The rapid progress in Deep Learning (DL) and Large Language Models (LLMs) has exponentially increased demands of computational power and bandwidth. This, combined with the high costs of faster computing chips and interconnects, has significantly inflated High Performance Computing (HPC) construction costs. To address these challenges, we introduce the Fire-Flyer AI-HPC architecture, a synergistic hardware-software co-design framework and its best practices. For DL training, we deployed the Fire-Flyer 2 with 10,000 PCIe A100 GPUs, achieved performance approximating the DGX-A100 while reducing costs by half and energy consumption by $40 \%$. We specifically engineered HFReduce to accelerate allreduce communication and implemented numerous measures to keep our Computation-Storage Integrated Network congestion-free. Through our software stack, including HaiScale, 3FS, and HAI-Platform, we achieved substantial scalability by overlapping computation and communication. Our system-oriented experience from DL training provides valuable insights to drive future advancements in AI-HPC.

A novel polarimetric calibration scheme on the basis of lexicographic matrix decomposition is proposed, and a new polarimetric active radar calibrator (PARC) with two independently rotatable antennas is designed to obtain the lexicographic matrices. Thus, the proposed method is realizable and can operate with the lexicographic target vectors instead of the polarization scattering matrix (PSM). The base elements of the lexicographic target vectors are the vectors corresponding to the new PARC with the antennas at different orientations. Moreover, the elements of the vector are just the elements of the PSM. Hence, the error coefficients corresponding to a polarimetric measurement system are directly achieved, and the polarimetric calibration is simple and accurate. Experimental results confirm the superiority of the presented strategy. A 35-dB improvement in the system cross-polarization isolation is obtained.