EMPIRE: An Efficient and Compact Multiple-Parameterized Model-Order Reduction Method for Physical Optimization

Parameterized model-order reduction is useful for very large-scale integration VLSI physical design and optimization. In this paper, we propose an efficient yet accurate parameterized model-order reduction method EMPIRE for multiple parameters. It uses implicit moment matching to efficiently handle high-order moments of a large number of parameters. In addition, it can match the moments of different parameters with different accuracy according to their influence on the objective under study, and such influence is measured by the 2-norm of their coefficient matrix in the canonical form. It develops three algorithms to further suppress the size of the reduced model by finding a projection matrix that has a much smaller number of columns than the original one. Experimental results show that compared with the best existing algorithm CORE that uses explicit moment matching for the parameters, EMPIRE reduces waveform error by 47.8 × at a similar runtime.