Search Results (41)

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

This paper presents a surrogate-based uncertainty quantification (UQ) framework for coupled structural–acoustic systems subject to material and geometric variability. The proposed methodology integrates the Finite Element Method (FEM) with two metamodeling techniques—the Quadratic Response Surface (QRS) and Kriging—and Monte Carlo Simulations (MCS), to efficiently characterize the probabilistic behavior of the acoustic response. Two accuracy metrics (cross-validation error and prediction error) are used to validate the surrogate models. Numerical experiments demonstrate that the Kriging metamodel trained with 30 Latin Hypercube Sampling (LHS) points achieves superior predictive accuracy, with a Relative Maximum Error of 4.125 × 10⁻⁷. Monte Carlo Simulations conducted via the Kriging surrogate reduce the computational cost by more than six orders of magnitude compared to direct FEM-based MCS, while maintaining high accuracy. The proposed framework is validated on a rectangular cavity coupled with two flexible aluminum plates, and provides an efficient and accurate tool for vibro-acoustic UQ in complex engineering systems. Full article

Accurate short-horizon downlink throughput prediction is essential for automation in high-density 5G deployments (e.g., stadiums and events), where user load, scheduling decisions, and interference conditions change rapidly and produce highly variable user-perceived rates. This paper benchmarks lightweight regression models for per-user throughput prediction from readily available radio access network (RAN) key performance indicators (KPIs) and studies a risk-aware extension that augments point forecasts with calibrated uncertainty and an abstention (deferral) rule. Experiments use a strictly time-ordered train/calibration/test protocol on the Liverpool 5G High-Density Demand (L5GHDD) dataset. The target is strongly zero-inflated (about 62% of samples at 0 Mbps) and heavy-tailed, creating regimes where average-error optimization can mask rare but operationally important bursts. In the point-prediction benchmark, the best model is a tuned two-stage support vector regressor with a mean absolute error (MAE) of $0.452$ Mbps, while the strongest single-stage model attains a weighted mean absolute percentage error (WMAPE) of $56.200\%$. For uncertainty quantification, we compare standard split conformal prediction against two input-adaptive alternatives. Constant-width split conformal attains $88.900\%$ marginal coverage for a nominal 90% target with an average interval width of $2.288$ Mbps, but width-based deferral is degenerate because all intervals have the same size. Variable-length conformal intervals preserve near-nominal coverage ($91.100\%$) while producing informative width variation: normalized conformal reduces the average width to $1.344$ Mbps, and conformalized quantile regression reduces it to $0.641$ Mbps. At a deferral threshold of $1.500$ Mbps, constant-width conformal defers all samples, whereas normalized conformal still acts on $61.200\%$ of samples with selective MAE $0.219$ Mbps. These results show that input-adaptive uncertainty is necessary for meaningful selective prediction in heteroscedastic 5G throughput dynamics. Full article

Extreme hydrological events fundamentally alter sediment transport dynamics across grain, reach, and watershed scales, rendering classical equilibrium-based transport formulations inadequate. This review synthesizes recent advances in multiscale sediment transport modeling under highly unsteady and high-magnitude forcing conditions. At the grain scale, particle-resolved simulations demonstrate that sediment entrainment is governed by turbulence intermittency and transient force exceedance rather than mean bed shear stress thresholds, particularly when the hydrograph rise timescale (T_h) becomes comparable to particle response times (T_p). At the reach scale, non-equilibrium transport emerges when the unsteadiness ratio T_h/T_a∼O(1), where T_a is the sediment adaptation timescale representing the time required for sediment flux to adjust toward transport capacity. Under these conditions, pronounced hysteresis between discharge and sediment flux is observed, requiring relaxation-based transport formulations instead of instantaneous equilibrium laws. At the watershed scale, the sediment delivery ratio (SDR), defined as the ratio of sediment yield at the basin outlet to total hillslope erosion, becomes highly time-dependent. Extreme precipitation events can activate hillslope-channel connectivity, increasing SDR by orders of magnitude relative to baseline conditions. A unified dimensionless scaling framework is presented based on mobility intensity (θ/θ_c, where θ is the Shields parameter and θ_c is its critical value for incipient motion), unsteadiness ratio (T_h/T_a), and morphodynamic coupling (T_f/T_m, where T_f is the hydraulic advection timescale and T_m is the morphodynamic adjustment timescale). This framework enables classification of sediment transport regimes ranging from quasi-equilibrium to cascade-dominated states. The synthesis demonstrates that predictive uncertainty increases nonlinearly across scales due to timescale compression, threshold activation, and feedback between flow hydraulics and evolving morphology. Recent developments in hybrid physics-AI approaches show promise in improving predictive capability by enabling dynamic transport closures, surrogate modeling of computationally expensive microscale processes, and data assimilation for real-time forecasting. However, these approaches remain limited by extrapolation uncertainty and the need to enforce physical constraints. Overall, this review concludes that regime-aware multiscale coupling, combined with uncertainty quantification and adaptive modeling strategies, is essential for robust sediment hazard prediction and climate-resilient infrastructure design under intensifying hydrological extremes. Full article

