Search Results (40)

Probabilistic streamflow models play a pivotal role in quantifying hydrological uncertainty and form the backbone of modern risk management strategies for flood and drought forecasting, water allocation planning, and the design of resilient infrastructure. Unlike deterministic approaches that yield single-point estimates, these models provide a spectrum of possible outcomes, enabling a more realistic assessment of extreme events and supporting informed, sustainable water resource decisions. By explicitly accounting for natural variability and uncertainty, probabilistic models promote transparent, robust, and equitable risk evaluations, helping decision-makers balance economic costs, societal benefits, and environmental protection for long-term sustainability. In this study, we introduce the bounded half-logistic distribution (BHLD), a novel heavy-tailed probability model constructed using the T–Y method for distribution generation, where T denotes a transformer distribution and Y represents a baseline generator. Although the BHLD is conceptually related to the Pareto and log-logistic families, it offers several distinctive advantages for streamflow modeling, including a flexible hazard rate that can be unimodal or monotonically decreasing, a finite lower bound, and closed-form expressions for key risk measures such as Value at Risk (VaR) and Tail Value at Risk (TVaR). The proposed distribution is defined on a lower-bounded domain, allowing it to realistically capture physical constraints inherent in flood processes, while a log-logistic-based tail structure provides the flexibility needed to model extreme hydrological events. Moreover, the BHLD is analytically characterized through a governing differential equation and further examined via its characteristic function and the maximum entropy principle, ensuring stable and efficient parameter estimation. It integrates a half-logistic generator with a log-logistic baseline, yielding a power-law tail decay governed by the parameter $\beta$, which is particularly effective for representing extreme flows. Fundamental properties, including the hazard rate function, moments, and entropy measures, are derived in closed form, and model parameters are estimated using the maximum likelihood method. Applied to four real streamflow data sets, the BHLD demonstrates superior performance over nine competing distributions in goodness-of-fit analyses, with notable improvements in tail representation. The model facilitates accurate computation of hydrological risk metrics such as VaR, TVaR, and tail variance, uncovering pronounced temporal variations in flood risk and establishing the BHLD as a powerful and reliable tool for streamflow modeling under changing environmental conditions. Full article

Background/Objectives: Glioblastoma (GBM) exhibits heterogeneous, nonlinear invasion patterns that challenge conventional modeling and radiomic prediction. Most deep learning approaches describe the morphology but rarely capture the dynamical stability of tumor evolution. We propose an AI framework that approximates a latent attractor landscape of GBM morphodynamics—stable basins in a continuous manifold that are consistent with reproducible morphologic regimes. Methods: Multimodal MRI scans from BraTS 2020 (n = 494) were standardized and embedded with a 3D autoencoder to obtain 128-D latent representations. Unsupervised clustering identified latent basins (“attractors”). A neural ordinary differential equation (neural-ODE) approximated latent dynamics. All dynamics were inferred from cross-sectional population variability rather than longitudinal follow-up, serving as a proof-of-concept approximation of morphologic continuity. Voxel-level perturbation quantified local morphodynamic sensitivity, and proof-of-concept control was explored by adding small inputs to the neural-ODE using both a deterministic controller and a reinforcement learning agent based on soft actor–critic (SAC). Survival analyses (Kaplan–Meier, log-rank, ridge-regularized Cox) assessed associations with outcomes. Results: The learned latent manifold was smooth and clinically organized. Three dominant attractor basins were identified with significant survival stratification (χ² = 31.8, p = 1.3 × 10⁻⁷) in the static model. Dynamic attractor basins derived from neural-ODE endpoints showed modest and non-significant survival differences, confirming that these dynamic labels primarily encode the morphodynamic structure rather than fixed prognostic strata. Dynamic basins inferred from neural-ODE flows were not independently prognostic, indicating that the inferred morphodynamic field captures geometric organization rather than additional clinical risk information. The latent stability index showed a weak but borderline significant negative association with survival (ρ = −0.13 [−0.26, −0.01]; p = 0.0499). In multivariable Cox models, age remained the dominant covariate (HR = 1.30 [1.16–1.45]; p = 5 × 10⁻⁶), with overall C-indices of 0.61–0.64. Voxel-level sensitivity maps highlighted enhancing rims and peri-necrotic interfaces as influential regions. In simulation, deterministic control redirected trajectories toward lower-risk basins (≈57% success; ≈96% terminal distance reduction), while a soft actor–critic (SAC) agent produced smoother trajectories and modest additional reductions in terminal distance, albeit without matching the deterministic controller’s success rate. The learned attractor classes were internally consistent and clinically distinct. Conclusions: Learning a latent attractor landscape links generative AI, dynamical systems theory, and clinical outcomes in GBM. Although limited by the cross-sectional nature of BraTS and modest prognostic gains beyond age, these results provide a mechanistic, controllable framework for tumor morphology in which inferred dynamic attractor-like flows describe latent organization rather than a clinically predictive temporal model, motivating prospective radiogenomic validation and adaptive therapy studies. Full article

