Article
Computer Science, Information Systems
Changxiao Cai, H. Vincent Poor, Yuxin Chen
Summary: We study the distribution and uncertainty of non-convex optimization for noisy tensor completion, focusing on a two-stage estimation algorithm that characterizes the distribution of this nonconvex estimator. Our findings unveil the statistical optimality of nonconvex tensor completion, achieving un-improvable l(2) accuracy when estimating unknown tensor and underlying tensor factors.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2023)
Article
Engineering, Civil
Yuhua Yan, Xiaojun Wang, Yunlong Li
Summary: A non-probabilistic credible set model is proposed for uncertainty quantification of structural parameters in this paper. This method surpasses probabilistic and traditional non-probabilistic methods by providing both the distribution range and credibility of uncertain parameters, resulting in reduced computation time and improved credibility. The average inverse-distance information entropy, expanded uncertainty, and credibility are introduced to establish a one-dimensional non-probabilistic credible set uncertainty quantification procedure. The theory of non-probabilistic sets and correlation analysis of multidimensional uncertain parameters are used to develop a multidimensional non-probabilistic credible set uncertainty quantification method. The feasibility of applying this method to various engineering problems is verified through case studies.
Article
Computer Science, Artificial Intelligence
Fabian Guignard, Federico Amato, Mikhail Kanevski
Summary: This paper introduces novel estimations to improve understanding of ELM variability by providing identification and interpretation of different variability sources.
Article
Statistics & Probability
Moumita Chakraborty, Subhashis Ghosal
Summary: This study investigates the coverage of a Bayesian credible interval for a regression function under a monotonicity constraint, using a projection-posterior distribution for analysis. Sample projections onto the space of monotone increasing functions are used to obtain credible intervals for a specific point. The study also examines the phenomenon of higher coverage compared to nominal credibility levels, with a proposed recalibration method for achieving the right asymptotic coverage.
ANNALS OF STATISTICS
(2021)
Article
Engineering, Geological
Weiwei Zhan, Laurie G. Baise, Babak Moaveni
Summary: This study introduces an uncertainty quantification framework for data-driven global natural hazard predictive models, which includes characterizing different sources of uncertainty, conducting sensitivity analysis, and propagating uncertainty. Parameter estimation uncertainty, modeling error, and geospatial input uncertainty are identified as the main sources of uncertainty. The proposed framework provides a measure of uncertainty on model predictions and can be applied to logistic-regression models and other geospatial modeling problems.
ENGINEERING GEOLOGY
(2023)
Article
Engineering, Biomedical
Selma Metzner, Gerd Wubbeler, Sebastian Flassbeck, Constance Gatefait, Christoph Kolbitsch, Clemens Elster
Summary: Magnetic Resonance Fingerprinting (MRF) is a promising technique for fast quantitative imaging of human tissue, providing valuable diagnostic parameters like T-1 and T-2 MR relaxation times. A Bayesian approach is proposed for uncertainty quantification of dictionary-based MRF, leading to probability distributions for T-1 and T-2 in every voxel. The method successfully characterizes uncertainties in relaxation time estimates and is consistent with observed variability in simulations and in vivo measurements.
PHYSICS IN MEDICINE AND BIOLOGY
(2021)
Article
Automation & Control Systems
Ruihan Wang, Hui Chen, Cong Guan
Summary: This paper introduces the application of Bayesian analysis in the performance prognostics of marine diesel engines, presents two Bayesian models, indirectly predicts engine performance through instantaneous angular speed signals, and demonstrates the superiority of online condition monitoring through this method.
Article
Engineering, Biomedical
Shi-ang Qi, Neeraj Kumar, Ruchika Verma, Jian-Yi Xu, Grace Shen-Tu, Russell Greiner
Summary: The research introduces a Bayesian-neural-network-based Individual Survival Distribution (ISD) model that accurately predicts a patient's survival probability and quantifies the uncertainty in parameter estimation. The model supports feature selection and computes credible intervals, aiding in assessing the model's confidence in its predictions.
