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Jingzhi Li

Jingzhi Li contributes to research discovery and scholarly infrastructure.

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Published work

11 published item(s)

preprint2026arXiv

Post-hoc Provider Fairness Adaptation via Hierarchical Exposure Alignment

Provider exposure fairness is crucial for sustaining a healthy content ecosystem and preventing monopolization in recommender systems. Yet, most existing methods either incorporate fairness constraints during model training, requiring expensive retraining when fairness objectives change, or rely on post-hoc reranking with fixed criteria, which lacks adaptability to diverse fairness requirements. To overcome these limitations, we propose Post-hoc Fairness Adaptation (PFA), a lightweight framework that equips a frozen recommender with a fairness adapter, enabling flexible fairness control without retraining the backbone model. Specifically, the fairness adapter learns personalized additive score adjustments from user-item embeddings, which are injected into the original ranking scores to steer provider exposure toward fairness. To train the adapter, we minimize the KL divergence between the actual and the target fair exposure distributions. However, this global objective implicitly treats all providers equally, ignoring structural disparities such as imbalanced provider group sizes and heterogeneous exposure within groups. Consequently, fairness may appear satisfied at an aggregate level while severe inter-group and intra-group exposure imbalances persist, undermining practical fairness. To address this, we design Hierarchical Exposure Fairness Alignment (HEFA), which explicitly balances inter- and intra-group provider exposure disparities, enabling flexible adaptation to diverse fairness requirements. To mitigate potential accuracy degradation, PFA jointly optimizes HEFA with a differentiable NDCG loss, enabling end-to-end fairness optimization while preserving ranking quality. Extensive experiments on three public datasets demonstrate that PFA achieves substantial fairness gains with negligible accuracy loss, consistently outperforming strong baselines.

preprint2024arXiv

Spatiotemporal Monitoring of Epidemics via Solution of a Coefficient Inverse Problem

Let S,I and R be susceptible, infected and recovered populations in a city affected by an epidemic. The SIR model of Lee, Liu, Tembine, Li and Osher, \emph{SIAM J. Appl. Math.},~81, 190--207, 2021 of the spatiotemoral spread of epidemics is considered. This model consists of a system of three nonlinear coupled parabolic Partial Differential Equations with respect to the space and time dependent functions S,I and R. For the first time, a Coefficient Inverse Problem (CIP) for this system is posed. The so-called \textquotedblleft convexification" numerical method for this inverse problem is constructed. The presence of the Carleman Weight Function (CWF) in the resulting regularization functional ensures the global convergence of the gradient descent method of the minimization of this functional to the true solution of the CIP, as long as the noise level tends to zero. The CWF is the function, which is used as the weight in the Carleman estimate for the corresponding Partial Differential Operator. Numerical studies demonstrate an accurate reconstruction of unknown coefficients as well as S,I,R functions inside of that city. As a by-product, uniqueness theorem for this CIP is proven. Since the minimal measured input data are required, then the proposed methodology has a potential of a significant decrease of the cost of monitoring of epidemics.

preprint2022arXiv

A $C^{0}$ interior penalty method for $m$th-Laplace equation

In this paper, we propose a $C^{0}$ interior penalty method for $m$th-Laplace equation on bounded Lipschitz polyhedral domain in $\mathbb{R}^{d}$, where $m$ and $d$ can be any positive integers. The standard $H^{1}$-conforming piecewise $r$-th order polynomial space is used to approximate the exact solution $u$, where $r$ can be any integer greater than or equal to $m$. Unlike the interior penalty method in [T.~Gudi and M.~Neilan, {\em An interior penalty method for a sixth-order elliptic equation}, IMA J. Numer. Anal., \textbf{31(4)} (2011), pp. 1734--1753], we avoid computing $D^{m}$ of numerical solution on each element and high order normal derivatives of numerical solution along mesh interfaces. Therefore our method can be easily implemented. After proving discrete $H^{m}$-norm bounded by the natural energy semi-norm associated with our method, we manage to obtain stability and optimal convergence with respect to discrete $H^{m}$-norm. Numerical experiments validate our theoretical estimate.

preprint2022arXiv

An Iterative Decoupled Algorithm with Unconditional Stability for Biot Model

This paper is concerned with numerical algorithms for Biot model. By introducing an intermediate variable, the classical 2-field Biot model is written into a 3-field formulation. Based on such a 3-field formulation, we propose a coupled algorithm, some time-extrapolation based decoupled algorithms, and an iterative decoupled algorithm. Our focus is the analysis of the iterative decoupled algorithm. It is shown that the convergence of the iterative decoupled algorithm requires no extra assumptions on physical parameters or stabilization parameters. Numerical experiments are provided to demonstrate the accuracy and efficiency of the proposed method.

preprint2022arXiv

Convexification for a CIP for the RTE]{Convexification Numerical Method for a Coefficient Inverse Problem for the Radiative Transport Equation