Thermodynamic entropy generation quantifies irreversibility in energy conversion processes, providing rigorous thermodynamic foundations for optimizing efficiency and sustainability in thermal and energy systems. This critical review synthesizes advances in computational entropy modeling across numerical methods, optimization strategies, and sustainable energy applications. Computational fluid dynamics, finite element methods, and lattice Boltzmann methods enable spatially resolved entropy analysis in convective, conjugate, and microscale systems, but exhibit varying maturity levels and accuracy–cost trade-offs. The minimization of entropy generation and the integration of artificial intelligence demonstrate quantifiable performance improvements in heat exchangers, renewable energy systems, and smart grids, with reported efficiency gains of 15 to 39% in specific applications under controlled conditions. While overall performance depends critically on system scale, operating regime, and baseline configuration, persistent limitations still constrain practical deployment. Systematic conflation between thermodynamic entropy (quantifying physical irreversibility) and information entropy (measuring statistical uncertainty) leads to inappropriate method selection; validation challenges arise from entropy’s status as a non-directly-measurable state function; high-order maximum entropy models achieve superior uncertainty quantification but require prohibitive computational resources; and standardized benchmarking protocols remain absent. Research fragmentation across thermodynamics, information theory, and machine learning communities limits integrated frameworks capable of addressing multi-scale, transient, multiphysics systems. This review provides structured, cross-method, application-aware synthesis identifying where computational entropy modeling achieves industrial readiness versus research-stage development, offering forward-looking insights on physics-informed machine learning, unified theoretical frameworks, and real-time entropy-aware control as critical directions for advancing sustainable energy system design. Full article

Carbon capture and storage (CCS) is essential for achieving net-zero emissions, yet amine-based capture systems face significant challenges including high energy penalties (20–30% of power plant output) and operational costs ($50–120/tonne CO₂). This study develops and validates a novel multi-scale Digital Twin (DT) framework integrating Physics-Informed Neural Networks (PINNs) to address these challenges through real-time optimization. The framework combines molecular dynamics, process simulation, computational fluid dynamics, and deep learning to enable real-time predictive control. A key innovation is the sequential training algorithm with domain decomposition, specifically designed to handle the nonlinear transport equations governing CO₂ absorption with enhanced convergence properties. The algorithm achieves prediction errors below 1% for key process variables (R² > 0.98) when validated against CFD simulations across 500 test cases. Experimental validation against pilot-scale absorber data (12 m packing, 30 wt% MEA) confirms good agreement with measured profiles, including temperature (RMSE = 1.2 K), CO₂ loading (RMSE = 0.015 mol/mol), and capture efficiency (RMSE = 0.6%). The trained surrogate enables computational speedups of up to four orders of magnitude, supporting real-time inference with response times below 100 ms suitable for closed-loop control. Under the conditions studied, the framework demonstrates reboiler duty reductions of 18.5% and operational cost reductions of approximately 31%. Sensitivity analysis identifies liquid-to-gas ratio and MEA concentration as the most influential parameters, with mechanistic explanations linking these to mass transfer enhancement and reaction kinetics. Techno-economic assessment indicates favorable investment metrics, though results depend on site-specific factors. The framework architecture is designed for extensibility to alternative solvent systems, with future work planned for industrial-scale validation and uncertainty quantification through Bayesian approaches. Full article

