arXiv subjects

Xue Luo

Publications and source records attributed to Xue Luo.

At least 19 recordsLinked to original sources

arXiv2026

HarnessEval-W: Agentifying the Evaluation of Visual Worlds

A benchmark should deliver more than a scalar score: what makes an evaluation trustworthy is the reasoning that justifies the score. This is especially critical for world models, where judging a rollout requires understanding whether physics, causality, and world state evolve correctly. Humans spot such violations naturally, yet no existing benchmark automates this capability: metrics are computed brute-force, leaving no reasoning chain that can be examined or verified. We introduce HarnessEval-W, an agentified evaluation pipeline that brings the harness paradigm from the LLM ecosystem to world model benchmarking. Rather than applying a fixed rubric, HarnessEval-W interprets the context of each evaluation case, decomposes the evaluation question into measurable subproblems, and spawns specialized sub-agents, each equipped with tailored context and diagnostic tools to reason over its own subproblem. The parent agent then validates the gathered evidence and summarizes it into the final verdict. This hierarchical workflow turns every evaluation into a transparent evidence tree whose complete reasoning chain justifies the result. We apply HarnessEval-W to 18 representative world models over 330 evaluation cases. Its judgments closely align with human preferences while providing verifiable, fine-grained diagnoses of every generated rollout. We open-source the full pipeline as a live benchmark and invite the broad community to contribute to grow new skills and evaluation cases as world models evolve.

cs.CV↗

arXiv2026

Error Estimates of the Gain Approximation by Hermite-Galerkin Method in Feedback Particle Filter

The feedback particle filter (FPF) is a promising nonlinear filtering (NLF) method, but its practical implementation is hindered by the intractability of the gain function, which satisfies a boundary value problem (BVP). This paper proposes a novel two-step Hermite-Galerkin spectral method to address this challenge. First, the unknown density in the BVP is approximated by a kernel density estimator, whose error bounds are well-established in the literature. Second, rather than directly approximating the gain function, we approximate an auxiliary variable via the Galerkin spectral method using generalized Hermite functions. This auxiliary variable inherits the rapid decay property of the density at infinity, which aligns perfectly with the exponential decay characteristic of generalized Hermite functions, thereby obviating the need for artificial boundary conditions or domain truncation. Furthermore, we rigorously establish two fundamental error estimates: the kernel approximation error decays at the rate $O(N_p^{-\frac{s}{2s+1}})$, while the spectral approximation error converges at $O(M^{-s+1}\log M)$, providing complete theoretical guarantees for the method's accuracy. Comprehensive numerical experiments validate the theoretical results and demonstrate that the proposed method outperforms existing gain approximation schemes in both accuracy and computational efficiency.

math.NA↗

arXiv2026

State estimations and noise identifications with intermittent corrupted observations via Bayesian variational inference

This paper focuses on the state estimation problem in distributed sensor networks, where intermittent packet dropouts, corrupted observations, and unknown noise covariances coexist. To tackle this challenge, we formulate the joint estimation of system states, noise parameters, and network reliability as a Bayesian variational inference problem, and propose a novel variational Bayesian adaptive Kalman filter (VB-AKF) to approximate the joint posterior probability densities of the latent parameters. Unlike existing AKF that separately handle missing data and measurement outliers, the proposed VB-AKF adopts a dual-mask generative model with two independent Bernoulli random variables, explicitly characterizing both observable communication losses and latent data authenticity. Additionally, the VB-AKF integrates multiple concurrent multiple observations into the adaptive filtering framework, which significantly enhances statistical identifiability. Comprehensive numerical experiments verify the effectiveness and asymptotic optimality of the proposed method, showing that both parameter identification and state estimation asymptotically converge to the theoretical optimal lower bound with the increase in the number of sensors.

stat.ML↗

arXiv2026

The minimax optimal convergence rate of posterior density in the weighted orthogonal polynomials