When the Colebrook equation is used in its original implicit form, the unknown pipe flow friction factor can only be obtained through time-consuming and computationally demanding iterative calculations. The empirical Colebrook equation relates the unknown Darcy friction factor to a known Reynolds number and a known relative roughness of a pipe’s inner surface. It is widely used in engineering. To simplify computations, a variety of explicit approximations have been developed, the accuracy of which must be carefully evaluated. For this purpose, this Data Descriptor gives a sufficient number of pipe flow friction factor values that are computed using a highly accurate iterative algorithm to solve the implicit Colebrook equation. These values serve as reference data, spanning the range relevant to engineering applications, and provide benchmarks for evaluating the accuracy of the approximations. The sampling points within the datasets are distributed in a way that minimizes gaps in the data. In this study, a Python Version v1 script was used to generate quasi-random samples, including Halton, Hammersley, Sobol, and deterministic lattice-based Korobov samples, which produce smaller gaps than purely random samples generated for comparison purposes. Using these sequences, a total of 2²⁰ = 1,048,576 data points were generated, and the corresponding datasets are provided in in the zenodo repositoryWhen a smaller subset of points is needed, the required number of initial points from these sequences can be used directly. Full article

This study presents an analysis of transverse vibration behavior of a fluid-conveying pipe mounted on an elastic foundation, incorporating both classical analytical techniques and modern physics-informed neural network (PINN) methodologies. A partial differential equation (PDE) architecture is developed to approximate the solution by embedding the physics PDE, initial, and boundary conditions directly into the loss function of a deep neural network. A one-dimensional fourth-order PDE is employed to model governing transverse displacement derived from Euler–Bernoulli beam theory, with additional terms representing fluid inertia, flow-induced excitation, and stochastic force modelled as Gaussian white noise. The governing PDE is decomposed via separation of variables into spatial and temporal components, and modal analysis is employed to determine the natural frequencies and mode shapes under free–free boundary conditions. The influence of varying flow velocities and excitation frequencies on critical buckling behavior and mode shape deformation is analyzed. The network is trained using the Resilient Backpropagation (RProp) optimizer. A preliminary validation study is presented in which a baseline PINN is benchmarked against analytical modal solutions for a fluid-conveying pipe on an elastic foundation under deterministic excitation. The results demonstrate the capability of PINNs to accurately capture complex vibrational phenomena, offering a robust framework for data-driven modelling of fluid–structure interactions in engineering applications. Full article

Imaging through dynamic scattering media remains a fundamental challenge because of severe information loss and the ill-posed nature of the inversion problem. Conventional methods often struggle to strike a balance between reconstruction fidelity and efficiency in evolving environments. In this study, we present DynaFlowNet, a framework that leverages conditional flow matching theory to establish a continuous, invertible mapping from speckle patterns to target images via deterministic ordinary differential equation (ODE) integration. Central to this is the novel temporal–conditional residual attention block (TCResAttnBlock), which is designed to model spatiotemporal scattering dynamics. DynaFlowNet achieves real-time performance at 134.77 frames per second (FPS), which is 117 times faster than diffusion-based models, while maintaining state-of-the-art reconstruction quality (28.46 dB peak signal-to-noise ratio (PSNR), 0.9112 structural similarity index (SSIM), and 0.8832 Pearson correlation coefficient (PCC)). In addition, the proposed framework demonstrates exceptional geometric generalization, with only a 1.05 dB PSNR degradation across unseen geometries, significantly outperforming existing methods. This study establishes a new paradigm for real-time high-fidelity imaging using dynamic scattering media, with direct implications for biomedical imaging, remote sensing, and underwater exploration. Full article