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING
(2023)
Article
Remote Sensing
Jin Xu, Lindi J. Quackenbush, Timothy A. Volk, Stephen Stehman
Summary: This study evaluated the uncertainty of shrub willow health characterization based on unmanned aerial systems (UAS) data. The results showed that regression models built at different spatial scales could be applied across time, space, and scales. The study also quantified the uncertainty of model parameters and found that the uncertainty increased as pixel size increased. The findings provide guidance for future experimental design to save resources.
INTERNATIONAL JOURNAL OF APPLIED EARTH OBSERVATION AND GEOINFORMATION
(2022)
Article
Mathematics, Interdisciplinary Applications
Paolo Giordani, Henk A. L. Kiers
Summary: Principal covariate regression (PCOVR) is a method for regressing a set of criterion variables with respect to a set of predictor variables when the latter are numerous and/or collinear. This study demonstrates how statistical uncertainties of the PCOVR parameter estimates can be estimated using bootstrap approach, with four strategies derived for estimating bootstrap confidence intervals. Overall, the four strategies showed appropriate statistical behavior in terms of coverage, with exceptions observed in cases with complex underlying structures of the components. The statistical behavior was more accurate when the correct number of components were extracted.
BRITISH JOURNAL OF MATHEMATICAL & STATISTICAL PSYCHOLOGY
(2021)
Article
Statistics & Probability
Kenneth Rice, Lingbo Ye
Summary: This article introduces a new method for determining credible intervals, based on the loss function and Bayes rule, which can be used for any model and prior, and justifies widely used choices for credible intervals.
AMERICAN STATISTICIAN
(2022)
Article
Biochemistry & Molecular Biology
David R. Bickel
Summary: Confidence intervals of divergence times and branch lengths do not reflect uncertainty about their clades or model assumptions. Uncertainty about clades can be adjusted by multiplying confidence level with bootstrap proportion, while uncertainty about the model can be propagated by reporting the union of confidence intervals from plausible models. The proposed methods of uncertainty quantification may be used together.
MOLECULAR PHYLOGENETICS AND EVOLUTION
(2022)
Review
Physics, Applied
Yarin Gal, Petros Koumoutsakos, Francois Lanusse, Gilles Louppe, Costas Papadimitriou
Summary: Five researchers discuss the quantification of uncertainty in machine-learned models, focusing on issues relevant to physics problems. It is crucial to be able to measure uncertainty when comparing theoretical or computational models with observations in order to conduct sound scientific investigations. With the increasing popularity of data-driven modeling, understanding different sources of uncertainty and developing methods to estimate them has become a renewed area of interest.
NATURE REVIEWS PHYSICS
(2022)
Article
Computer Science, Artificial Intelligence
Nicolas Dewolf, Bernard De Baets, Willem Waegeman
Summary: In this independent comparative study, four classes of methods, including Bayesian methods, ensemble methods, direct interval estimation methods, and conformal prediction methods, are reviewed for their validity and calibration in the regression setting. Results on benchmark data sets show large fluctuations in performance across different domains. Conformal prediction can be used as a general calibration procedure for methods that deliver poor results without calibration.
ARTIFICIAL INTELLIGENCE REVIEW
(2023)
Article
Automation & Control Systems
Shailesh Garg, Souvik Chakraborty
Summary: VB-DeepONet is a Bayesian operator learning framework that addresses the challenges faced by the deterministic DeepONet architecture. It provides better resistance against overfitting, improved generalization, and allows for the quantification of predictive uncertainty. The results from various mechanics problems demonstrate the effectiveness of VB-DeepONet in uncertainty quantification.
ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE
(2023)
Article
Agronomy
Yang Yang, Yan Zhu, Jingwei Wu, Wei Mao, Ming Ye, Jinzhong Yang
Summary: A new subsurface drainage (SDR) package based on the Hooghoudt equation was developed to accurately simulate the effects of subsurface drainage pipes on groundwater flow and salt dynamics. The accuracy and applicability of SDR were tested through synthetic and field experiments, demonstrating its ability to accurately model leaching water and solute transport. Applied in the Yonglian irrigation area of Inner Mongolia, China, the SDR system increased total salt discharge by 38-54%, with 36-45% discharged by subsurface drainage pipes, providing a pilot example for regional subsurface drainage system design.
AGRICULTURAL WATER MANAGEMENT
(2022)
Article
Engineering, Multidisciplinary
Jing Hu, Qimin Zhang, Anke Meyer-Baese, Ming Ye
Summary: This study introduces a new model to address the increasing prevalence of Alzheimer's disease in today's society, using a stochastic reaction-diffusion approach to calculate the progression of AD and providing conditions for finite-time stability. Furthermore, an optimal control problem is formulated to minimize pathogenic proteins and control costs, with specific examples provided for demonstration.
APPLIED MATHEMATICAL MODELLING
(2022)
Article
Agronomy
Wei Mao, Yan Zhu, Jingwei Wu, Ming Ye, Jinzhong Yang
Summary: This study evaluated the effects of limited irrigation on water movement and salt accumulation in agricultural areas. The results showed that limited irrigation led to a decline in groundwater level, increased soil salt storage, and a threat of soil salinization.
AGRICULTURAL WATER MANAGEMENT
(2022)
Article
Agronomy
Tianxing Zhao, Yan Zhu, Ming Ye, Jinzhong Yang, Biao Jia, Wei Mao, Jingwei Wu
Summary: Accurate estimation of phreatic evapotranspiration (ET) is crucial for water resource management and prevention of soil salinization. This study developed a new approach based on NDVI and measured water table depths to estimate the spatial-temporal distribution of phreatic ET. The results matched well with the groundwater balance model and showed the importance of phreatic ET in supporting crop growth and the ecological environment in arid areas.
AGRICULTURAL WATER MANAGEMENT
(2022)
Article
Environmental Sciences
Ahmed S. Elshall, Ming Ye, Sven A. Kranz, Julie Harrington, Xiaojuan Yang, Yongshan Wan, Mathew Maltrud
Summary: Earth system models are valuable tools for climate services, but their potential for regional environmental management is yet to be fully explored. This article demonstrates the use of high-resolution models to study the Florida Red Tide and establishes a causal link between the position of Loop Current and red tide occurrences. The study highlights the prospects of utilizing publicly available data for regional management and discusses the importance of stakeholder participation in future model development.
ENVIRONMENTAL EARTH SCIENCES
(2022)
Article
Mathematics, Interdisciplinary Applications
Jing Hu, Qimin Zhang, Anke Meyer-Baese, Ming Ye
Summary: In this paper, two classes of mathematical models associated with Alzheimer's disease (AD) are developed, considering reaction-diffusion, delay and random disturbances. The stability of the equilibrium and the Hopf bifurcation in the deterministic AD model are analyzed. The finite-time contractive stability (FTCS) for the stochastic AD model modulated by Markov switching process is investigated, focusing on the influence of uncertain factors in the environment on AD.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2022)
Article
Engineering, Civil
Qi Liu, Heng Dai, Dongwei Gui, Bill X. Hu, Ming Ye, Guanghui Wei, Jingxiu Qin, Jin Zhang
Summary: This study used wavelet analysis to evaluate the effects of flow regimes of ecological water transport projects (EWTP) on ecohydrological system dynamics. The results showed that the restoration flow exhibited seasonal periodicities different from natural streams, leading to distinct groundwater dynamics and mismatched growth rhythm of riparian vegetation. Two designed flow schemes based on time lags between flow and vegetation growth were proposed to optimize the EWTP and improve ecosystem restoration efficiency. The NARX network was used for ecological restoration prediction, showing a significant increase in restoration flow compared to the original flow. The methodologies used in this study are rigorous and applicable to other EWTPs.
