Solving a significant portion of the eigensystem is a critical problem in numerical linear algebra and is widely applied in real-world applications.As problem sizes increase, the twostage tridiagonalization method has emerged as the state-ofthe-art approach and has been implemented in well-known libraries such as LAPACK, PLASMA, and MAGMA.Its major performance bottleneck is the tridiagonal-to-band back transformation of eigenvectors (st2sb) due to the dilemma between limited operational intensity and excessive computational cost.This challenge is further exacerbated by the growing imbalance between computational speed and memory bandwidth in modern heterogeneous architectures.To address this challenge, this paper introduces a 2D Fusion method to decouple the operational intensity from the computational cost of st2sb.To reduce the intrinsic overhead of 2D Fusion for large fusion factors, we further propose an effective skipping strategy.Our 2D Fusion enhances the performance of all existing two-stage eigensolvers without loss of accuracy.We evaluated the effectiveness of 2D Fusion in MAGMA and LAPACK across various problem sizes: on the Nvidia A100 GPU, 2D Fusion improves the performance of eigenvalue decomposition in MAGMA by an average speedup of 1.06× for matrices larger than 24k×24k

Atmospheric data assimilation is essential for numerical weather prediction. Ensemble data assimilation connects multiple instances of an atmospheric model through a Kalman filter-based algorithm, which is regarded as a challenging computing task today. In this work, we build a fast, low-cost, and scalable atmospheric data assimilation prototype, DIDA, for the new-generation Sunway supercomputer, including: (1) a framework that enables flexible deployment of components, and manages and optimizes data communication among modules, achieving maximum resource efficiency; (2) an accurate, robust, UNet-based surrogate model for atmospheric dynamic simulation to generate the background ensemble; (3) a batch-LETKF algorithm with high-performance eigenvalue decomposition, which is up to 7.37 times faster than existing numerical libraries while exhibiting almost linear scalability. Experimental evaluations show that our AI-integrated ensemble data assimilation prototype can complete hour-cycle assimilation in minutes, maintain linear scalability, and save an order of magnitude of computing resources, compared with the traditional method.

Concentration gradient generation is of great importance for high-throughput drug screening. The classic Christmas tree structure is typically used for generating concentration gradients with uniform distribution. However, the variation in lengths of the outlet channels of the Christmas-tree structure causes serious biases in the generated concentration values. This paper first quantifies the biases in concentration gradients, and then proposes a fast look-up table-based method, along with a further Bayesian Optimization method for tuning the outlet channels of a given Christmas tree in order to enhance the uniformity of the generated concentration gradients. Specifically, the look-up table is based on the kd-tree data structure, and thus is very efficient and effective. Moreover, the table entries are generated by COMSOL simulation, which guarantees the accuracy of the predicted concentration values. Computational simulation results are promising, which verify the effectiveness of the proposed method.