An $\left( n+1\right) -$D coefficient inverse problem for the radiative stationary transport equation is considered for the first time. A globally convergent so-called convexification numerical \ method is developed and its convergence analysis is provided. The analysis is based on a Carleman estimate. In particular, convergence analysis implies a certain uniqueness theorem. Extensive numerical studies in the 2-D case are presented.

preprint2021arXiv

Computation of transmission eigenvalues by the regularized Schur complement for the boundary integral operators

This paper is devoted to the computation of transmission eigenvalues in the inverse acoustic scattering theory. This problem is first reformulated as a two by two boundary system of boundary integral equations. Next, utilizing the Schur complement technique, we develop a Schur complement operator with regularization to obtain a reduced system of boundary integral equations. The Nyström discretization is then used to obtain an eigenvalue problem for a matrix. We employ the recursive integral method for the numerical computation of the matrix eigenvalue. Numerical results show that the proposed method is efficient and reduces computational costs.

preprint2020arXiv

Convexification for an Inverse Parabolic Problem

A convexification-based numerical method for a Coefficient Inverse Problem for a parabolic PDE is presented. The key element of this method is the presence of the so-called Carleman Weight Function in the numerical scheme. Convergence analysis ensures the global convergence of this method, as opposed to the local convergence of the conventional least squares minimization techniques. Numerical results demonstrate a good performance.

preprint2020arXiv

Inverse source problems in an inhomogeneous medium with a single far-field pattern

This paper concerns time-harmonic inverse source problems with a single far-field pattern in two dimensions, where the source term is compactly supported in an a priori given inhomogeneous background medium. For convex-polygonal source terms, we prove that the source support together with the zeroth and first order derivatives of the source function at corner points can be uniquely determined. Further, we prove that an admissible set of source functions (including harmonic functions) having a convex-polygonal support can be uniquely identified by a single far-field pattern. A class of radiating sources is characterized and the extension of the radiated field across a corner point is proven impossible. The corner scattering theory leads to a data-driven inversion scheme for imaging an arbitrarily convex-polygonal source support.

preprint2020arXiv

Modeling the Control of COVID-19: Impact of Policy Interventions and Meteorological Factors

In this paper, we propose a dynamical model to describe the transmission of COVID-19, which is spreading in China and many other countries. To avoid a larger outbreak in the worldwide, Chinese government carried out a series of strong strategies to prevent the situation from deteriorating. Home quarantine is the most important one to prevent the spread of COVID-19. In order to estimate the effect of population quarantine, we divide the population into seven categories for simulation. Based on a Least-Squares procedure and officially published data, the estimation of parameters for the proposed model is given. Numerical simulations show that the proposed model can describe the transmission of COVID-19 accurately, the corresponding prediction of the trend of the disease is given. The home quarantine strategy plays an important role in controlling the disease spread and speeding up the decline of COVID-19. The control reproduction number of most provinces in China are analyzed and discussed adequately. We should pay attention to that, though the epidemic is in decline in China, the disease still has high risk of human-to-human transmission continuously. Once the control strategy is removed, COVID-19 may become a normal epidemic disease just like flu. Further control for the disease is still necessary, we focus on the relationship between the spread rate of the virus and the meteorological conditions. A comprehensive meteorological index is introduced to represent the impact of meteorological factors on both high and low migration groups. As the progress on the new vaccine, we design detail vaccination strategies for COVID-19 in different control phases and show the effectiveness of efficient vaccination. Once the vaccine comes into use, the numerical simulation provide a promptly prospective research.

preprint2019arXiv

Determining a random Schrödinger equation with unknown source and potential

We are concerned with the direct and inverse scattering problems associated with a time-harmonic random Schrödinger equation with unknown source and potential terms. The well-posedness of the direct scattering problem is first established. Three uniqueness results are then obtained for the corresponding inverse problems in determining the variance of the source, the potential and the expectation of the source, respectively, by the associated far-field measurements. First, a single realization of the passive scattering measurement can uniquely recover the variance of the source without the a priori knowledge of the other unknowns. Second, if active scattering measurement can be further obtained, a single realization can uniquely recover the potential function without knowing the source. Finally, both the potential and the first two statistic moments of the random source can be uniquely recovered with full measurement data. The major novelty of our study is that on the one hand, both the random source and the potential are unknown, and on the other hand, both passive and active scattering measurements are used for the recovery in different scenarios.

preprint2019arXiv

Uniqueness in inverse cavity scattering problems with phaseless near-field data

This paper is concerned with the uniqueness of inverse acoustic scattering problem for cavities with the modulus of the near-fields. With the aid of the reference ball technique and the superpositions of two point sources as the incident waves, we rigorously prove that the location and shape of the cavity as well as its boundary condition can be uniquely determined by the modulus of near-fields at an admissible surface. To our knowledge, this is the first uniqueness result in inverse cavity scattering problems with phaseless near-field data. In this paper, we make use of the phaseless near-field data incurred by the cavity and the point sources, and thus the configuration is more feasible in practice.