JOURNAL OF HYDROLOGY
(2022)
Article
Engineering, Civil
Mengqin Wang, Yan Zhu, Tianxing Zhao, Lihong Cui, Wei Mao, Ming Ye, Jingwei Wu, Jinzhong Yang
Summary: Field experiments were conducted to analyze the non-synchronized movement of soil water and salt during freezing-thawing periods, with a focus on soil salt composition and convection-diffusion theory. The results shed light on the mechanisms underlying soil water and salt dynamics in agricultural systems with shallow groundwater tables.
JOURNAL OF HYDROLOGY
(2022)
Article
Mathematics, Applied
Wenrui Li, Ming Ye, Qimin Zhang, Meyer-Baese Anke, Yan Li
Summary: This paper introduces a periodic averaging method for impulsive stochastic age-structured population models in a polluted environment. It demonstrates the uniqueness of the solutions and the mean-square convergence criteria of numerical solutions, and validates the efficiency of the method through a simulation example.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Engineering, Mechanical
Jing Hu, Qimin Zhang, Anke Meyer-Baese, Ming Ye
Summary: In this paper, a stochastic model is proposed to describe the dynamics of substances related to Alzheimer's disease. The theoretical results are validated by numerical simulations.
NONLINEAR DYNAMICS
(2022)
Article
Environmental Sciences
Tian Jiao, Ming Ye, Menggui Jin, Jing Yang
Summary: The Smoothed Particle Hydrodynamics (SPH) method is a Lagrangian approach widely used for solving numerical dispersion problems in groundwater solute transport. To improve accuracy in models with irregular particle distribution, an Interactively Corrected SPH (IC-SPH) method was developed. IC-SPH uses interactively corrected kernel gradients to construct concentration gradients, resulting in more accurate and faster converging solutions.
WATER RESOURCES RESEARCH
(2022)
Article
Mathematics, Applied
Wenjuan Guo, Qimin Zhang, Ming Ye
Summary: This paper develops an age-structured HIV model considering age of infected cells and intracellular delay, and a stochastic age-structured HIV model with Markovian switching to study finite-time contraction stability. Theoretical and numerical results illustrate the impact of noise intensity and delay on stability of the HIV models.
Article
Engineering, Civil
Yan Zhu, Tianxing Zhao, Wei Mao, Ming Ye, Xudong Han, Biao Jia, Jinzhong Yang
Summary: A modified UBMOD flow model was developed to accurately estimate soil water content and water table depth in arid agricultural areas with shallow water table depth. The model incorporates the impact of capillary rise and calculates water table depth using the water table depth fluctuation analysis. The results demonstrated its effectiveness and low computational cost, making it a valuable tool for hydrodynamic studies in areas with shallow water table depths.
JOURNAL OF HYDROLOGY
(2023)
Article
Engineering, Civil
Mengqin Wang, Yan Zhu, Wei Mao, Ming Ye, Jinzhong Yang
Summary: Current research on soil salt movement during the freeze and thaw period has focused mainly on total salt concentration, neglecting the phase change of multi-component salts. This study investigated the potential transport capability of soil water and salt ions in the frozen layer using chemical characteristics and solute convection-diffusion theory. Field experiments were conducted to measure changes in total soil water, soil salt, and its ion components. The results showed different migration directions and quantities of various salt ions due to concentration gradients and diffusion coefficients, with Na+, Cl-, and SO42- exhibiting larger potential convection and dispersion quantities than Ca2+, Mg2+, and HCO3-. This study provides a new perspective on soil salt movement in frozen agricultural areas with shallow groundwater tables.
JOURNAL OF HYDROLOGY
(2023)
Article
Mathematics, Applied
Yanyan Du, Ming Ye, Qimin Zhang
Summary: In this paper, a stochastic population-toxicant model with cross-diffusion is developed and the local boundedness of strong solutions is studied. The existence of a global martingale solution in a Hilbert space is obtained using the Galerkin approximation method, the tightness criterion, and the energy estimation.
APPLIED MATHEMATICS LETTERS
(2023)