Application of tensor arithmetic to efficient circuit modeling and simulation

Abstract

Electronic design automation (EDA) is an important research area in integrated circuit design. The main purpose of EDA is to model and simulate an integrated circuit or module on computer before the actual fabrication, which could accelerate the design cycle significantly. After the rapid development of recent years, numerous EDA algorithms and tools emerged which truly saved intensive work for electronic system designers.

One of the most intractable problems in EDA area is the efficient computation when modeling, simulating and optimizing a large scale circuit system. Till now, many matrix-based and vector-based algorithms have been proposed and developed to solve the computational problems.

However, traditional matrix-based and vector-based algorithms may meet the bottleneck when applied to high-dimension problems which commonly involve an exponentially large number of parameters or variables. Fortunately, the recent advances in tensors have brought about an elegant way to combat the high dimension problem. Tensors, as high-dimensional generalization of matrices, were developed over one hundred years ago, but mainly focused on physics and chemometrics. In recent years, tensors are beginning to be applied to engineering fields frequently due to their natural capability of handling high dimension and huge data problems. These engineering fields include but are not limited to nonlinear system identification, face recognition, machine learning and signal processing. To solve the high dimensional problems in EDA field, it is natural to employ tensors to model nonlinear circuits and further reduce the computation complexity by exploiting the tensor structure.

This thesis mainly focuses on developing the tensor-based circuit modeling and simulation methods, which alleviates the curse of dimensionality well. On the one hand, inspired by the recent proposed tensor-network-based multiple-input multiple-output (MIMO) Volterra series modeling of nonlinear systems, this thesis studies the nonlinear MIMO predistorter design technique, which is widely employed to linearize the response of nonlinear modules such as power amplifiers and semiconductor optical amplifiers. Two tensor-network-based predistorter design schemes are demonstrated for the first time. On the other hand, a novel Tucker-Tensor-Train model compression (T3MC) method is proposed to accelerate large-scale nonlinear circuit simulation. Specifically, instead of treating the different order polynomial nonlinear terms separately, T3MC incorporates them all into a big tensor and utilize two classical tensor decomposition methods, namely Tucker and tensor train decomposition, to compress the big tensor. Numerical experiments are conducted to demonstrate the superiority of T3MC over the existing model compression methods. (Total words: 392)