We investigate Bayesian nonparametric density estimation via orthogonal polynomial expansions in weighted Sobolev spaces. A core challenge is establishing minimax optimal posterior convergence rates, especially for densities on unbounded domains without a strictly positive lower bound. For densities bounded away from zero, we give sufficient conditions under which the framework of \cite{shen2001} applies directly. For densities lacking a positive lower bound, the equivalence between Hellinger and weighted $L_2$-norm distance fails, invalidating the original theory. We propose a novel shifting method that lifts the true density $g_0$ to a sequence of proxy densities $g_{0,n}$. We prove a modified convergence theorem applicable to these shifted densities, preserving the optimal rate. We also construct a Gaussian sieve prior that achieves the minimax rate $\varepsilon_n=n^{-p/(2p+1)}$ for any integer $p\geq1$. Numerical results confirm that our estimator approximates the true density well and validates the theoretical convergence rate.

math.ST↗

arXiv2025

A decomposition method in the multivariate feedback particle filter via tensor product Hermite polynomials

The feedback particle filter (FPF), a resampling-free algorithm proposed over a decade ago, modifies the particle filter (PF) by incorporating a feedback structure. Each particle in FPF is regulated via a feedback gain function (lacking a closed-form expression), which solves a Poisson's equation with a probability-weighted Laplacian. While approximate solutions to this equation have been extensively studied in recent literature, no efficient multivariate algorithm exists. In this paper, we focus on the decomposition method for multivariate gain functions in FPF, which has been proven efficient for scalar FPF with polynomial observation functions. Its core is splitting the Poisson's equation into two exactly solvable sub-equations. Key challenges in extending it to multivariate FPF include ensuring the invertibility of the coefficient matrix in one sub-equation and constructing a weighted-radial solution in the other. The proposed method's computational complexity grows at most polynomially with the state dimension, a dramatic improvement over the exponential growth of most particle-based algorithms. Numerical experiments compare the decomposition method with traditional methods: the extended Kalman filter (EKF), PF, and FPF with constant-gain or kernel-based gain approximations. Results show it outperforms PF and FPF with other gain approximations in both accuracy and efficiency, achieving the shortest CPU time among methods with comparable performance.

math.OC↗

arXiv2025

Bayesian Forecast Combination with Predictive Priors via Particle Filtering

We propose a Bayesian forecast combination framework that, for the first time, embeds forward-looking signals, formulated as predictive priors, directly into the time-varying weight-updating process. This approach enables weights to adapt using both historical forecast performance and anticipated future model behavior. We implement the framework with model diversity as the forward-looking signal, yielding the diversity-driven time-varying weights (DTVW) method. Compared with the standard time-varying weights (TVW) approach, DTVW embeds diversity-driven predictive priors that penalize redundancy and encourage informative contributions across constituent models. Simulation experiments, covering both a simple complete model set and a complex misspecified environment, show that DTVW improves forecast accuracy by dynamically focusing on well-performing models. Empirical applications to multi-step-ahead oil price forecasts and bivariate forecasts of U.S. inflation and GDP growth confirm its superiority over benchmarks including Equal weighting, Bayesian Model Averaging, and standard TVW. Beyond accuracy gains, diversity-based predictive priors provide diagnostic insights into model incompleteness and forecast uncertainty, making DTVW both more adaptive and more informative than existing Bayesian combination methods.

stat.ME↗

arXiv2025

A Decomposition Approach for the Gain Function in the Feedback Particle Filter

The feedback particle filter (FPF) is an innovative, control-oriented and resampling-free adaptation of the traditional particle filter (PF). In the FPF, individual particles are regulated via a feedback gain, and the corresponding gain function serves as the solution to the Poisson's equation equipped with a probability-weighted Laplacian. Owing to the fact that closed-form expressions can only be computed under specific circumstances, approximate solutions are typically indispensable. This paper is centered around the development of a novel algorithm for approximating the gain function in the FPF. The fundamental concept lies in decomposing the Poisson's equation into two equations that can be precisely solved, provided that the observation function is a polynomial. A free parameter is astutely incorporated to guarantee exact solvability. The computational complexity of the proposed decomposition method shows a linear correlation with the number of particles and the polynomial degree of the observation function. We perform comprehensive numerical comparisons between our method, the PF, and the FPF using the constant-gain approximation and the kernel-based approach. Our decomposition method outperforms the PF and the FPF with constant-gain approximation in terms of accuracy. Additionally, it has the shortest CPU time among all the compared methods with comparable performance.

