arXiv subjects

Shijie Zhong

Publications and source records attributed to Shijie Zhong.

12 recordsLinked to original sources

arXiv2026

Hybrid Uncertainty Sensitivity Analysis Based on the HSIC for High-Dimensional Responses with Aleatory--Epistemic Separation

Quantifying the influence of hybrid aleatory and epistemic uncertainties on high-dimensional system responses remains a major challenge in global sensitivity analysis (GSA). Existing Hilbert--Schmidt Independence Criterion (HSIC)-based approaches are primarily restricted to single-output settings and lack a rigorous decomposition of heterogeneous uncertainty sources and their interactions. To address this limitation, a novel double-space tensor-product RKHS framework is proposed for sensitivity analysis under hybrid uncertainty. By constructing factorized kernels over both the latent input space and the multidimensional output space, a concurrent double Möbius inversion is derived to orthogonally decompose the global dependence measure into pure aleatory effects, pure epistemic effects, and their interaction contributions. The resulting dimension-wise sensitivity indices preserve the uncertainty attribution structure across all output dimensions. To satisfy the independence assumptions required by the decomposition, an auxiliary-variable representation based on the inverse probability integral transform is introduced, enabling the treatment of hierarchical uncertainties and Copula-induced correlations within a unified latent space. A fully vectorized single-loop implementation is further developed to avoid the computational burden of nested Monte Carlo simulation. Statistical significance and estimation uncertainty are quantified through permutation testing and Bootstrap confidence intervals. Numerical studies on a modified multi-output Ishigami function and an aerodynamic pressure-field problem demonstrate the accuracy, scalability, and practical applicability of the proposed framework.

stat.ML↗

arXiv2026

Finite-Sample Unbiased Variance of MMD under Unbalanced Sampling: Exact Estimation and Quasi-Linear Computation

Accurately and efficiently estimating the variance of the Maximum Mean Discrepancy (MMD) remains challenging, particularly for unbalanced sample sizes. In this paper, we derive a finite-sample unbiased estimator of the MMD variance. To overcome the traditional $\mathcal{O}(N^2)$ computational bottleneck, we develop a recursive prefix-suffix accumulation scheme for the Laplace kernel, reducing the computational complexity to $\mathcal{O}(N \log N)$ while requiring $\mathcal{O}(N)$ memory. Experimental results verify the theoretical exactness and numerical stability of the proposed estimator and demonstrate its scalability on large datasets. Furthermore, the method proves effective for monitoring distributional convergence during the training of Time-series Generative Adversarial Networks (TimeGAN).

stat.ML↗

arXiv2026

A Bayesian Model Updating Framework for Systems Under Hybrid Uncertainties via Probability Integral Transform and Maximum Mean Discrepancy

Model updating under hybrid uncertainty is challenging because aleatory input variability makes the simulator output a probability distribution rather than a scalar, rendering the likelihood analytically intractable. Existing Approximate Bayesian Computation (ABC) methods typically employ nested Monte Carlo sampling, where aleatory samples are redrawn for each epistemic parameter evaluation, introducing sampling noise into the discrepancy and consequently affecting posterior inference and model evidence. This paper eliminates this resampling noise by construction. The probability integral transform (PIT) converts the stochastic simulator into a deterministic map of distribution-free latent variables and epistemic parameters. By freezing a set of stratified quantile particles, the resulting discrepancy becomes a deterministic, sampling-noise-free function of the unknown parameters. Transitional Markov Chain Monte Carlo (TMCMC) is then employed for posterior inference and model evidence estimation. The framework is validated on a two-dimensional benchmark, a high-dimensional transient oscillator, and Subproblem A of the NASA Langley Multidisciplinary Uncertainty Quantification Challenge. The complete Bayesian analysis is achieved in approximately half a minute on a standard desktop workstation.

cs.CE↗

arXiv2026

Directional Kernel Mean Difference: A Fast Signed Statistic for Univariate Distribution Comparison

We introduce the Directional Kernel Mean Difference (DKMD), a signed statistic for univariate distribution comparison that preserves the direction of distributional shifts. Unlike the squared Maximum Mean Discrepancy (MMD), which discards directional information by squaring the RKHS distance, DKMD integrates the difference of kernel mean embeddings against a fixed odd weighting function. This construction yields three structural properties: antisymmetry, immunity to symmetric distributional differences, and directional monotonicity under stochastic dominance. We derive a data-driven Riemann estimator that ensures asymptotic consistency with the continuous formulation, strictly preserving the theoretical guarantees of the signed statistic in empirical evaluations. To overcome the quadratic computational cost of kernel methods, we develop an $O(N \log N)$ prefix--suffix scanning algorithm that exploits the total order of the real line while requiring only $O(N)$ memory. Experiments on synthetic benchmarks demonstrate that DKMD correctly isolates directional shifts from symmetric perturbations, remains robust to heavy-tailed outliers that can flip the sign of the mean difference, and scales to millions of samples in seconds.

