autocorrelation and calibrated predictive distributions. Three theoretical results are established: an identifiability theorem guarantees joint recoverability of the nonparametric and GP components; a consistency theorem showing that the penalised maximum likelihood estimator converges at a rate $n^{-1/(2+d_{\mathrm{eff}})}$; and a coverage theorem proving asymptotic nominal coverage of the GP’s credible intervals. The framework enables an entropy-regulated trading module where predictive differential entropy informs position sizing via an uncertainty-penalised Kelly criterion, Kullback–Leibler divergence quantifies model uncertainty, and CVaR-constrained optimisation controls the tail risk. Simulations show the method outperforms the CNN, long short-term memory (LSTM), Transformer, XGBoost, random forest, least absolute shrinkage and selection operator (LASSO), and standard GP regression approaches. Backtesting on four Chinese A-share stocks yielded annualised returns of 15.9–22.4% with Sharpe ratios of 0.49–0.62, maximum drawdowns below 15%, and daily 95% CVaR reductions of 28–31% relative to a full-Kelly baseline, confirming both predictive accuracy and risk management effectiveness. Full article

Groundwater is a vital freshwater resource that supports domestic, agricultural, and industrial activities in many regions worldwide. Accurate groundwater potential mapping (GPM) is essential for sustainable water resource management; however, traditional empirical and statistical approaches often struggle to capture the complex, nonlinear relationships among hydrogeological variables. In recent years, machine learning (ML) has emerged as a powerful data-driven approach for improving GPM accuracy and efficiency. This review synthesizes findings from 83 peer-reviewed studies published between 2015 and 2025, focusing on widely used ML algorithms such as Random Forest, Support Vector Machines, Artificial Neural Networks, and hybrid models. The review evaluates key methodological aspects, including input parameter selection, data partitioning, integration with GIS and remote sensing, and model justification techniques. It also discusses common challenges such as data limitations, regional variability, and model interpretability. The results indicate that ML-based approaches can significantly enhance groundwater prediction when supported by appropriate data and validation strategies. Future research directions include explainable artificial intelligence, uncertainty quantification, multi-source data integration, and improved model transferability. This review provides a comprehensive reference for advancing reliable and sustainable groundwater potential mapping. Full article

Offshore wind energy has developed rapidly in recent years as a crucial component of renewable energy. However, offshore wind turbines (OWTs) face significant challenges in operations under complex marine environmental conditions, such as multimodal nonlinear vibrations, reliable structural monitoring, efficient maintenance, and sustainable long-term operations. The model-updating-based parameter identification takes advantages of structural vibration measurements, assisting in structural health monitoring. However, the traditional methods have not fully accounted for the parameter uncertainties and the need for real-time state updating, making them insufficient to meet the long-term online monitoring requirements for OWTs. This study introduces an innovative structural parameter identification framework that integrates modal parameter identification with Bayesian recursive updating. The proposed framework enables more efficient updates and uncertainty quantification of critical physical parameters for OWTs. It combines the covariance-driven stochastic subspace identification (COV-SSI) method for automatic modal parameter identification with the unscented Kalman filter (UKF) for parameter estimation. A 10 MW jacket-type offshore wind turbine was used as a case study. First, the numerical simulations were conducted to generate synthetic measurements for method validation and demonstration, enabling stepwise updating of the tower material’s elastic modulus across different sea conditions. A comparison of update speed and the convergence rate with the traditional time-step-based UKF method demonstrated the superiority of the proposed sea-condition-based approach in terms of computational efficiency and stability. Finally, the proposed framework was systematically validated using scaled model experimental data of a jacket-type OWT with a 4.2% identification error, confirming its engineering applicability. This research provides reliable technical support for the safety assessment of offshore wind turbine structures. Full article

