Peijun Li, Ying Liang
This paper is concerned with the stability estimates for inverse source problems of the stochastic Helmholtz equation driven by white noise. The well-posedness is established for the direct source problems, which ensures the existence and uniqueness of solutions. The stability estimates are deduced for the inverse source problems, which aim to determine the strength of the random source. To enhance the stability of the inverse source problems, we incorporate a priori information regarding the regularity and support of the strength. In the case of homogeneous media, a Hölder stability estimate is established, providing a quantitative measure of the stability for reconstructing the source strength. For the more challenging scenario of inhomogeneous media, a logarithmic stability estimate is presented, capturing the intricate interactions between the source and the varying medium properties.
Kazufumi Ito, Ying Liang, Jun Zou
We present a two-stage least-squares method to inverse medium problems of reconstructing multiple unknown coefficients simultaneously from noisy data. A direct sampling method is applied to detect the location of the inhomogeneity in the first stage, while a total least-squares method with mixed regularization is used to recover the medium profile in the second stage. The total least-squares method is designed to minimize the residual of the model equation and the data fitting, along with an appropriate regularization, in an attempt to significantly improve the accuracy of the approximation obtained from the first stage. We shall also present an analysis on the well-posedness and convergence of this algorithm. Numerical experiments are carried out to verify the accuracies and robustness of this novel two-stage least-squares algorithm, with great tolerance of noise.
Ying Liang
This paper evaluates the impact of the German minimum wage policy on firms' financial leverage. By using a comprehensive firm-establishment-employee linked dataset and a difference-in-differences estimation with firm-level variation in treatment intensity, the analysis shows that the average minimum wage level reduces firms' financial leverage by about 0.5 to 0.9 percentage points, corresponding to 1 to 2 percent of the mean of financial leverage. Further investigation of the mechanism shows that the minimum wage does not lead to significant capital-labor substitution; therefore, the labor share increases. Firms react to the increased labor share by deleveraging. The results suggest that while the minimum wage benefits workers by allocating more earnings to the labor force, it also introduces greater operating risks and encourages conservative financial behavior among firms.
Ying Liang, Jun Zou
We study the acoustic field enhancement through a circular hole in a hard plate of finite thickness in this work. We derive the boundary-integral equations corresponding to the acoustic scattering to investigate the Fabry-Perot type resonant frequencies that induce the field enhancement. The asymptotic expansions of Fabry-Perot type resonances with respect to the size of the hole are derived, and the quantitative analysis of the field enhancement caused by the configuration at the resonant frequencies is presented with both the enhancement order and the shapes of resonant modes characterized. The transmission in the nonresonant quasi-static regime is also investigated.
Peijun Li, Zhenqian Li, Ying Liang
This paper investigates stability estimates for inverse source problems in the stochastic polyharmonic wave equation, where the source is represented by white noise. The study examines the well-posedness of the direct problem and derives stability estimates for identifying the strength of the random source. Assuming a priori information of the regularity and support of the source strength, the Hölder stability is established in the absence of a potential. In the more challenging case where a potential is present, the logarithmic stability estimate is obtained by constructing specialized solutions to the polyharmonic wave equation.
Yiwen Wang, Ying Liang, Yuxuan Zhang, Xinning Chai, Zhengxue Cheng, Yingsheng Qin, Yucai Yang, Rong Xie, Li Song
Due to the disparity between real-world degradations in user-generated content(UGC) images and synthetic degradations, traditional super-resolution methods struggle to generalize effectively, necessitating a more robust approach to model real-world distortions. In this paper, we propose a novel approach to UGC image super-resolution by integrating semantic guidance into a diffusion framework. Our method addresses the inconsistency between degradations in wild and synthetic datasets by separately simulating the degradation processes on the LSDIR dataset and combining them with the official paired training set. Furthermore, we enhance degradation removal and detail generation by incorporating a pretrained semantic extraction model (SAM2) and fine-tuning key hyperparameters for improved perceptual fidelity. Extensive experiments demonstrate the superiority of our approach against state-of-the-art methods. Additionally, the proposed model won second place in the CVPR NTIRE 2025 Short-form UGC Image Super-Resolution Challenge, further validating its effectiveness. The code is available at https://github.c10pom/Moonsofang/NTIRE-2025-SRlab.