stat.ML↗

arXiv2026

Analytical Extraction of Conditional Aleatory Sensitivities Across Epistemic Space via a Single PCE Model

In hybrid uncertainty quantification, evaluating how aleatory sensitivities vary under epistemic uncertainty, referred to as conditional Sobol' indices, is typically hindered by the computationally expensive double-loop procedure. Classical Polynomial Chaos Expansion (PCE) provides efficient access to global sensitivity measures but cannot directly resolve sensitivity variation across the epistemic space without repeated surrogate reconstruction. This study proposes a unified Bayesian framework that extracts continuous conditional Sobol' fields from a single global PCE representation. By exploiting the tensor-product structure of orthogonal polynomial bases in an augmented stochastic space, the global expansion is analytically decomposed into epistemic-dependent coefficient fields, enabling a closed-form variance decomposition. As a result, conditional Sobol' indices can be computed through a purely algebraic post-processing step without additional model evaluations or retraining. In addition, a Reversible Jump Markov Chain Monte Carlo (RJMCMC) scheme is incorporated to perform adaptive basis selection and trans-dimensional inference, while simultaneously providing Bayesian credible intervals for the conditional sensitivity measures. Numerical experiments on a high-dimensional groundwater flow model demonstrate that the proposed method significantly reduces computational cost while maintaining smooth sensitivity fields and statistically consistent uncertainty quantification across the epistemic domain.

stat.ME↗

arXiv2026

NGDBench: Towards Neural Graph Data Management

Data critical to real-world decision-making is increasingly found within organizations. Such data is heterogeneous, constantly evolving, and only imperfectly captured. However, current data management systems remain largely passive, retrieving what is explicitly stored while offering limited support for uncovering implicit structure or reasoning under noise, incompleteness, and continuous updates. We argue that next-generation data management requires neural capabilities, which can uncover complex latent relationships, distinguish reliable signals from noise, and remain consistent as the underlying data state evolves. To support this direction, we introduce NGDBench, a benchmark across five domains that unifies structured and unstructured sources. NGDBench adopts a graph view because graphs provide a flexible abstraction for modeling complex systems, capturing latent relationships, and subsuming structured formats such as relational tables. Each instance pairs a clean latent graph with a realistically perturbed observed graph. NGDBench supports full Cypher queries and dynamic data management operations. Evaluations of state-of-the-art Text-to-Cypher by LLMs and GraphRAG pipelines reveal that current neural query methods remain sensitive to noise and struggle with dynamic state tracking, highlighting the need for resilient, inference-capable data management. Our code is available at https://github.com/HKUST-KnowComp/NGDBench.

cs.DB↗

arXiv2026

Analytical Extraction of Conditional Sobol' Indices via Basis Decomposition of Polynomial Chaos Expansions

In uncertainty quantification, evaluating sensitivity measures under specific conditions (i.e., conditional Sobol' indices) is essential for systems with parameterized responses, such as spatial fields or varying operating conditions. Traditional approaches often rely on point-wise modeling, which is computationally expensive and may lack consistency across the parameter space. This paper demonstrates that for a pre-trained global Polynomial Chaos Expansion (PCE) model, the analytical conditional Sobol' indices are inherently embedded within its basis functions. By leveraging the tensor-product property of PCE bases, we reformulate the global expansion into a set of analytical coefficient fields that depend on the conditioning variables. Based on the preservation of orthogonality under conditional probability measures, we derive closed-form expressions for conditional variances and Sobol' indices. This framework bypasses the need for repetitive modeling or additional sampling, transforming conditional sensitivity analysis into a purely algebraic post-processing step. Numerical benchmarks indicate that the proposed method ensures physical coherence and offers superior numerical robustness and computational efficiency compared to conventional point-wise approaches.

stat.ML↗

arXiv2025

Goal-Oriented Bayesian Optimal Experimental Design for Nonlinear Models using Markov Chain Monte Carlo

