Siheng Li, Kejiao Li, Zenan Xu, Guanhua Huang, Kun Li, Haoyuan Wu, Wujiajia, Zihao Zheng, Chenchen Zhang, Kun Shi, Xue Gong, Qi Yi, Ruibin Xiong, Tingqiang Xu, Yuhao Jiang, Jianfeng Yan, Yuyuan Zeng, Guanghui Xu, Jinbao Xue, Zhijiang xu, Zheng Fang, Shuai LI, Qibin Liu, Xiaoxue Li, Zhuoyu Li, Yangyu Tao, Fei Gao, Cheng Jiang, Bochao Wang, Kai Liu, Jianchen Zhu, Wai Lam, Bo Zhou, Di Wang. Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2026.

PDE-Constrained Optimization (PDECO) problems can be accelerated significantly by employing gradient-based methods with surrogate models like neural operators compared to traditional numerical solvers. However, this approach faces two key challenges: (1) Data inefficiency: Lack of efficient data sampling and effective training for neural operators, particularly for optimization purpose. (2) Instability: High risk of optimization derailment due to inaccurate neural operator predictions and gradients. To address these challenges, we propose a novel framework: (1) Optimization-oriented training: we leverage data from full steps of traditional optimization algorithms and employ a specialized training method for neural operators. (2) Enhanced derivative learning: We introduce a Virtual-Fourier layer to enhance derivative learning within the neural operator, a crucial aspect for gradient-based optimization. (3) Hybrid optimization: We implement a hybrid approach that integrates neural operators with numerical solvers, providing robust regularization for the optimization process. Our extensive experimental results demonstrate the effectiveness of our model in accurately learning operators and their derivatives. Furthermore, our hybrid optimization approach exhibits robust convergence.

Fluorescence in situ hybridization (FISH) is a well-recognized technique for evaluating the human epidermal growth factor receptor 2 (HER2) gene status in breast cancer, where HER2 genes are seen as the red stained spots, and the chromosome centromere (CEN17) on which HER2 is located are visible as the green stained spots under a fluorescent microscope. The traditional manual analysis of FISH images is low efficient and has great subjective differences. Many researches focus on automatically calculating the average ratio of red/green spots in a cell and have achieved good performance. However, there are still a need to improve the segmentation accuracy of cells and HER2/CEN17 signals in FISH images with poor quality. In this paper, we propose a robust approach to locate HER2 and CEN17 signals based on the image standardization of varied FISH images. First we propose to use offset operation to reduce the fluorescence scattering, and to use exposure ratio map estimation and brightness transformation to enhance the weak fluorescence. Then we detect red/green spots by sequentially using top-hat filtering, thresholding and post-processing operations. The experimental results have shown that our proposed method can work well for the clinical FISH images with different quality.