Search for: All records

The Boltzmann Transport Equation (BTE) for phonons is often used to predict thermal transport at submicron scales in semiconductors. The BTE is a seven-dimensional nonlinear integro-differential equation, resulting in difficulty in its solution even after linearization under the single relaxation time approximation. Furthermore, parallelization and load balancing are challenging, given the high dimensionality and variability of the linear systems' conditioning. This work presents a 'synthetic' scalable parallelization method for solving the BTE on large-scale systems. The method includes cell-based parallelization, combined band+cell-based parallelization, and batching technique. The essential computational ingredient of cell-based parallelization is a sparse matrix-vector product (SpMV) that can be integrated with an existing linear algebra library like PETSc. The combined approach enhances the cell-based method by further parallelizing the band dimension to take advantage of low inter-band communication costs. For the batched approach, we developed a batched SpMV that enables multiple linear systems to be solved simultaneously, merging many MPI messages to reduce communication costs, thus maintaining scalability when the grain size becomes very small. We present numerical experiments to demonstrate our method's excellent speedups and scalability up to 16384 cores for a problem with 12.6 billion unknowns. 

Tucker decomposition is one of the SOTA CNN model compression techniques. However, unlike the FLOPs reduction, we observe very limited inference time reduction with Tucker-compressed models using existing GPU software such as cuDNN. To this end, we propose an efficient end-to-end framework that can generate highly accurate and compact CNN models via Tucker decomposition and optimized inference code on GPUs. Specifically, we propose an ADMM-based training algorithm that can achieve highly accurate Tucker-format models. We also develop a high-performance kernel for Tucker-format convolutions and analytical performance models to guide the selection of execution parameters. We further propose a co-design framework to determine the proper Tucker ranks driven by practical inference time (rather than FLOPs). Our evaluation on five modern CNNs with A100 demonstrates that our compressed models with our optimized code achieve up to 2.21× speedup over cuDNN, 1.12× speedup over TVM, and 3.27× over the original models using cuDNN with at most 0.05% accuracy loss.