Optimal experimental design (OED) provides a systematic approach to quantify and maximize the value of experimental data. Under a Bayesian approach, conventional OED maximizes the expected information gain (EIG) on model parameters. However, we are often interested in not the parameters themselves, but predictive quantities of interest (QoIs) that depend on the parameters in a nonlinear manner. We present a computational framework of predictive goal-oriented OED (GO-OED) suitable for nonlinear observation and prediction models, which seeks the experimental design providing the greatest EIG on the QoIs. In particular, we propose a nested Monte Carlo estimator for the QoI EIG, featuring Markov chain Monte Carlo for posterior sampling and kernel density estimation for evaluating the posterior-predictive density and its Kullback-Leibler divergence from the prior-predictive. The GO-OED design is then found by maximizing the EIG over the design space using Bayesian optimization. We demonstrate the effectiveness of the overall nonlinear GO-OED method, and illustrate its differences versus conventional non-GO-OED, through various test problems and an application of sensor placement for source inversion in a convection-diffusion field.

stat.CO↗

arXiv2024

Intermittency of bubble deformation in turbulence

The deformation of finite-sized bubbles in intense turbulence exhibits complex geometries beyond simple spheroids as the bubbles exchange energy with the surrounding eddies across a wide range of scales. This study investigates deformation via the velocity of the most stretched tip of the deformed bubble in 3D, as the tip extension results from the compression of the rest of the interface by surrounding eddies. The results show that the power spectrum based on the tip velocity exhibits a scaling akin to that of the Lagrangian statistics of fluid elements, but decays with a distinct timescale and magnitude modulated by the Weber number based on the bubble size. This indicates that the interfacial energy is primarily siphoned from eddies of similar sizes as the bubble. Moreover, the tip velocity appears much more intermittent than the velocity increment, and its distribution near the extreme tails can be explained by the proposed model that accounts for the fact that small eddies with sufficient energy can contribute to extreme deformation. These findings provide a framework for understanding the energy transfer between deformable objects and multiscale eddies in intense turbulence.

physics.flu-dyn↗

arXiv2024

Breaking bubbles across multiple timescales in turbulence

The familiar process of bubbles generated via breaking waves in the ocean is foundational to many natural and industrial applications. In this process, large pockets of entrained gas are successively fragmented by the ambient turbulence into smaller and smaller bubbles. The key question is how long it takes for the bubbles to reach terminal sizes for a given system. Despite decades of effort, the reported breakup time from multiple experiments differs significantly. Here, to reconcile those results, rather than focusing on one scale, we measure multiple timescales associated with the process through a unique experiment that resolves bubbles' local deformation and curvature. The results emphasize that the scale separation among various timescales is controlled by the Weber number, similar to how the Reynolds number determines the scale separation in single-phase turbulence, but shows a distinct transition at a critical Weber number.

physics.flu-dyn↗

arXiv2023

On the breakup frequency of bubbles and droplets in turbulence: a compilation and evaluation of experimental data

The dispersed phase in liquid-liquid emulsions and air-liquid mixtures can often be fragmented into smaller sizes by the surrounding turbulent carrier phase. The critical parameter that controls this process is the breakup frequency, which is defined from the breakup kernel in the population balance equation. The breakup frequency controls how long it takes for the dispersed phase reaches the terminal size distribution for given turbulence. In this article, we try to summarize the key experimental results and compile the existing datasets under a consistent framework to find out what is the characteristic timescale of the problem and how to account for the inner density and viscosity of the dispersed phase. Furthermore, by pointing out the inconsistency of existing experimental data, the key important unsolved questions and related problems on the breakup frequency of bubbles and droplets are discussed.

physics.flu-dyn↗

arXiv2012

Geophysical and geochemical constraints on geoneutrino fluxes from Earth's mantle

Knowledge of the amount and distribution of radiogenic heating in the mantle is crucial for understanding the dynamics of the Earth, including its thermal evolution, the style and planform of mantle convection, and the energetics of the core. Although the flux of heat from the surface of the planet is robustly estimated, the contributions of radiogenic heating and secular cooling remain poorly defined. Constraining the amount of heat-producing elements in the Earth will provide clues to understanding nebula condensation and planetary formation processes in early Solar System. Mantle radioactivity supplies power for mantle convection and plate tectonics, but estimates of mantle radiogenic heat production vary by a factor of more than 20. Recent experimental results demonstrate the potential for direct assessment of mantle radioactivity through observations of geoneutrinos, which are emitted by naturally occurring radionuclides. Predictions of the geoneutrino signal from the mantle exist for several established estimates of mantle composition. Here we present novel analyses, illustrating surface variations of the mantle geoneutrino signal for models of the deep mantle structure, including those based on seismic tomography. These variations have measurable differences for some models, allowing new and meaningful constraints on the dynamics of the planet. An ocean based geoneutrino detector deployed at several strategic locations will be able to discriminate between competing compositional models of the bulk silicate Earth.

physics.geo-ph↗