A high-performance parallel algorithm based on problem independent machine learning (PIML) for large-scale topology optimization

Although supplying extensive design space, the curse of dimensionality restricts the widespread application of large-scale topology optimization in practical engineering. Various acceleration techniques have been integrated with topology optimization, achieving significant attention and progress in large-scale problems. This work aims to investigate how much benefit can be obtained by combining parallel computing and machine learning techniques to enhance the efficiency of large-scale topology optimization algorithms. Accordingly, a parallel problem independent machine learning (PIML)-enhanced topology optimization method is proposed. The PIML model substantially reduces the dimension of the condensed stiffness matrix and its computational cost, and parallel computing reduces the workload per process and enables the application of a parallel multigrid solver. Besides, several techniques, such as matrix-free implementation, direct condensation of uniform coarse elements, and adjusting computational resource limits, have been developed to enhance computational efficiency. The weak scaling efficiency, strong scaling speedup, and maximum achievable efficiency of the proposed method are validated across multiple numerical examples, showing significant improvement in the tractable problem size and solution efficiency compared to traditional topology optimization algorithms.