The rapid electrification of transportation and the proliferation of rooftop solar photovoltaics (PVs) in urban environments are reshaping the operational dynamics of power distribution networks. However, the inherent uncertainty in electric vehicle (EV) behavior—including arrival times, charging preferences, and state-of-charge—as well as spatially and temporally variable solar generation, presents a profound challenge to existing scheduling frameworks. This paper proposes a novel data-driven distributionally robust optimization (DDRO) framework for solar-powered EV charging coordination under spatiotemporal uncertainty. Leveraging empirical datasets of EV usage and solar irradiance from a smart city deployment, the framework constructs Wasserstein ambiguity sets around historical distributions, enabling worst-case-aware decision-making without requiring the assumption of probability laws. The problem is formulated as a two-stage optimization model. The first stage determines day-ahead charging schedules, solar utilization levels, and grid allocations across an urban-scale distribution feeder. The second stage models real-time recourse actions—such as dynamic curtailment or demand reshaping—after uncertainties are realized. Physical grid constraints are modeled using convexified LinDistFlow equations, while EV behavior is segmented into user classes with individualized uncertainty structures. The model is evaluated on a modified IEEE 123-bus feeder with 52 EV-PV nodes, using 15 min resolution over a 24 h horizon and 12 months of real-world data. Comparative results demonstrate that the proposed DDRO method reduces total operational costs by up to 15%, eliminates voltage violations entirely, and improves EV service satisfaction by more than 30% relative to deterministic and stochastic baselines. This work makes three primary contributions: it introduces a robust, tractable optimization architecture that captures spatiotemporal uncertainty using empirical Wasserstein sets; it integrates behavioral and physical modeling within a unified dispatch framework for urban energy-mobility systems; and it demonstrates the value of robust coordination in simultaneously improving grid resilience, renewable utilization, and EV user satisfaction. The results offer practical insights for city-scale planners seeking to enable the reliable and efficient electrification of mobility infrastructure under uncertainty. Full article

Stream–aquifer interactions, as well as surface water/groundwater interactions within wetlands, require a solution of complex partial differential equations of flow and contaminant transport, namely a deterministic approach. Groundwater level (GWL) responses to precipitation, particularly for extreme value events such as annual maxima, require a probabilistic approach to evaluate potential climate trends. It is commonly assumed that the distribution of annual maxima series (AMS) precipitation follows the generalized extreme value distribution (GEV). If the extremes of the data are nonstationary, it is possible to incorporate this knowledge into the parameters of the GEV. This approach is also applied to the computed annual maxima of daily groundwater level data. Nonstationary versus stationary time series for both groundwater level and AMS 24-h duration precipitation are compared for National Oceanic and Atmospheric Administration (NOAA) stations with nearby wells. Predicted extreme value analysis (EVA) climate trends for wells penetrating limestone aquifers directly beneath rainfall monitoring stations at major airports indicate similar GWL response. Groundwater levels at wells located near coastlines are partially impacted by sea level rise. An extreme value analysis of the GWL is shown to be a useful tool to confirm hydrologic connections and long-term climate trends. Full article

The main aim of this study is to achieve the numerical solution for the Navier–Stokes equations for incompressible, non-turbulent, and subsonic fluid flows with some Gaussian physical uncertainties. The higher-order stochastic finite volume method (SFVM), implemented according to the iterative generalized stochastic perturbation technique and the Monte Carlo scheme, are engaged for this purpose. It is implemented with the aid of the polynomial bases for the pressure–velocity–temperature (PVT) solutions, for which the weighted least squares method (WLSM) algorithm is applicable. The deterministic problem is solved using the freeware OpenFVM, the computer algebra software MAPLE 2019 is employed for the LSM local fittings, and the resulting probabilistic quantities are computed. The first two probabilistic moments, as well as the Shannon entropy spatial distributions, are determined with this apparatus and visualized in the FEPlot software. This approach is validated using the 2D heat conduction benchmark test and then applied for the probabilistic version of the 3D coupled lid-driven cavity flow analysis. Such an implementation of the SFVM is applied to model the 2D lid-driven cavity flow problem for statistically homogeneous fluid with limited uncertainty in its viscosity and heat conductivity. Further numerical extension of this technique is seen in an application of the artificial neural networks, where polynomial approximation may be replaced automatically by some optimal, and not necessarily polynomial, bases. Full article

