17 citations · 58 across the 19 of their papers we have counts for
19 papers
Identifying unknown time delay and spatially varying coefficients in a reaction-diffusion equation from boundary measurements
Ming-Hui Ding, Hongyu Liu, Catharine W. K. Lo
This work investigates an inverse problem for a general class of linear reaction-diffusion systems incorporating multiple delayed contributions, namely retarded diffusion, retarded…
Derivative-Free Recovery of a Nonlinearity in a Free-Boundary DCIS Model
De-Han Chen, Hongyu Liu, Keji Liu
We investigate an inverse coefficient problem for a multidimensional free-boundary model of ductal carcinoma in situ (DCIS), in which the tumor interface is governed by the nonline…
A Measure-Consistent Operator Learning Method for Infinite-Dimensional Master Equations
Chenyao Wang, Hongyu Liu, Hui Liang
Master equations in mean field game theory characterize feedback value functions that depend on time, state (space), and the population distribution. Their numerical approximation…
Travel-time tomography from mean field game dynamics
Longqiang Xu, Weishi Yin, Hongyu Liu
Travel-time tomography seeks to recover a hidden environment from external measurements generated by propagation through an anomalous region. Standard formulations treat propagatio…
Symmetrization of the Maxwell--Neumann--Poincar'e operator, spectral decomposition in traces, and boundary localisation of SPRs
Bochao Chen, Yixian Gao, Hongyu Liu
The Neumann--Poincaré (NP) operator, a fundamental operator in potential theory, has attracted renewed attention for its central role in the analysis of surface plasmon resonances…
Determining habitat anomalies in cross-diffusion predator-prey chemotaxis models
Yuhan Li, Hongyu Liu, Catharine W. K. Lo
This paper addresses an open inverse problem at the interface of mathematical analysis and spatial ecology: the unique identification of unknown spatial anomalies -- interpreted as…
Topological Braiding and Dynamic Probing of Phase Transitions at Temporal Interfaces in Non-Hermitian Synthetic Dimensions
Yuanhang Jiang, Jianfei Li, Chengxi Yang +6
Non-Hermitian systems give rise to distinct topological phenomena, yet their manifestations at temporal interfaces characterized by abrupt changes in system parameters remain large…
Parameter Identification in Reaction-Diffusion-Chemotaxis Systems from Single Turing Pattern Amplitudes
Yuhan Li, Hongyu Liu, Catharine W. K. Lo
Turing patterns encode key information about biological mechanisms, yet traditional inverse problems rely on non-biological data like boundary measurements, neglecting the patterns…
Determining a parabolic-elliptic-elliptic system by boundary observation of its non-negative solutions under chemotaxis background
Yuhan Li, Hongyu Liu, Catharine W. K. Lo
This paper addresses a profoundly challenging inverse problem that has remained largely unexplored due to its mathematical complexity: the unique identification of all unknown coef…
Determining evolutionary equations from a single passive boundary observation
Lu Chen, Yan Jiang, Hongyu Liu +2
We study inverse boundary problems for evolutionary PDEs using only a single passive boundary observation, where data from an unknown internal source propagate through an unknown m…
Inverse Problems for Mean Field Games
Hongyu Liu, Catharine W. K. Lo, Shen Zhang
In this book, we present a curated collection of existing results on inverse problems for Mean Field Games (MFGs), a cutting-edge and rapidly evolving field of research. Our aim is…
Simultaneously decoding the unknown stationary state and function parameters for mean field games
Hongyu Liu, Catharine W. K. Lo
Mean field games (MFGs) offer a versatile framework for modeling large-scale interactive systems across multiple domains. This paper builds upon a previous work, by developing a st…
Inverse problems for coupled nonlocal nonlinear systems arising in mathematical biology
Ming-Hui Ding, Hongyu Liu, Catharine W. K. Lo
In this paper, we propose and study several inverse problems of determining unknown parameters in nonlocal nonlinear coupled PDE systems, including the potentials, nonlinear intera…
Determining state space anomalies in mean field games
Hongyu Liu, Catharine W. K. Lo
In this paper, we are concerned with the inverse problem of determining anomalies in the state space associated with the stationary mean field game (MFG) system. We establish novel…
Decoding a mean field game by the Cauchy data around its unknown stationary states
Hongyu Liu, Catharine W. K. Lo, Shen Zhang
In recent years, mean field games (MFGs) have garnered considerable attention and emerged as a dynamic and actively researched field across various domains, including economics, so…
On inverse problems in multi-population aggregation models
Yuhan Li, Hongyu Liu, Catharine W. K. Lo
This paper focuses on inverse problems arising in studying multi-population aggregations. The goal is to reconstruct the diffusion coefficient, advection coefficient, and interacti…
Inverse boundary problem for a mean field game system with probability density constraint
Hongyu Liu, Shen Zhang
By following the study in [24], we consider an inverse boundary problem for the mean field game system where a probability density constraint is enforced on the game agents. That i…
On inverse problems in predator-prey models
Yuhan Li, Hongyu Liu, Catharine W. K. Lo
In this paper, we consider the inverse problem of determining the coefficients of interaction terms within some Lotka-Volterra models, with support from boundary observation of its…
Determining Sources in the Bioluminescence Tomography Problem
Ming-Hui Ding, Rongfang Gong, Hongyu Liu +1
In this paper, we revisit the bioluminescence tomography (BLT) problem, where one seeks to reconstruct bioluminescence signals (an internal light source) from external measurements…