math.OC↗

arXiv2021

Improved Sensitivity of Base Layer on the Performance of Rigid Pavement

The performance of rigid pavement is greatly affected by the properties of base/subbase as well as subgrade layer. However, the performance predicted by the AASHTOWare Pavement ME design shows low sensitivity to the properties of base and subgrade layers. To improve the sensitivity and better reflect the influence of unbound layers a new set of improved models i.e., resilient modulus (MR) and modulus of subgrade reaction (k-value) are adopted in this study. An Artificial Neural Network (ANN) model is developed to predict the modified k-value based on finite element (FE) analysis. The training and validation datasets in the ANN model consist of 27000 simulation cases with different combinations of pavement layer thickness, layer modulus and slab-base interface bond ratio. To examine the sensitivity of modified MR and k-values on pavement response, eight pavement sections data are collected from the Long-Term Pavement performance (LTPP) database and modeled by using the FE software ISLAB2000. The computational results indicate that the modified MR values have higher sensitivity to water content in base layer on critical stress and deflection response of rigid pavements compared to the results using the Pavement ME design model. It is also observed that the k-values using ANN model has the capability of predicting critical pavement response at any partially bonded conditions whereas the Pavement ME design model can only calculate at two extreme bonding conditions (i.e., fully bonding and no bonding).

cs.AI↗

arXiv2019

Multivariate Feedback Particle Filter via F-divergence and the Well-posedness of its Admissible Control Input

In this paper, we shall first derive the admissible control input of the multivariate feedback particle filter (FPF) by minimizing the f-divergence of the posterior conditional density function and the empirical conditional density of the controlled particles. On the contrast, in the original derivation \cite{YMM}, a special f-divergence, Kullback-Leibler (K-L) divergence, is used in the 1-dimensional nonlinear filtering problems. We show that the control input is invariant under the f-divergence class. That is, the control input satisfies exactly the same equations as those obtained by minimizing K-L divergence, no matter what f-divergence in use. In the latter half of this paper, we show the existence and uniqueness of the control input under suitable regular conditions. We confirm that the explicit expression of the control input given in \cite{YLMM} is the only admissible one.

math.OC↗

arXiv2016

Addendum: 2D homogeneous solutions to the Euler equation

In this addendum note we fill in the gap left in \cite{ls} in the description of 2D homogeneous solutions to the stationary Euler system with the help of the results of \cite{sd}. This gives a complete classification of all solutions. The note includes updated classification tables, and a reverse application to the results of \cite{sd}.

math.AP↗

arXiv2014

Time-dependent Hermite-Galerkin spectral method and its applications

A time-dependent Hermite-Galerkin spectral method (THGSM) is investigated in this paper for the nonlinear convection-diffusion equations in the unbounded domains. The time-dependent scaling factor and translating factor are introduced in the definition of the generalized Hermite functions (GHF). As a consequence, the THGSM based on these GHF has many advantages, not only in theorethical proofs, but also in numerical implementations. The stability and spectral convergence of our proposed method have been established in this paper. The Korteweg-de Vries-Burgers (KdVB) equation and its special cases, including the heat equation and the Burgers' equation, as the examples, have been numerically solved by our method. The numerical results are presented, and it surpasses the existing methods in accuracy. Our theoretical proof of the spectral convergence has been supported by the numerical results.

math.NA↗

arXiv2014

2D homogeneous solutions to the Euler equation

In this paper we study classification of homogeneous solutions to the stationary Euler equation with locally finite energy. Written in the form $u = \nabla^\perp Ψ$, $Ψ(r,θ) = r^λ ψ(θ)$, for $λ>0$, we show that only trivial solutions exist in the range $0<λ<1/2$, i.e. parallel shear and rotational flows. In other cases many new solutions are exhibited that have hyperbolic, parabolic and elliptic structure of streamlines. In particular, for $λ>9/2$ the number of different non-trivial elliptic solutions is equal to the cardinality of the set $(2,\sqrt{2λ}) \cap \mathbb{N}$. The case $λ= 2/3$ is relevant to Onsager's conjecture. We underline the reasons why no anomalous dissipation of energy occurs for such solutions despite their critical Besov regularity 1/3.

math.AP↗

arXiv2014

On Classification of Toric Surface Codes of Low Dimension

This work is a natural continuation of our previous work \cite{yz}. In this paper, we give a complete classification of toric surface codes of dimension less than or equal to 6, except a special pair, $C_{P_6^{(4)}}$ and $C_{P_6^{(5)}}$ over $\mathbb{F}_8$. Also, we give an example, $C_{P_6^{(5)}}$ and $C_{P_6^{(6)}}$ over $\mathbb{F}_7$, to illustrate that two monomially equivalent toric codes can be constructed from two lattice non-equivalent polygons.

