Bo Zhang, Tzu-Yen Ma, Zichen Tang, Junpeng Ding, Zirui Wang, Yizhuo Zhao, Peilin Gao, Zijie Xi, Zixin Ding, Haiyang Sun, Haocheng Gao, Yuan Liu, Liangjia Wang, Yiling Huang, Yujie Wang, Yuyue Zhang, Ronghui Xi, Yuanze Li, Jiacheng Liu, Zhongjun Yang, Haihong E. Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2026.

This paper presents a modified frequency-hopping deep learning fusion framework (MFHFF) to solve multifrequency electromagnetic (EM) inverse scattering problems (ISPs) in real-time with high accuracy. The proposed MFHFF integrates advantages of the high accuracy of frequency-hopping method and the improved stability of simultaneous inversion strategy. First, the MFHFF cascades multiple monofrequency solvers, each combines a scattered field encoder and a pre-reconstructed result encoder. Additionally, the scattered field encoder utilizes adaptive average pooling to dynamically adjust scattered field data dimensions into standardized input specifications for subsequent convolutional layers. Second, the frequency-hopping connection (FHC) is implemented in the MFHFF by concatenating low-frequency inversion result to high-frequency pre-reconstructed result encoder. The low-frequency results serve as initial estimates for the high-frequency solver according to the FHC, thereby reducing the nonlinearity of high-frequency inversion and improving the accuracy of MFHFF. Third, the simultaneous inversion connection (SIC) is integrated into MFHFF to incorporate low-frequency features into high-frequency solver, facilitating simultaneous processing of multifrequency information and ensuring enhanced stability of MFHFF. The proposed MFHFF exploits an effective framework for solving multifrequency ISPs. The superior stability, accuracy, flexibility and generalization ability of the MFHFF have been demonstrated by the synthetic and the experimental results.

With the proliferation of distributed generators (DGs), multimicrogrid distribution systems (MMDSs) have emerged, where cooperative optimal operation plays a crucial role in improving operational flexibility and economy. On the other hand, when considering distribution network reconfiguration (DNR), traditional iterative distributed algorithms can protect privacy but face challenges, such as high computational complexity and poor convergence. To address these issues, this article proposes a cooperative operation method for MMDSs based on an equivalent projection (EP) theory. Specifically, a bi-level cooperative method for MMDSs is first proposed. Therein, the flexible resources within the MMDS are identified, while DNR and soft open point (SOP) technologies are considered. Second, to protect privacy of the lower-level microgrids (MGs), the improved Fourier–Motzkin elimination (IFME) and Gaussian elimination methods are used to derive the low-dimensional projection feasible region (PFR) of the lower-level MGs. Third, a noniterative solution method based on the EP theory is developed to efficiently solve the bilevel cooperation model, while addressing the privacy concerns from participants. Numerical results show that the third-order approximate PFR model can achieve a lossless transformation of the bilevel model, effectively balancing computational efficiency and accuracy. Compared to traditional distributed algorithms, the developed noniterative solution method exhibits superior performance in solving mixed-integer programming (MIP) problems. Moreover, the proposed cooperative approach improves the operational performance of the MMDS, achieving a 7.22% reduction in operating costs.

The electromagnetic (EM) inverse scattering problems (ISPs) exhibit strong nonlinearity, making it a challenge to reconstruct relative permittivity of strong scatterers with high quality. Joint inversion can leverage the satisfactory solution obtained from acoustic inversion to mitigates the impact of strong nonlinearity on EM inversion. However, how to improve the precision of reconstructing the internal electrical parameter distribution through this kind of joint inversion approach is still a challenge. Aim to improve the quality of reconstruction, a new joint inversion method based on the framework of the subspace-based optimization method (SOM) is proposed in this paper. This new method utilizes the Pearson correlation coefficient (PCC) to construct structural similarity constraints, thereby enhancing the linear correlation between EM and acoustic parameters. In inversion process, all data obtained from acoustic inversion can offer effective constraints. In order to improve convergence speed and stability of the proposed method, a constraint which is consisted of CGF is induced in the object function. And by utilizing the results of the results of acoustic inversion, the inversion domain can be further refined, giving rise to better computational efficiency. With these treatments, the proposed method has better performance in both accuracy and efficiency. The effectiveness and advantages of the proposed method is validated through several numerical examples.

Due to the strong nonlinearity, it is always a challenge to reconstruct strong scatterers with high contrasts and/or large dimensions. This article proposes an iterative domain decomposition technique (IDDT) based on the framework of the subspace-based optimization method (SOM) to solve highly nonlinear inverse scattering problems (ISPs). This method takes advantage of the fact that the reduction of unknowns can reduce the nonlinearity of ISPs and different parts of scatterers have different effects on scattered fields. In the inversion procedure, the domain of scatterers (DoS) is obtained by refining the domain of interests (DoI) first. Then, the DoS is divided into two subdomains according to their contributions to scattered fields: the dominant subdomain and the subordinate subdomain. The induced current of the subordinate subdomain is approximated by its deterministic part. Therefore, only the induced current of the dominant subdomain needs to be reconstructed, greatly reducing the dimensions of the solution domain. Then the properties of the entire DoS are retrieved with the properties of the dominant subdomain as initial guesses. This technique can be used repeatedly to improve the reconstruction quality. Compared with the original SOM, this method can reduce the nonlinearity of ISPs and reconstruct stronger scatterers with better reconstruction qualities and less computation loads. The feasibility and efficiency of IDDT-SOM are discussed from the perspective of the relative distribution of induced current by numerical and experimental examples.

Because of strong nonlinearity, it is always a challenge to acquire fine resolution reconstruction results for electric strong scatterers with high contrasts using electromagnetic (EM) data. Many electric strong scatterers have weak nonlinearity in acoustic inversion. To make full use of the advantages of acoustic inversion, two joint inversion methods based on the structural constraints to reconstruct electric strong scatterers using EM and acoustic data are proposed in this article. These two methods utilize the framework of the subspace-based optimization method (SOM). In the inversion process, one of the methods utilizes a cross-gradient function to link the EM and the acoustic inversions, enforcing the structural similarity between the permittivity and the sound velocity. The second method is to utilize the reconstruction result of acoustic data as initial structural information for the EM inversion process. Compared with conventional separate SOM, these two methods achieve finer EM reconstruction for electric strong scatterers. Both structure and contrast values are well reconstructed. The efficiency and the robustness of the methods are validated through numerical experiments.