Heng Wu

Heng Wu, Xiongfei Wang

Differing from synchronous generators, there are lack of physical laws governing the synchronization dynamics of voltage-source converters (VSCs). The widely used phase-locked loop (PLL) plays a critical role in maintaining the synchronism of current-controlled VSCs, whose dynamics are highly affected by the power exchange between VSCs and the grid. This paper presents a design-oriented analysis on the transient stability of PLL-synchronized VSCs, i.e., the synchronization stability of VSCs under large disturbances, by employing the phase portrait approach. Insights into the stabilizing effects of the first- and second-order PLLs are provided with the quantitative analysis. It is revealed that simply increasing the damping ratio of the second-order PLL may fail to stabilize VSCs during severe grid faults, while the first-order PLL can always guarantee the transient stability of VSCs when equilibrium operation points exist. An adaptive PLL that switches between the second-order and the first-order PLL during the fault-occurring/-clearing transient is proposed for preserving both the transient stability and the phase tracking accuracy. Time-domain simulations and experimental tests, considering both the grid fault and the fault recovery, are performed, and the obtained results validate the theoretical findings.

Heng Wu, Xiongfei Wang

The power synchronization control (PSC) has been increasingly used with voltage-source converters (VSCs) connected to the weak ac grid. This paper presents an in-depth analysis on the transient stability of the PSC-VSC by means of the phase portrait. It is revealed that the PSC-VSC will maintain synchronization with the grid as long as there are equilibrium points after the transient disturbance. In contrast, during grid faults without any equilibrium points, the critical clearing angle (CCA) for the PSC-VSC is identified, which is found equal to the power angle at the unstable equilibrium point of the post-fault operation. This fixed CCA facilitates the design of power system protection. Moreover, it is also found that the PSC-VSC can still re-synchronize with the grid after around one cycle of oscillation, even if the fault-clearing angle is beyond the CCA. This feature reduces the risk of system collapse caused by the delayed fault clearance. These findings are corroborated by simulations and experimental tests.

Henrik Sandberg, Kamil Hassan, Heng Wu

In this paper, we investigate a class of port-Hamiltonian systems with singular vector fields. We show that, under suitable conditions, their interconnection with passive systems ensures convergence to a prescribed non-equilibrium steady state. At first glance, this behavior appears to contradict the seemingly passive structure of port-Hamiltonian systems, since sustaining a non-equilibrium steady state requires continuous power injection. We resolve this apparent paradox by showing that the singularity in the vector field induces a sliding mode that contributes effective energy, enabling maintenance of the steady state and demonstrating that the system is not passive. Furthermore, we consider regularizations of the singular dynamics and show that the resulting systems are cyclo-passive, while still capable of supplying the required steady-state power. These results clarify the role of singularities in port-Hamiltonian systems and provide new insight into their energetic properties.

Heng Wu, Junjie Wang, Benzhuo Lu

Neural operator learning directly constructs the mapping relationship from the equation parameter space to the solution space, enabling efficient direct inference in practical applications without the need for repeated solution of partial differential equations (PDEs) - an advantage that is difficult to achieve with traditional numerical methods. In this work, we find that explicitly decoupling linear and nonlinear effects within such operator mappings leads to markedly improved learning efficiency. This yields a novel network structure, namely the Linear-Nonlinear Fusion Neural Operator (LNF-NO), which models operator mappings via the multiplicative fusion of a linear component and a nonlinear component, thus achieving a lightweight and interpretable representation. This linear-nonlinear decoupling enables efficient capture of complex solution features at the operator level while maintaining stability and generality. LNF-NO naturally supports multiple functional inputs and is applicable to both regular grids and irregular geometries. Across a diverse suite of PDE operator-learning benchmarks, including nonlinear Poisson-Boltzmann equations and multi-physics coupled systems, LNF-NO is typically substantially faster to train than Deep Operator Networks (DeepONet) and Fourier Neural Operators (FNO), while achieving comparable or better accuracy in most cases. On the tested 3D Poisson-Boltzmann case, LNF-NO attains the best accuracy among the compared models and trains approximately 2.7x faster than a 3D FNO baseline.

