10 papers
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…
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…
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…