Roy Y. He, Ying Liang, Hongkai Zhao, Yimin Zhong
When neural networks (NNs) are used as a type of nonlinear parametric representation to solve partial differential equations (PDEs), they often display frequency-dependent learning dynamics that can differ from those seen in direct function approximation tasks, resulting from a balance between the frequency bias of the NN representation and that of the underlying differential operator. Although many commonly used NNs exhibit a bias towards low-frequency modes in representation, the presence of differential operators in the loss function, which amplifies high-frequency components, can lead to high frequency bias. In this work, using second order elliptic PDEs as an example, we show how these two factors compete and lead to an overall frequency bias in different situations. Once the balance is determined, it is important to design computational strategies to counter the resulting bias to improve training efficiency. We propose a simple operator-aware preconditioning strategy that rebalances the optimization landscape and the learning dynamics by applying an auxiliary integral operator to the residual. The integral kernel can be the Green's function of a reference elliptic operator or an approximation, and integrates easily with common NN solvers for PDEs. Extensive experiments, including multiscale and variable-coefficient problems, show that the approach restores more balanced learning dynamics across modes and substantially improves both convergency and accuracy.
Ying Liang, Bao-Yun Dong, Zi-Jian Xiong, Xue-Feng Zhang
Rydberg atom triangular arrays in an optical cavity serve as an ideal platform for understanding the interplay between geometric frustration and quantized photons. Using a large-scale quantum Monte Carlo method, we obtain a rich ground state phase diagram. Around half-filling, the infinite long-range light-matter interaction lifts the ground state degeneracy, resulting in a novel order-coexisted superradiant clock phase that completely destroys the fragile order-by-disorder phase observed in classical light fields. According to the Ginzburg-Landau theory, this replacement may result from the competition between threefold and sixfold clock terms. Similar to the spin supersolid, the clear first-order phase transition at the $Z_2$ symmetry line is attributed to the nonzero photon density, which couples to the threefold clock term. Finally, we discuss the low-energy physics in the dimer language and propose that cavity-mediated nonlocal ring exchange interactions may play a critical role in the rich physics induced by the attachment of cavity-QED. Our work opens a new arena of research on the emergent phenomena of quantum phase transitions in many-body quantum optics.
Ying Liang, Yi-Da Chu, Shi-Jie Hu, Xue-Feng Zhang
Scanning tunneling microscopy (STM) serves as a powerful pictorial tool for visualizing the local density of states (LDOS) of an individual stripe, which strongly intertwines with superconductivity in the underdoped cuprates. The exotic LDOS map patterns thus appear as the key to uncovering the mystery of the underlying microscopic mechanisms. With the quantum color string model framework, we reveal that the microscopic origin of the ubiquitous $4a_0\times4a_0$ plaquettes is closely related to spinon singlet pairs. Moreover, by comparing our data with LDOS of cuprates, we identify an effect of particle-hole symmetry breaking (PHSB): a $2a_0$ shift, which is confirmed in a longer stripe ($L=18$).Our work offers a fresh wavefunction-based perspective for interpreting STM signals in experiments and may advance the microscopic comprehension of high-$T_c$ cuprates.
Ying Liang, Hai Zhang
In this paper, we revisit the classic problem of diffraction of electromagnetic waves by an aperture in a perfectly conducting plane. We formulate the diffraction problem using a boundary integral equation that is defined on the aperture using Dyadic Green's function. This integral equation turns out to align with the one derived by Bethe using fictitious magnetic charges and currents. We then investigate the boundary integral equation using a saddle point formulation and establish the well-posedness of the boundary integral equation, including the existence and uniqueness of the solution in an appropriately defined Sobolev space.
Ying Liang, Jun Zou
In this work, we propose and analyse a weak Galerkin method for the electrical impedance tomography based on a bounded variation regularization. We use the complete electrode model as the forward system that is approximated by a weak Galerkin method with lowest order. The error estimates are studied for the forward problem, which are used to establish the convergence of this weak Galerkin algorithm for the inverse problem. Numerical examples are presented to verify the effectiveness and efficiency of the weak Galerkin algorithm for the electrical impedance tomography.