This study develops a tri-level adversarial robust optimization framework for cyber–physical scheduling in smart grids, addressing the intertwined challenges of coordinated cyberattacks, defensive resource allocation, and stochastic operational uncertainties. The upper level represents the attacker’s objective to maximize system disruption and conceal detection, the middle level models the defender’s optimization of detection and redundancy deployment under budgetary constraints, and the lower level performs economic dispatch given tampered data and uncertain renewable generation. The model integrates Distributionally Robust Optimization (DRO) based on a Wasserstein ambiguity set to safeguard against worst-case probability distributions, ensuring operational stability even under unobserved adversarial scenarios. A hierarchical reformulation using Karush–Kuhn–Tucker (KKT) conditions and Mixed-Integer Second-Order Cone Programming (MISOCP) transformation converts the nonconvex tri-level problem into a tractable bilevel surrogate solvable through alternating direction optimization. Numerical case studies on multi-node systems demonstrate that the proposed method reduces system loss by up to 36% compared to conventional stochastic scheduling, while maintaining 92% dispatch efficiency under high-severity attack scenarios. The results further reveal that adaptive defense allocation accelerates robustness convergence by over 50%, and that the risk–reward frontier stabilizes near a Pareto-optimal equilibrium between cost and resilience. This work provides a unified theoretical and computational foundation for adversarially resilient smart grid operation, bridging cyber-defense strategy, uncertainty quantification, and real-time economic scheduling into one coherent optimization paradigm. Full article

In the modern business environment, where uncertainty and complexity make decision-making difficult, the need for robust, transparent and adaptable support tools is highlighted. The proposed method, named Flexible Decision Navigator for Evaluating Trends and Strategies (F-DeNETS), offers a complementary perspective to classic Artificial Intelligence (AI), Big Data and Multi-Criteria Decision-Making (MCDM) tools. Despite their broad use, these methods frequently suffer from critical sensitivities in the weighting of criteria and the handling of uncertainty, leading to compromised reliability and limited practical utility in environments with limited data availability. To bridge this gap, F-DeNETS integrates intuition and uncertainty into a transparent and statistically grounded process. It introduces a balanced approach that combines statistical evidence with human judgment, extending the boundaries of classic AI, Big Data and MCDM methods. Classic MCDM methods, although useful, are sometimes limited by subjectivity, staticity and dependence on large volumes of data. To fill this gap, F-DeNETS, a hybrid framework combining Fuzzy Decision-Making Trial and Evaluation Laboratory (DEMATEL), Non-Asymptotic Fuzzy Estimators (NAFEs) and Fuzzy Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), transforms expert judgments into statistically sound fuzzy quantifications, incorporates dynamic adaptation to new data, reduces bias and enhances reliability. A numerical application from the shipping industry demonstrates that F-DeNETS offers a flexible and interpretable methodology for optimal decisions in environments of high uncertainty. Full article

Accurate short-term wind speed forecasting is essential for the sustainable operation and planning of coastal wind farms. This study develops an improved BP-PSO hybrid model that integrates particle-swarm optimization, time-ordered walk-forward validation, and uncertainty quantification through block-bootstrap confidence intervals and Monte-Carlo dropout prediction intervals. Using multi-year and seasonal datasets from four coastal stations in China—from Bohai Bay (LHT, XCS, ZFD) to Zhejiang Province (SSN)—the proposed model achieves high predictive accuracy, with RMSE values between 1.09 and 1.54 m/s, MAE between 0.79 and 1.10 m/s, and R² exceeding 0.70 at most sites. The multi-year configuration provides the most stable and robust results, while autumn at ZFD yields the highest errors due to intensified turbulence. XCS and SSN exhibit the most consistent performance, confirming the model’s spatial adaptability across distinct climatic regions. Compared with the ARIMA and persistence baselines, BP-PSO reduces RMSE by over 50%, demonstrating improved efficiency and generalization. These results highlight the potential of intelligent data-driven forecasting frameworks to enhance renewable energy reliability and sustainability by enabling more accurate wind-power scheduling, grid stability, and coastal energy system resilience. Full article

High-fidelity propagation of dynamical systems can become a cumbersome task when dealing with uncertainties modeled as random processes. The random ordinary differential equations usually describing the uncertain dynamics can be numerically integrated, but they are challenging from the computational point of view. Traditional methods usually require either the storage of a relevant amount of data or small integration steps. In this work, a hybrid method, embedding a stochastic integration method in a deterministic higher-order scheme, is conceived to obtain fast and stochastically correct results. The method is used for uncertainty propagation and quantification of aerospace problems. Results show a reduction of at least one order of magnitude for both computational time and memory usage with respect to state-of-the-art techniques, while it is able to provide statistically correct results. Full article