Accurate prediction of the Remaining Useful Life (RUL) of lithium-ion batteries is essential for improving the reliability, safety, and maintenance planning of electric vehicles and energy storage systems. However, battery degradation is a complex and nonlinear process influenced by multiple operational conditions, making reliable RUL estimation a challenging task. Although numerous data-driven approaches have been proposed in the literature, many studies focus primarily on improving prediction accuracy using a single modeling technique, while limited attention has been given to systematic comparisons of different algorithms and the quantification of prediction uncertainty. This study proposes a comprehensive data-driven framework for lithium-ion battery RUL prediction by integrating both traditional machine learning and deep learning approaches. A Convolutional Neural Network (CNN) model is developed to capture nonlinear degradation patterns from battery cycling data. The dataset was divided using a battery-wise validation strategy to evaluate model generalization. In addition, conventional machine learning algorithms, including k-Nearest Neighbors (KNNs), Random Forest (RF), and Extreme Gradient Boosting (XGBoost), are implemented to perform a comparative analysis of different predictive models. Key degradation-related features derived from voltage, current, temperature, and cycle information are extracted through a structured preprocessing pipeline. Furthermore, prediction uncertainty is quantified by constructing confidence intervals around the estimated RUL values. The predictive performance of the models is evaluated using prognostic metrics such as Root Mean Square Error (RMSE), Relative Prediction Error (RPE), and Prognostic Horizon (PH). The performance of the models is evaluated using multiple prognostic metrics, including Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and the coefficient of determination (R²), to ensure a comprehensive assessment of prediction accuracy. The experimental results demonstrate that the proposed framework provides accurate RUL predictions. Among the evaluated models, the CNN achieved the best performance with a Mean Absolute Error (MAE) of 7.75 and a Root Mean Square Error (RMSE) of 10.80, outperforming traditional machine learning models such as Random Forest and XGBoost. The KNN model also showed competitive performance with an RMSE of 12.07 and an R² value of 0.64, indicating that similarity-based learning can effectively capture battery degradation patterns. Full article

Accurate estimation of forest soil organic carbon (SOC) is considered critical for understanding terrestrial carbon cycling and supporting climate change mitigation strategies. However, the canopy block, intricate vertical structure of forests, and the constraints of single-source remote sensing data have presented considerable obstacles for estimating forest SOC. This study proposes a forest SOC estimation and uncertainty analysis (ForSOC-UA) framework to enhance forest SOC estimation and quantify its uncertainty in the natural secondary forests of northern China by integrating hyperspectral imagery (ZY-1F), synthetic aperture radar data (Sentinel-1), and environmental covariates (such as topography, vegetation, and soil indices). The performance of traditional machine learning models (RF, SVM, and CNN), geographically weighted regression (GWR), and a geographically weighted random forest (GWRF) model was compared across three different soil depths (0–5 cm, 5–10 cm, and 10–30 cm). The results showed that GWRF consistently outperformed all other models across all soil depth layers, with the highest accuracy achieved using multi-source data (R² = 0.58, RMSE = 27.49 g/kg, rRMSE = 0.31). Analysis of feature importance revealed that soil moisture, terrain characteristics, and Sentinel-1 polarization attributes were the primary predictors, while spectral derivatives in the red and near-infrared bands from ZY-1F also played a significant role for forest SOC estimation. The uncertainty analysis indicated a forest SOC estimation uncertainty of 37.2 g/kg in the 0–5 cm soil layer, with a decreasing trend as depth increased. This pattern is associated with the vertical spatial distribution of the measured forest SOC. This integrated approach effectively captures spatial heterogeneity and nonlinear relationships between feature and forest SOC, while also assessing estimation uncertainty, so providing a robust methodology for predicting forest SOC. The ForSOC-UA framework addresses the uncertainty quantification of SOC estimation at different vertical depths based on machine learning, providing methodological enhancements for the assessment of large-scale forest SOC and the monitoring of carbon sinks within forest ecosystems. Full article