Surface runoff flows must be drained safely through culverts in ephemeral flow streams and bridges in perennial streams without any damage to the road or highway infrastructure stability. In practice, bridges cross drainage basin channels reliably, and they are more carefully planned, designed, constructed, and maintained against extreme water passages, but culverts are subject to even less frequent and intensive rainfall consequent surface runoff occurrences with higher risk potential. It is, therefore, necessary to design culverts more carefully in such a way that they drain down the upstream surface water without any critical problem to the road downstream of the road stream channels. Most of the hydrological, hydraulic, and sedimentological formulations are empirical expressions that are widely valid for locations where culverts are suitably developed based on simple bivalent logical rules between factors involved in upstream inlet locations of culverts. One of the first logic rule-based methods in the literature is Talbot’s procedural approach to culvert design. This approach is based not only on an explicit equation, but also on a set of linguistically proposed design rules that are expressed deterministically to effectively eliminate most of the ambiguities. This paper proposes a modified approach with additional logistic structural features based on a bivalent logic inference system, which is an improved version of the Talbot procedure and leads to better culvert transition surface flow prediction. The proposed method is applied to a local area in Tekirdağ City, Türkiye, where a serious train accident occurred due to a poorly maintained culvert. Full article

Hydrodynamic traffic models are crucial to optimizing transportation efficiency and urban planning. They usually comprise a set of coupled partial differential equations featuring an arbitrary number of terms that aim to describe the different nuances of traffic flow. Consequently, traffic models quickly become complicated to solve and difficult to interpret. In this article, we present a general traffic model that includes a relaxation term and an inflow of vehicles term and utilize the mathematical technique of nondimensionalisation to obtain universal solutions to the model. Thus, we are able to show extreme sensitivity to initial conditions and parameter changes, a classical signature of deterministic chaos. Moreover, we obtain simple relations among the different variables governing traffic, thus managing to efficiently describe the onset of traffic jams. We validate our model by comparing different scenarios and highlighting the model’s applicability regimes in traffic equations. We show that extreme speed values, or heavy traffic inflow, lead to divergences in the model, showing its limitations but also demonstrating how the problem of traffic jams can be alleviated. Our results pave the way to simulating and predicting traffic accurately on a real-time basis. Full article

The influence of a background vortex flow on the clustering of floating tracers is addressed. The vortex flow considered is induced by an ellipsoidal vortex evolving in a deformation. The system exhibits various vortex motion regimes: (1) a steady state, (2) oscillation and (3) rotation of the ellipsoidal vortex core. The latter two induce an unsteady velocity field for the tracer, thus leading to irregular (chaotic) tracer motion. Superimposing a stochastic divergent velocity field onto the deterministic vortex flow allows us to observe significantly different tracer evolution. An ellipsoidal vortex has ellipsoidal symmetry, and the tracer’s trajectories exhibit the same symmetry inside the vortex. Outside the vortex, the external deformation flow symmetry dominates. Diffusion scattering and chaotic advection give tracers the opportunity to leave the region of ellipsoidal symmetry and form a picture of shear flow symmetry. We use the method of characteristics to integrate the floating tracer density evolution equation and the Euler Ito scheme for obtaining the floating tracer trajectories with a random velocity field. The cluster area and cluster mass from the statistical topography are used as the quantitative diagnostics of a floating tracer’s clustering. For the case of a steady ellipsoidal vortex embedded into the deformation flow with a random velocity field component, we found that the clustering characteristics were weakened by the steady vortex. For the cases of an unsteady ellipsoidal vortex, we observed clustering in the floating tracer density field if the contribution of the divergent component was greater than or equal to that of the rotational (nondivergent) component. Even when the initial floating tracer patch was set on the boundary of the oscillating ellipsoidal vortex, we observed the formation of clusters. In the case of a rotating ellipsoidal vortex, we also observed pronounced clustering. Thus, we argue that unsteady ellipsoidal vortex regimes (oscillation and rotation), which induce chaotic motion of the nearby passive tracer’s trajectories, are still conducive to clustering of floating tracers observed in the density field, despite the intense deformation introduced by strain and shear. Full article