To provide reliable safety margins in reactor design and safety analysis, the best estimate plus uncertainty (BEPU) analysis, which is recommended by the International Atomic Energy Agency (IAEA), has drawn increasing attention worldwide. In order to systematically evaluate the sensitivity and uncertainty in the design and safety analysis of molten salt reactors (MSRs), a sensitivity and uncertainty analysis framework has been developed by integrating the reactor system safety analysis code RELAP5-TMSR with the data analysis code RAVEN. The framework is tested using the transient scenarios of the molten salt reactor experiment (MSRE): reactivity insertion accident (RIA) and station blackout (SBO). The testing results demonstrate that the proposed framework effectively conducts sensitivity and uncertainty analysis. Sensitivity analyses identify key input parameters, including the primary exchanger parameters, air radiator parameters, initial temperatures, delayed neutron parameters and volumetric heat capacity of the INOR-8 alloy. Uncertainty quantification provides 95% confidence intervals for the figures of merit (FOMs) and the steady-state and RIA scenarios remained within safety limits. The developed framework enables automated, efficient, and high-capacity sensitivity and uncertainty analysis across multiple parameters and transient scenarios. The systematic analysis provides sensitivity indicators and uncertainty distributions, offering quantitative insights into the safety margins and supporting the design and safety analysis of MSRs. Full article

Missing values in time series data present a significant challenge, often degrading the performance of downstream tasks such as classification and forecasting. Traditional approaches address this issue by first imputing the missing values and then independently solving the predictive tasks. Recent methods have leveraged self-attention models to enhance imputation quality and accelerate inference. These models, however, predict values based on all input observations—including the missing values—thereby potentially compromising the fidelity of the imputed data. In this paper, we propose the Uncertainty-Aware Self-Attention (UASA) model to overcome these limitations. Our approach introduces two novel techniques: (i) A self-attention mechanism with a partially observed diagonal that effectively captures complex non-local dependencies in time series data—a characteristic also observed in fractional-order systems. This approach draws inspiration from fractional calculus, where non-integer-order derivatives better characterize complex dynamical systems with long-memory effects, providing a more comprehensive mathematical framework for handling temporal data. And (ii) uncertainty quantification in data imputation to better inform downstream tasks. The UASA model comprises an upstream component for data imputation and a downstream component for time series prediction, trained jointly in an end-to-end fashion to optimize both imputation accuracy and task-specific objectives simultaneously. For classification tasks, the UASA model demonstrates remarkable performance even under high missing data rates, achieving a ROC-AUC of $99.5\%$, a PR-AUC of $58.5\%$, and an F1-SCORE of $49.3\%$. For forecasting tasks on the AUST-Gait dataset, the UASA model achieves a Mean Squared Error (MSE) of 0.72 under $0\%$ missing data conditions (i.e., complete data input). Under the end-to-end training strategy evaluated across all missing data rates, the model achieves an average MSE of 0.74, showcasing its adaptability and robustness across diverse missing data scenarios. Full article

This is a comprehensive overview on our research work to link interdisciplinary modeling and simulation techniques to improve the predictability and reliability simulations (PARs) of compressible turbulence with shock waves for general audiences who are not familiar with our nonlinear approach. This focused nonlinear approach is to integrate our “nonlinear dynamical approach” with our “newly developed high order entropy-conserving, momentum-conserving and kinetic energy-preserving methods” in the quantification of numerical uncertainty in highly nonlinear flow simulations. The central issue is that the solution space of discrete genuinely nonlinear systems is much larger than that of the corresponding genuinely nonlinear continuous systems, thus obtaining numerical solutions that might not be solutions of the continuous systems. Traditional uncertainty quantification (UQ) approaches in numerical simulations commonly employ linearized analysis that might not provide the true behavior of genuinely nonlinear physical fluid flows. Due to the rapid development of high-performance computing, the last two decades have been an era when computation is ahead of analysis and when very large-scale practical computations are increasingly used in poorly understood multiscale data-limited complex nonlinear physical problems and non-traditional fields. This is compounded by the fact that the numerical schemes used in production computational fluid dynamics (CFD) computer codes often do not take into consideration the genuinely nonlinear behavior of numerical methods for more realistic modeling and simulations. Often, the numerical methods used might have been developed for weakly nonlinear flow or different flow types other than the flow being investigated. In addition, some of these methods are not discretely physics-preserving (structure-preserving); this includes but is not limited to entropy-conserving, momentum-conserving and kinetic energy-preserving methods. Employing theories of nonlinear dynamics to guide the construction of more appropriate, stable and accurate numerical methods could help, e.g., (a) delineate solutions of the discretized counterparts but not solutions of the governing equations; (b) prevent numerical chaos or numerical “turbulence” leading to FALSE predication of transition to turbulence; (c) provide more reliable numerical simulations of nonlinear fluid dynamical systems, especially by direct numerical simulations (DNS), large eddy simulations (LES) and implicit large eddy simulations (ILES) simulations; and (d) prevent incorrect computed shock speeds for problems containing stiff nonlinear source terms, if present. For computation intensive turbulent flows, the desirable methods should also be efficient and exhibit scalable parallelism for current high-performance computing. Selected numerical examples to illustrate the genuinely nonlinear behavior of numerical methods and our integrated approach to improve PARs are included. Full article