Roy Y. He, Ying Liang, Hongkai Zhao, Yimin Zhong
We use elliptic partial differential equations (PDEs) as examples to show various properties and behaviors when shallow neural networks (SNNs) are used to represent the solutions. In particular, we study the numerical ill-conditioning, frequency bias, and the balance between the differential operator and the shallow network representation for different formulations of the PDEs and with various activation functions. Our study shows that the performance of Physics-Informed Neural Networks (PINNs) or Deep Ritz Method (DRM) using linear SNNs with power ReLU activation is dominated by their inherent ill-conditioning and spectral bias against high frequencies. Although this can be alleviated by using non-homogeneous activation functions with proper scaling, achieving such adaptivity for nonlinear SNNs remains costly due to ill-conditioning.
Peijun Li, Ying Liang, Xu Wang
This paper focuses on stability estimates of the inverse random source problems for the polyharmonic, electromagnetic, and elastic wave equations. The source is represented as a microlocally isotropic Gaussian random field, which is defined by its covariance operator in the form of a classical pseudo-differential operator. The inverse problem is to determine the strength function of the principal symbol by exploiting the correlation of far-field patterns associated with the stochastic wave equations at a single frequency. For the first time, we show in a unified framework that the optimal Lipschitz-type stability can be attained across all the considered wave equations through the utilization of correlation-based data.
Ying Siu Liang, Dongkyu Choi, Kenneth Kwok
Reliable perception is essential for robots that interact with the world. But sensors alone are often insufficient to provide this capability, and they are prone to errors due to various conditions in the environment. Furthermore, there is a need for robots to maintain a model of its surroundings even when objects go out of view and are no longer visible. This requires anchoring perceptual information onto symbols that represent the objects in the environment. In this paper, we present a model for action-aware perceptual anchoring that enables robots to track objects in a persistent manner. Our rule-based approach considers inductive biases to perform high-level reasoning over the results from low-level object detection, and it improves the robot's perceptual capability for complex tasks. We evaluate our model against existing baseline models for object permanence and show that it outperforms these on a snitch localisation task using a dataset of 1,371 videos. We also integrate our action-aware perceptual anchoring in the context of a cognitive architecture and demonstrate its benefits in a realistic gearbox assembly task on a Universal Robot.
Ying Siu Liang, Chen Zhang, Dongkyu Choi, Kenneth Kwok
Object permanence in psychology means knowing that objects still exist even if they are no longer visible. It is a crucial concept for robots to operate autonomously in uncontrolled environments. Existing approaches learn object permanence from low-level perception, but perform poorly on more complex scenarios, like when objects are contained and carried by others. Knowledge about manipulation actions performed on an object prior to its disappearance allows us to reason about its location, e.g., that the object has been placed in a carrier. In this paper we argue that object permanence can be improved when the robot uses knowledge about executed actions and describe an approach to infer hidden object states from agent actions. We show that considering agent actions not only improves rule-based reasoning models but also purely neural approaches, showing its general applicability. Then, we conduct quantitative experiments on a snitch localization task using a dataset of 1,371 synthesized videos, where we compare the performance of different object permanence models with and without action annotations. We demonstrate that models with action annotations can significantly increase performance of both neural and rule-based approaches. Finally, we evaluate the usability of our approach in real-world applications by conducting qualitative experiments with two Universal Robots (UR5 and UR16e) in both lab and industrial settings. The robots complete benchmark tasks for a gearbox assembly and demonstrate the object permanence capabilities with real sensor data in an industrial environment.
Ying Siu Liang, Damien Pellier, Humbert Fiorino, Sylvie Pesty
Programming robots for general purpose applications is extremely challenging due to the great diversity of end-user tasks ranging from manufacturing environments to personal homes. Recent work has focused on enabling end-users to program robots using Programming by Demonstration. However, teaching robots new actions from scratch that can be reused for unseen tasks remains a difficult challenge and is generally left up to robotic experts. We propose iRoPro, an interactive Robot Programming framework that allows end-users to teach robots new actions from scratch and reuse them with a task planner. In this work we provide a system implementation on a two-armed Baxter robot that (i) allows simultaneous teaching of low- and high-level actions by demonstration, (ii) includes a user interface for action creation with condition inference and modification, and (iii) allows creating and solving previously unseen problems using a task planner for the robot to execute in real-time. We evaluate the generalisation power of the system on six benchmark tasks and show how taught actions can be easily reused for complex tasks. We further demonstrate its usability with a user study (N=21), where users completed eight tasks to teach the robot new actions that are reused with a task planner. The study demonstrates that users with any programming level and educational background can easily learn and use the system.