Water distribution networks (WDNs) are defined as the planning for the development, distribution, and utilization of water resources. The main challenge of WDNs is to preserve limited water resources while providing effective benefits from these resources in accordance with environmental considerations. Water distribution networks use hydraulic components to connect water resources to consumers. The diameter of each pipe, the layout of the pipe network, and the total length of pipes all contribute to the most effective layout for a water distribution system. This study considers the assurance that the flow (discharge) of water is in accordance with what is expected, with such aspects apt to be described as a particular form of reliability. As a result, this study proposes a stochastic optimization model with non-linear probability constraints for overcoming the challenges of water distribution networks while taking water flow reliability into account. The pressure drop equation causes the non-linear shape. The stochastic model of the opportunity constraint is changed to a deterministic multi-objective model using an approach based on integer programming and sample averaging to solve the resulting model. The direct search approach (neighbourhood search) is then applied to tackle the integer part. Full article

For a new power system using high-penetration renewable energy, the traditional deterministic power flow analysis method cannot accurately represent the stochastic characteristics of each state variable. The aggregation of renewable energy with different meteorological characteristics in the AC/DC interconnected grid significantly increases the difficulty of establishing a steady-state model. Therefore, this study proposes an improved Latin hypercube sampling algorithm using the van der Waerden scores and diffusion kernel density estimation to overcome the limitations of a priori assumption on probability distributions in uncertainty modeling and to retain the correlations among random variables in the sampling data. Interconnected grids are constructed with IEEE 9-bus and IEEE 14-bus and modified with IEEE 57-bus to describe common application cases of aggregated renewable energy. On this basis, the approximation errors of the proposed probabilistic power flow algorithm to the statistical characteristics of the power parameters are evaluated by setting the Nataf algorithm and the Latin hypercube algorithm using adaptive kernel density estimation as the control group. The results show that the improved Latin hypercube sampling algorithm can exhibit high computational accuracy and strong adaptability, both in severe operating scenarios with large amplitude of load fluctuations and with nonlinear power balance equations incorporating high dimensional random variables. Full article

The flood peak is commonly estimated using the rational method for the design of hydraulic structures. The method is mainly used in a deterministic context. However, there is often uncertainty in flood predictions, which should be incorporated in the design of mitigation schemes. This research proposes a methodology to cope with uncertainty in the rational method via the application of a stochastic framework. Data from 158 storms, recorded in the period 1984–1987 in 19 subbasins in the southwestern part of Saudi Arabia, were used to implement the proposed methodology. A tri-variate log-normal probability density function was used to model the joint relationship between the rational method parameters. The model considered the parameters as random variables. The uncertainty in the rainstorms was represented by intensity or depth; the uncertainty in basin delineation (due to the use of different digital elevation model resolution) was represented by the basin area; and the uncertainty in the land use/land cover was represented by the runoff coefficient. The Monte Carlo method was used to generate realizations of the peak flow and runoff volume with 95% and 99% confidence levels from the input parameters. Although the correlation between the parameters was weak, the model was capable of simulating the rational model parameters and estimating the peak flow and runoff volume relatively well, and the generated realizations fell within the confidence levels, except for a few marginal cases. The model can be used to generate peak flows and the associated confidence limits in ungauged basins from the statistics of the input parameters using the equations developed in this study. Full article

Stochastic simulations enable researchers to incorporate uncertainties beyond numerical discretization errors in computational fluid dynamics (CFD). Here, the authors provide examples of stochastic simulations of incompressible flows and numerical solutions for validating these newly emerging stochastic modeling methods. A numerical scheme is constructed for finding solutions to stochastic parabolic equations. The scheme is second-order accurate in time for the constant coefficient of the Wiener process term. The stability analysis of the scheme is also provided. The scheme is applied to the dimensionless heat and mass transfer model of mixed convective non-Newtonian nanofluid flow over oscillatory sheets. Both the deterministic and stochastic energy equations use temperature-dependent thermal conductivity. The stochastic model is more general than the deterministic model. The results are calculated for both flat and oscillatory plates. Casson parameter, mixed convective parameter, thermophoresis, Brownian motion parameter, Prandtl number, Schmidt number, and reaction rate parameter all impact the velocities, temperatures, and concentrations shown in the graphs. Under the influence of the oscillating plate, the results reveal that the concentration profile decreases with increasing Brownian motion parameters and increases with increasing thermophoresis parameters. The behavior of the velocity profile for the deterministic and stochastic models is provided, and contour plots for the stochastic model are also displayed. This article aims to provide a state-of-the-art overview of recent achievements in the field of stochastic computational fluid dynamics (SCFD) while also pointing out potential future avenues and unresolved challenges for the computational mathematics community to investigate. Full article