arXiv subjects

Boqian Zhang

Publications and source records attributed to Boqian Zhang.

5 recordsLinked to original sources

arXiv2026

Bayesian Repulsive Mixture Modeling with Matérn Point Processes

Mixture models are a standard tool in statistical analyses, widely used for density modeling and model-based clustering. In this work, we propose a Bayesian mixture model with repulsion between mixture components. Such repulsion helps address the problem of overlapping or poorly separated clusters, and assists with model interpretibility and robustness. Our modeling approach introduces repulsion via a generalized Matérn type-III repulsive point process model, and proceeds by applying a dependent sequential thinning scheme to a latent Poisson point process. A key feature of our model is that in contrast to most existing approaches to modeling repulsion, efficient posterior inference is possible via a Gibbs sampler, one that exploits the latent Poisson of our problem. This novel sampler also allows posterior inference over the number of clusters, and is of independent interest even in standard clustering applications without repulsion. We demonstrate the utility of the proposed method on a number of synthetic and real-world problems.

stat.ME↗

arXiv2025

HDW-SR: High-Frequency Guided Diffusion Model based on Wavelet Decomposition for Image Super-Resolution

Diffusion-based methods have shown great promise in single image super-resolution (SISR); however, existing approaches often produce blurred fine details due to insufficient guidance in the high-frequency domain. To address this issue, we propose a High-Frequency Guided Diffusion Network based on Wavelet Decomposition (HDW-SR), which replaces the conventional U-Net backbone in diffusion frameworks. Specifically, we perform diffusion only on the residual map, allowing the network to focus more effectively on high-frequency information restoration. We then introduce wavelet-based downsampling in place of standard CNN downsampling to achieve multi-scale frequency decomposition, enabling sparse cross-attention between the high-frequency subbands of the pre-super-resolved image and the low-frequency subbands of the diffused image for explicit high-frequency guidance. Moreover, a Dynamic Thresholding Block (DTB) is designed to refine high-frequency selection during the sparse attention process. During upsampling, the invertibility of the wavelet transform ensures low-loss feature reconstruction. Experiments on both synthetic and real-world datasets demonstrate that HDW-SR achieves competitive super-resolution performance, excelling particularly in recovering fine-grained image details. The code will be available after acceptance.

cs.CV↗

arXiv2025

Interpretable data-driven turbulence modeling for separated flows using symbolic regression with unit constraints

Machine learning techniques have been applied to enhance turbulence modeling in recent years. However, the "black box" nature of most machine learning techniques poses significant interpretability challenges in improving turbulence models. This paper introduces a novel unit-constrained turbulence modeling framework using symbolic regression to overcome these challenges. The framework amends the constitutive equation of linear eddy viscosity models (LEVMs) by establishing explicit equations between the Reynolds stress deviation and mean flow quantities, thereby improving the LEVM model's predictive capability for large separated turbulence. Unit consistency constraints are applied to the symbolic expressions to ensure physical realizability. The effectiveness of the framework and the generalization capability of the learned model are demonstrated through its application to the separated flow over 2D periodic hills and a backward-facing step. Compared to the standard k-ε model, the learned model shows significantly improved predictive accuracy for anisotropic Reynolds stresses, velocity and skin friction, while exhibiting promising generalization capabilities across various scenarios.

physics.flu-dyn↗

arXiv2025

CTSR: Cartesian tensor-based sparse regression for data-driven discovery of high-dimensional invariant governing equations

Accurate and concise governing equations are crucial for understanding system dynamics. Recently, data-driven methods such as sparse regression have been employed to automatically uncover governing equations from data, representing a significant shift from traditional first-principles modeling. However, most existing methods focus on scalar equations, limiting their applicability to simple, low-dimensional scenarios, and failing to ensure rotation and reflection invariance without incurring significant computational cost or requiring additional prior knowledge. This paper proposes a Cartesian tensor-based sparse regression (CTSR) technique to accurately and efficiently uncover complex, high-dimensional governing equations while ensuring invariance. Evaluations on two two-dimensional (2D) and two three-dimensional (3D) test cases demonstrate that the proposed method achieves superior accuracy and efficiency compared to the conventional technique.

cs.LG↗

arXiv2020

Efficient parameter sampling for Markov jump processes

Markov jump processes (MJPs) are continuous-time stochastic processes widely used in a variety of applied disciplines. Inference for MJPs typically proceeds via Markov chain Monte Carlo, the state-of-the-art being a uniformization-based auxiliary variable Gibbs sampler. This was designed for situations where the MJP parameters are known, and Bayesian inference over unknown parameters is typically carried out by incorporating it into a larger Gibbs sampler. This strategy of sampling parameters given path, and path given parameters can result in poor Markov chain mixing. In this work, we propose a simple and elegant algorithm to address this problem. Our scheme brings Metropolis-Hastings approaches for discrete-time hidden Markov models to the continuous-time setting, resulting in a complete and clean recipe for parameter and path inference in MJPs. In our experiments, we demonstrate superior performance over Gibbs sampling, as well as another popular approach, particle MCMC. We also show our sampler inherits geometric mixing from an `ideal' sampler that operates without computational constraints.

stat.CO↗