Caixia Cai, Ying Siu Liang, Nikhil Somani, Wu Yan
In this paper we present a framework to learn skills from human demonstrations in the form of geometric nullspaces, which can be executed using a robot. We collect data of human demonstrations, fit geometric nullspaces to them, and also infer their corresponding geometric constraint models. These geometric constraints provide a powerful mathematical model as well as an intuitive representation of the skill in terms of the involved objects. To execute the skill using a robot, we combine this geometric skill description with the robot's kinematics and other environmental constraints, from which poses can be sampled for the robot's execution. The result of our framework is a system that takes the human demonstrations as input, learns the underlying skill model, and executes the learnt skill with different robots in different dynamic environments. We evaluate our approach on a simulated industrial robot, and execute the final task on the iCub humanoid robot.
Ying Hao Matthew Liang, Valerian Hongjie Hall-Chen, Terry L. Rhodes, Yumin Wang, Yihang Zhao
The EXL-50U spherical tokamak was built by Energy iNNovation to develop technologies for proton-boron fusion in spherical tokamaks (Liu et al., Phys. Plasmas 2024). We present a conceptual design of the Doppler backscattering (DBS) diagnostic for the EXL-50U spherical tokamak. DBS is a diagnostic capable of measuring plasma turbulence, which is especially important for transport in tokamaks. Starting from a set of physical design constraints, such as port window availability and in-vessel space, we used SCOTTY (Hall-Chen et al., PPCF 2022), an in-house beam tracing code, to predict the location of the cutoffs and the corresponding scattering wavenumbers for several EXL-50U plasma scenarios. We find that we are able to measure scattering locations of 0.15 $<$ $ρ$ $<$ 1, with corresponding turbulent wavenumbers of 2.47 cm$^{-1}$$<$ $k_{\perp}$ $<$ 9.49 cm$^{-1}$. Here, $ρ$ is the normalised radial coordinate of the scattering location, and $k_{\perp}$ is the corresponding turbulent wavenumber. We then determine the optimal toroidal launch angles to ensure that the probe beam's wavevector is perpendicular to the magnetic field at the cutoff location, thereby maximising the backscattered signal. This matching is crucial due to the EXL-50U's high magnetic pitch angle, $\sim35^{\circ}$ at the outboard midplane. Given our results, we propose the use of toroidal steering and tunable frequency channels to ensure beams are well-matched with the magnetic pitch angle. We propose a quasioptical system that covers the U-band range (40--60 GHz).
Ruben Otin, Ying Hao Matthew Liang, Thomas Wilson, Simon Freethy, Valerian Hall-Chen
This study presents the validation of the frequency-domain finite element code ERMES 20.0, benchmarked against Finite Difference Time Domain (FDTD) solvers. The simulations focus on Ordinary-Extraordinary (O-X) mode conversion in the Electron Bernstein Wave (EBW) regime of the MAST Upgrade experiment. Validation is performed in terms of mode conversion efficiency and wave propagation characteristics. Several finite element formulations are tested and compared with the FDTD results. The simulations demonstrate excellent agreement between the different approaches, confirming the accuracy and robustness of ERMES 20.0 for modeling cold plasma wave interactions.
Huijia Dai, Junchen Hou, Xiao Zhang, Ying Liang, Tianxing Ma
Motivated by the recently experimental reported signatures of the tunable Mott insulating state and superconductivity in an ABC graphene trilayer superlattice, we investigate the charge compressibility, the spin correlation, and the superconducting instability within the Hubbard model on a three-layer honeycomb lattice. It is found that an antiferromagnetically ordered Mott insulator emerges beyond a critical $U_c$ at half-filling, and the electronic correlation drives a $d+id$ superconducting pairing to be dominant over other pairing patterns in a wide doped region. The effective pairing interaction with $d+id$ pairing symmetry is strongly enhanced with the increasing of on-site interaction, and suppressed as the interlayer coupling strength increases. Our intensive numerical results demonstrate that the insulating state and superconductivity in an ABC graphene trilayer are driven by strong electric correlation, and it may offer an attractive systems to explore rich correlated behaviors.