Haochen Wu, Heng Wu, Benzhuo Lu

For linear partial differential equations with known fundamental solutions, this work introduces a novel operator learning framework that relies exclusively on domain boundary data, including solution values and normal derivatives, rather than full-domain sampling. By integrating the previously developed Mathematical Artificial Data (MAD) method, which enforces physical consistency, all training data are synthesized directly from the fundamental solutions of the target problems, resulting in a fully data-driven pipeline without the need for external measurements or numerical simulations. We refer to this approach as the Mathematical Artificial Data Boundary Neural Operator (MAD-BNO), which learns boundary-to-boundary mappings using MAD-generated Dirichlet-Neumann data pairs. Once trained, the interior solution at arbitrary locations can be efficiently recovered through boundary integral formulations, supporting Dirichlet, Neumann, and mixed boundary conditions as well as general source terms. The proposed method is validated on benchmark operator learning tasks for two-dimensional Laplace, Poisson, and Helmholtz equations, where it achieves accuracy comparable to or better than existing neural operator approaches while significantly reducing training time. The framework is naturally extensible to three-dimensional problems and complex geometries.

Heng Wu, Qian Zhang, Guixu Zhang

Accurate monocular depth estimation remains a challenging problem due to the inherent ambiguity that stems from the ill-posed nature of recovering 3D structure from a single view, where multiple plausible depth configurations can produce identical 2D projections. In this paper, we present a novel depth estimation method that combines both local and global cues to improve prediction accuracy. Specifically, we propose the Gated Large Kernel Attention Module (GLKAM) to effectively capture multi-scale local structural information by leveraging large kernel convolutions with a gated mechanism. To further enhance the global perception of the network, we introduce the Global Bin Prediction Module (GBPM), which estimates the global distribution of depth bins and provides structural guidance for depth regression. Extensive experiments on the NYU-V2 and KITTI dataset demonstrate that our method achieves competitive performance and outperforms existing approaches, validating the effectiveness of each proposed component.

Heng Wu, Benzhuo Lu

Machine learning has emerged as a transformative tool for solving differential equations (DEs), yet prevailing methodologies remain constrained by dual limitations: data-driven methods demand costly labeled datasets while model-driven techniques face efficiency-accuracy trade-offs. We present the Mathematical Artificial Data (MAD) framework, a new paradigm that integrates physical laws with data-driven learning to facilitate large-scale operator discovery. By exploiting DEs' intrinsic mathematical structure to generate physics-embedded analytical solutions and associated synthetic data, MAD fundamentally eliminates dependence on experimental or simulated training data. This enables computationally efficient operator learning across multi-parameter systems while maintaining mathematical rigor. Through numerical demonstrations spanning 2D parametric problems where both the boundary values and source term are functions, we showcase MAD's generalizability and superior efficiency/accuracy across various DE scenarios. This physics-embedded-data-driven framework and its capacity to handle complex parameter spaces gives it the potential to become a universal paradigm for physics-informed machine intelligence in scientific computing.

Meng Li, Changyan Lin, Heng Wu et al.

Since the mapping relationship between definitized intra-interventional X-ray and undefined pre-interventional Computed Tomography(CT) is uncertain, auxiliary positioning devices or body markers, such as medical implants, are commonly used to determine this relationship. However, such approaches can not be widely used in clinical due to the complex realities. To determine the mapping relationship, and achieve a initializtion post estimation of human body without auxiliary equipment or markers, proposed method applies image segmentation and deep feature matching to directly match the X-ray and CT images. As a result, the well-trained network can directly predict the spatial correspondence between arbitrary X-ray and CT. The experimental results show that when combining our approach with the conventional approach, the achieved accuracy and speed can meet the basic clinical intervention needs, and it provides a new direction for intra-interventional registration.