This work continues the review and illustrative application to energy systems of the “Fourth-Order Best-Estimate Results with Reduced Uncertainties Predictive Modeling” (4th-BERRU-PM) methodology. The 4th-BERRU-PM methodology uses the Maximum Entropy (MaxEnt) principle to incorporate fourth-order experimental and computational information, including fourth (and higher) order sensitivities of computed model responses with respect to model parameters. The 4th-BERRU-PM methodology yields the fourth-order MaxEnt posterior distribution of experimentally measured and computed model responses and parameters in the combined phase space of model responses and parameters. The 4th-BERRU-PM methodology encompasses fourth-order sensitivity analysis (SA) and uncertainty quantification (UQ), which were reviewed in the accompanying work (Part 1), as well as fourth-order data assimilation (DA) and model calibration (MC) capabilities, which will be reviewed and illustrated in this work (Part 2). The applicability of the 4th-BERRU-PM methodology to energy systems is illustrated by using the Polyethylene-Reflected Plutonium (acronym: PERP) OECD/NEA reactor physics benchmark, which is modeled using the linear neutron transport Boltzmann equation, involving 21,976 imprecisely known parameters. This benchmark is representative of “large-scale computations” such as those involved in the modeling of energy systems. The result (“response”) of interest for the PERP benchmark is the leakage of neutrons through the outer surface of this spherical benchmark, which can be computed numerically and measured experimentally. The impact of the high-order sensitivities of the response with respect to the PERP model parameters is quantified for “high-precision” parameters (2% standard deviations) and “typical-precision” parameters (5% standard deviations). Analyzing the best-estimate results with reduced uncertainties for the 1st—through 4th-order moments (mean values, covariance, skewness, and kurtosis) produced by the 4th-BERRU-PM methodology for the PERP benchmark indicates that, even for systems modeled by linear equations (e.g., the PERP benchmark), retaining only first-order sensitivities is insufficient for reliable predictive modeling (including SA, UQ, DA, and MC). At least second-order sensitivities should be retained in order to obtain reliable predictions. Full article

This work (in two parts) will review the recently developed predictive modeling methodology called “4th-BERRU-PM” and its applicability to nuclear energy systems as exemplified by an illustrative application to the Polyethylene-Reflected Plutonium (acronym: PERP) OECD/NEA reactor physics benchmark. The acronym 4th-BERRU-PM designates the “Fourth-Order Best-Estimate Results with Reduced Uncertainties Predictive Modeling” methodology, which uses the Maximum Entropy (MaxEnt) principle to incorporate fourth-order experimental and computational information, including fourth (and higher) order sensitivities of computed model responses to model parameters, while yielding best-estimate results with reduced uncertainties for the first fourth-order moments (mean values, covariance, skewness, and kurtosis) of the optimally predicted posterior distribution of model results and calibrated model parameters. The 4th-BERRU-PM methodology encompasses the scopes of high-order sensitivity analysis (SA), uncertainty quantification (UQ), data assimilation (DA) and model calibration (MC), as will be illustrated in this work by means of the above-mentioned OECD/NEA reactor physics benchmark. This benchmark is modeled using the neutron transport Boltzmann equation involving 21,976 imprecisely known parameters, the solution of which is representative of “large-scale computations”. The model result (“response”) of interest is the leakage of neutrons through the outer surface of this spherical benchmark, which can be computed numerically and measured experimentally. Part 1 of this work illustrates the impact of high-order sensitivities, in conjunction with parameter standard deviations of various magnitudes, on the determination of the expected value and variance of the computed response in terms of the first four moments of the distribution of the uncertain model parameters. Part 2 of this work will illustrate the capabilities of the 4th-BERRU-PM methodology for combining computational and experimental information, up to and including forth-order sensitivities and distributional moments, for producing best-estimate values for the predicted responses and model parameters while reducing their accompanying uncertainties. Full article