arXiv subjects

Zewen Wang

Publications and source records attributed to Zewen Wang.

7 recordsLinked to original sources

arXiv2026

Inverse Source Problem for a Time-Fractional Diffusion-Wave Equation with a Singular Inverse-Square Potential

This paper investigates an inverse source problem for a time-fractional diffusion-wave equation with a singular inverse-square potential. The source term is assumed to consist of a known temporal factor and an unknown spatial component, which is to be recovered from terminal-state measurements. The well-posedness and regularity of the forward problem are established within an appropriate energy framework by exploiting Hardy-type inequalities and the spectral properties of the associated singular elliptic operator. The terminal observation operator is then shown to be compact, and uniqueness of the spatial source is established under a suitable nondegeneracy condition on the temporal factor. To stabilize the resulting ill-posed inverse problem, a Tikhonov regularization approach is introduced. The gradient of the regularized functional is derived through an adjoint problem involving a right-sided fractional derivative, leading to an adjoint-based conjugate gradient method with an exact line search for the numerical reconstruction of the unknown source. Numerical experiments are conducted on both one-and two-dimensional spatial domains, using both exact and noisy terminal data, to demonstrate the effectiveness and stability of the proposed source reconstruction method.

math.NA↗

arXiv2026

Inverse Source Problems for a Class of Fractional Elliptic Equations with Singular Coefficients

An inverse source problem for a class of fractional elliptic equations with singular coefficients is investigated in this paper. For the corresponding direct problem, a formal solution is derived and the well-posedness of the solution is established. For the inverse problem, a H\"older-type conditional stability estimate is obtained in a Hilbert scale associated with exponential operators. Based on this stability framework, two regularization methods are proposed for reconstructing the unknown source term: the exponential-type Tikhonov regularization method and the exponential quasi-boundary value regularization method. Convergence estimates for the regularized solutions are derived under both a priori and a posteriori choices of the regularization parameter. In addition, finite-dimensional spectral approximation results show that the proposed methods are also applicable to general square-integrable source terms, without requiring the exact source to satisfy an exponential-type source condition. Numerical experiments demonstrate that the proposed methods provide stable and accurate reconstructions for both smooth and piecewise smooth sources even under low signal-to-noise ratio conditions.

math.NA↗

arXiv2025

Conditional stability for an inverse problem of a fully-discrete stochastic hyperbolic equation

In this paper, we investigate a discrete inverse problem of determining three unknowns, i.e. initial displacement, initial velocity and random source term, in a fully discrete approximation of one-dimensional stochastic hyperbolic equation. We firstly prove a new Carleman estimate for the fully-discrete stochastic hyperbolic equation. Based on this Carleman estimate, we then establish a Lipschitz stability for this discrete inverse problem by the discrete spatial derivative data at the left endpoint and the measurements of the solution and its time derivative at the final time. Owing to the discrete setting, an extra term with respect to mesh size arises in the right-hand side of the stability estimate.

math.AP↗

arXiv2025

Scalable and Reliable Multi-agent Reinforcement Learning for Traffic Assignment

The evolution of metropolitan cities and the increase in travel demands impose stringent requirements on traffic assignment methods. Multi-agent reinforcement learning (MARL) approaches outperform traditional methods in modeling adaptive routing behavior without requiring explicit system dynamics, which is beneficial for real-world deployment. However, MARL frameworks face challenges in scalability and reliability when managing extensive networks with substantial travel demand, which limiting their practical applicability in solving large-scale traffic assignment problems. To address these challenges, this study introduces MARL-OD-DA, a new MARL framework for the traffic assignment problem, which redefines agents as origin-destination (OD) pair routers rather than individual travelers, significantly enhancing scalability. Additionally, a Dirichlet-based action space with action pruning and a reward function based on the local relative gap are designed to enhance solution reliability and improve convergence efficiency. Experiments demonstrate that the proposed MARL framework effectively handles medium-sized networks with extensive and varied city-level OD demand, surpassing existing MARL methods. When implemented in the SiouxFalls network, MARL-OD-DA achieves better assignment solutions in 10 steps, with a relative gap that is 94.99% lower than that of conventional methods.

cs.LG↗

arXiv2024

Carleman estimates for space semi-discrete approximations of one-dimensional stochastic parabolic equation and its applications

In this paper, we study discrete Carleman estimates for space semi-discrete approximations of one-dimensional stochastic parabolic equation. As applications of these discrete Carleman estimates, we apply them to study two inverse problems for the spatial semi-discrete stochastic parabolic equations, including a discrete inverse random source problem and a discrete Cauchy problem. We firstly establish two Carleman estimates for a one-dimensional semi-discrete stochastic parabolic equation, one for homogeneous boundary and the other for non-homogeneous boundary. Then we apply these two estimates separately to derive two stability results. The first one is the Lipschitz stability for the discrete inverse random source problem. The second one is the Hölder stability for the discrete Cauchy problem.

math.PR↗

arXiv2023

Multi-Energy Guided Image Translation with Stochastic Differential Equations for Near-Infrared Facial Expression Recognition

Illumination variation has been a long-term challenge in real-world facial expression recognition(FER). Under uncontrolled or non-visible light conditions, Near-infrared (NIR) can provide a simple and alternative solution to obtain high-quality images and supplement the geometric and texture details that are missing in the visible domain. Due to the lack of existing large-scale NIR facial expression datasets, directly extending VIS FER methods to the NIR spectrum may be ineffective. Additionally, previous heterogeneous image synthesis methods are restricted by low controllability without prior task knowledge. To tackle these issues, we present the first approach, called for NIR-FER Stochastic Differential Equations (NFER-SDE), that transforms face expression appearance between heterogeneous modalities to the overfitting problem on small-scale NIR data. NFER-SDE is able to take the whole VIS source image as input and, together with domain-specific knowledge, guide the preservation of modality-invariant information in the high-frequency content of the image. Extensive experiments and ablation studies show that NFER-SDE significantly improves the performance of NIR FER and achieves state-of-the-art results on the only two available NIR FER datasets, Oulu-CASIA and Large-HFE.

cs.CV↗

arXiv2020

Carleman estimates for a stochastic degenerate parabolic equation and applications to null controllability and an inverse random source problem

In this paper, we establish two Carleman estimates for a stochastic degenerate parabolic equation. The first one is for the backward stochastic degenerate parabolic equation with singular weight function. Combining this Carleman estimate and an approximate argument, we prove the null controllability of the forward stochastic degenerate parabolic equation with the gradient term. The second one is for the forward stochastic degenerate parabolic equation with regular weighted function, based on which we obtain the Lipschitz stability for an inverse problem of determining a random source depending only on time in the forward stochastic degenerate parabolic equation.

math.OC↗