Tensor Computation: A New Framework for High-Dimensional Problems in EDA

TL;DR

This paper introduces tensor computation as a powerful framework to address high-dimensional problems in electronic design automation, offering a more efficient alternative to traditional matrix-based methods.

Contribution

It presents tensor computation as a novel approach for high-dimensional EDA problems, including tutorials, applications, and future research directions.

Findings

Tensor methods improve computational efficiency for high-dimensional problems.

Applications include nonlinear circuit modeling and uncertainty quantification.

Tensor frameworks can handle complex, multi-parameter EDA tasks effectively.

Abstract

Many critical EDA problems suffer from the curse of dimensionality, i.e. the very fast-scaling computational burden produced by large number of parameters and/or unknown variables. This phenomenon may be caused by multiple spatial or temporal factors (e.g. 3-D field solvers discretizations and multi-rate circuit simulation), nonlinearity of devices and circuits, large number of design or optimization parameters (e.g. full-chip routing/placement and circuit sizing), or extensive process variations (e.g. variability/reliability analysis and design for manufacturability). The computational challenges generated by such high dimensional problems are generally hard to handle efficiently with traditional EDA core algorithms that are based on matrix and vector computation. This paper presents "tensor computation" as an alternative general framework for the development of efficient EDA algorithms and tools. A tensor is a high-dimensional generalization of a matrix and a vector, and is a natural choice for both storing and solving efficiently high-dimensional EDA problems. This paper gives a basic tutorial on tensors, demonstrates some recent examples of EDA applications (e.g., nonlinear circuit modeling and high-dimensional uncertainty quantification), and suggests further open EDA problems where the use of tensor computation could be of advantage.