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Researcher profile

Dunhui Xiao

Dunhui Xiao contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
math.NANumerical AnalysisComputationMachine LearningNeural and Evolutionary Computing

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Published work

4 published item(s)

preprint2026arXiv

Coupling-Informed Transport Maps for Bayesian Filtering in Nonlinear Dynamical Systems

A likelihood-free transport filtering method is proposed based on the couplings between state and observation variables. By exploiting a block-triangular structure in the transport map, the analysis step of filtering is reformulated as the minimization of the maximum mean discrepancy (MMD) between the true joint measure and its transport-based approximation. To circumvent the non-convexity in the MMD optimization, we introduce a training-free transport filter method via gradient flows, which leads to an analytic computation for the transport map that implies the steepest descent direction of the MMD. The proposed approach accurately approximates non-Gaussian filtering posteriors and avoids particle collapse. We provide a convergence analysis for the expectation of the MMD between the approximated posterior and the truth posterior. Finally, we extend the method to high-dimensional problems through domain localization. Numerical examples demonstrate the superior performance of our approach over conventional filtering methods in nonlinear, non-Gaussian scenarios.

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preprint2026arXiv

Parametric Probabilistic Manifold Decomposition for Nonlinear Model Reduction

Probabilistic Manifold Decomposition (PMD)\cite{doi:10.1137/25M1738863}, developed in our earlier work, provides a nonlinear model reduction by embedding high-dimensional dynamics onto low-dimensional probabilistic manifolds. The PMD has demonstrated strong performance for time-dependent systems. However, its formulation is for temporal dynamics and does not directly accommodate parametric variability, which limits its applicability to tasks such as design optimization, control, and uncertainty quantification. In order to address the limitations, a \emph{Parametric Probabilistic Manifold Decomposition} (PPMD) is presented to deal with parametric problems. The central advantage of PPMD is its ability to construct continuous, high-fidelity parametric surrogates while retaining the transparency and non-intrusive workflow of PMD. By integrating probabilistic-manifold embeddings with parameter-aware latent learning, PPMD enables smooth predictions across unseen parameter values (such as different boundary or initial conditions). To validate the proposed method, a comprehensive convergence analysis is established for PPMD, covering the approximation of the linear principal subspace, the geometric recovery of the nonlinear solution manifold, and the statistical consistency of the kernel ridge regression used for latent learning. The framework is then numerically demonstrated on two classic flow configurations: flow past a cylinder and backward-facing step flow. Results confirm that PPMD achieves superior accuracy and generalization beyond the training parameter range compared to the conventional proper orthogonal decomposition with Gaussian process regression (POD+GPR) method.

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preprint2025arXiv

Nonlinear Model Reduction by Probabilistic Manifold Decomposition

This paper presents a novel non-linear model reduction method: Probabilistic Manifold Decomposition (PMD), which provides a powerful framework for constructing non-intrusive reduced-order models (ROMs) by embedding a high-dimensional system into a low-dimensional probabilistic manifold and predicting the dynamics. Through explicit mappings, PMD captures both linearity and non-linearity of the system. A key strength of PMD lies in its predictive capabilities, allowing it to generate stable dynamic states based on embedded representations. The method also offers a mathematically rigorous approach to analyze the convergence of linear feature matrices and low-dimensional probabilistic manifolds, ensuring that sample-based approximations converge to the true data distributions as sample sizes increase. These properties, combined with its computational efficiency, make PMD a versatile tool for applications requiring high accuracy and scalability, such as fluid dynamics simulations and other engineering problems. By preserving the geometric and probabilistic structures of the high-dimensional system, PMD achieves a balance between computational speed, accuracy, and predictive capabilities, positioning itself as a robust alternative to the traditional model reduction method.

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preprint2022arXiv

Egret Swarm Optimization Algorithm: An Evolutionary Computation Approach for Model Free Optimization

A novel meta-heuristic algorithm, Egret Swarm Optimization Algorithm (ESOA), is proposed in this paper, which is inspired by two egret species' (Great Egret and Snowy Egret) hunting behavior. ESOA consists of three primary components: Sit-And-Wait Strategy, Aggressive Strategy as well as Discriminant Conditions. The performance of ESOA on 36 benchmark functions as well as 2 engineering problems are compared with Particle Swarm Optimization (PSO), Genetic Algorithm (GA), Differential Evolution (DE), Grey Wolf Optimizer (GWO), and Harris Hawks Optimization (HHO). The result proves the superior effectiveness and robustness of ESOA. The source code used in this work can be retrieved from https://github.com/Knightsll/Egret_Swarm_Optimization_Algorithm; https://ww2.mathworks.cn/matlabcentral/fileexchange/115595-egret-swarm-optimization-algorithm-esoa.

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