cs.IT↗

arXiv2014

Spectral viscosity method with generalized Hermite functions for nonlinear conservation laws

In this paper, we propose new spectral viscosity methods based on the generalized Hermite functions for the solution of nonlinear scalar conservation laws in the whole line. It is shown rigorously that these schemes converge to the unique entropy solution by using compensated compactness arguments, under some conditions. The numerical experiments of the inviscid Burger's equation support our result, and it verifies the reasonableness of the conditions.

math.NA↗

arXiv2014

On the quenching behavior of the MEMS with fringing field

The singular parabolic problem $u_t-\triangle u=λ{\frac{1+δ|\nabla u|^2}{(1-u)^2}}$ on a bounded domain $Ω$ of $\mathbb{R}^n$ with Dirichlet boundary condition, models the Microelectromechanical systems (MEMS) device with fringing field. In this paper, we focus on the quenching behavior of the solution to this equation. We first show that there exists a critical value $λ_δ^*>0$ such that if $0<λ<λ_δ^*$, all solutions exist globally; while for $λ>λ_δ^*$, all the solution will quench in finite time. The estimate of the quenching time in terms of large voltage $λ$ is investigated. Furthermore, the quenching set is a compact subset of $Ω$, provided $Ω$ is a convex bounded domain in $\mathbb{R}^n$. In particular, if the domain $Ω$ is radially symmetric, then the origin is the only quenching point. We not only derive the one-side estimate of the quenching rate, but also further study the refined asymptotic behavior of the finite quenching solution.

math.AP↗

arXiv2014

Hermite spectral method to 1D forward Kolmogorov equation and its application to nonlinear filtering problems

In this paper, we investigate the Hermite spectral method (HSM) to numerically solve the forward Kolmogorov equation (FKE). A useful guideline of choosing the scaling factor of the generalized Hermite functions is given in this paper. It greatly improves the resolution of HSM. The convergence rate of HSM to FKE is analyzed in the suitable function space and has been verified by the numerical simulation. As an important application and our primary motivation to study the HSM to FKE, we work on the implementation of the nonlinear filtering (NLF) problem with a real-time algorithm developed in [17]. The HSM to FKE is served as the off-line computation in this algorithm. The translating factor of the generalized Hermite functions and the moving-window technique are introduced to deal with the drifting of the posterior conditional density function of the states in the on-line experiments. Two numerical experiments of NLF problems are carried out to illustrate the feasibility of our algorithm. Moreover, our algorithm surpasses the particle filter as a real-time solver to NLF.

math.OC↗

arXiv2014

Complete Real Time Solution of the General Nonlinear Filtering Problem without Memory

It is well known that the nonlinear filtering problem has important applications in both military and civil industries. The central problem of nonlinear filtering is to solve the Duncan-Mortensen-Zakai (DMZ) equation in real time and in a memoryless manner. In this paper, we shall extend the algorithm developed previously by S.-T. Yau and the second author to the most general setting of nonlinear filterings, where the explicit time-dependence is in the drift term, observation term, and the variance of the noises could be a matrix of functions of both time and the states. To preserve the off-line virture of the algorithm, necessary modifications are illustrated clearly. Moreover, it is shown rigorously that the approximated solution obtained by the algorithm converges to the real solution in the $L^1$ sense. And the precise error has been estimated. Finally, the numerical simulation support the feasibility and efficiency of our algorithm.

math.OC↗

arXiv2013

Hermite spectral method with hyperbolic cross approximations to high-dimensional parabolic PDEs

It is well-known that sparse grid algorithm has been widely accepted as an efficient tool to overcome the "curse of dimensionality" in some degree. In this note, we first give the error estimate of hyperbolic cross (HC) approximations with generalized Hermite functions. The exponential convergence in both regular and optimized hyperbolic cross approximations has been shown. Moreover, the error estimate of Hermite spectral method to high-dimensional linear parabolic PDEs with HC approximations has been investigated in the properly weighted Korobov spaces. The numerical result verifies the exponential convergence of this approach.

math.NA↗