This paper introduces a novel metric-driven evaluation framework for Remaining Useful Life (RUL) prognosis in rotating machinery, featuring robust uncertainty quantification. Accurate RUL prediction is vital for optimizing maintenance and preventing failures, but existing methods often struggle with complex nonlinear degradation or lack reliable uncertainty estimates. Our proposed framework integrates a probabilistic Deep State Space Model (DSSM) with a variational inference approach to model complex, non-linear degradation trends and inherent aleatoric uncertainty. A key innovation is the use of the Slime Mold Algorithm (SMA) for efficient hyperparameter optimization, ensuring maximum accuracy. Furthermore, an online adaptation mechanism, governed by a heuristic reinforcement learning agent, allows the model to continuously update its knowledge and adapt to concept drift in real-time. Experimental validation on the IMS bearing dataset demonstrates superior RUL prediction accuracy, evidenced by the lowest Root Mean Square Error (RMSE) of 8.1829 cycles, and a PICP of 0.59416. This dual capability makes the framework highly suitable for real-world predictive maintenance, enhancing safety and reliability. Full article

This study develops and evaluates three complementary predictive modeling frameworks for gearbox oil temperature forecasting: Stochastic Differential Equation (SDE) modeling with iterative Markov correction, multi-objective genetic algorithm-enhanced grey modeling (MOGA-GM(1,N)), and multi-output Gaussian Process Regression (MO-GPR). The study used supervisory control and data acquisition (SCADA) data from a 1.5 MW wind turbine gearbox, comprising 14 temperature measurements spanning 789 operational hours. The SDE framework partitions temperature evolution into deterministic aging effects and stochastic environmental perturbations, achieving a fitting accuracy of 2.5% and testing accuracy of 8.0% after thirty iterative corrections. The MOGA-GM(1,N) approach optimizes weight coefficients through the dual objective of minimizing the posterior difference ratio and maximizing small error probability, attaining first-class accuracy classification ($C=0.06$; $P=0.99$) while identifying mechanical loads and rotational speeds as dominant thermal drivers. MO-GPR demonstrates competitive performance with uncertainty quantification capabilities, achieving RMSE values of 2.51–7.48 depending on training SCADA data proportions. Comparative analysis shows that the iteratively refined SDE methodachieves the best prediction accuracy in this case study for continuous thermal trajectory forecasting, while MOGA-GM(1,N) excels at wear source diagnostics and operational factor analysis. The proposed framework addresses persistent challenges in wind turbine condition monitoring, including extreme nonlinearity, discontinuous data, and unpredictable thermal spikes. The results suggest potential for implementation in preventive maintenance systems, enabling timely intervention before critical thermal thresholds that precipitate component failure. Full article

Environmental monitoring systems require robust uncertainty quantification for effective decision-making in complex ecological processes. Harmful algal blooms represent a critical challenge where prediction uncertainty directly impacts resource allocation and response timing, yet current remote sensing-based prediction systems provide only deterministic classifications without confidence measures. This gap between algorithmic predictions and actionable risk assessment limits operational utility for stakeholders managing water quality under varying risk tolerances. This study developed a transferable probabilistic forecasting framework integrating Sentinel-2 multispectral imagery with quantile regression and ensemble machine learning to generate continuous confidence indicators for cyanobacteria density prediction, demonstrated through its application to Lake Okeechobee, Florida. The methodology combines spectral indices extracted from Sentinel-2 data with XGBoost for quantile regression at 0.05, 0.50, and 0.95 probability levels, and LightGBM for multi-horizon temporal forecasting. Sentinel-2’s 13 spectral bands spanning visible to shortwave infrared wavelengths, combined with its 5-day revisit frequency provide a spectrally rich and temporally dense input space that is well-suited to gradient boosting methods such as XGBoost, which can exploit complex nonlinear interactions among spectral features to distinguish cyanobacterial signatures from background water constituents. LightGBM achieved mean absolute percentage errors of 2.9% for 10-day forecasts and 5.7% for 20-day forecasts, outperforming conventional regression models. The framework generates 90% prediction intervals that enable reliable risk classifications for operational bloom management. This approach bridges the gap between satellite-based algal bloom detection and actionable decision-making by quantifying predictive uncertainty, representing a shift from binary classifications to probability-based environmental monitoring systems that accommodate varying stakeholder risk tolerances in water quality management applications. Full article