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

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.

14 figures. Accepted by IEEE Trans. CAD of Integrated Circuits and Systems

References in corpus (4)

• Tensorizing Neural Networks
• Speeding-up Convolutional Neural Networks Using Fine-tuned CP-Decomposition
• Bayesian Sparse Tucker Models for Dimension Reduction and Tensor Completion
• A Big-Data Approach to Handle Many Process Variations: Tensor Recovery and Applications

Cited by in corpus (8)

• Sparse Tucker Tensor Decomposition on a Hybrid FPGA-CPU Platform
• Fast and Accurate Tensor Completion with Total Variation Regularized Tensor Trains
• Faster Tensor Train Decomposition for Sparse Data
• Superfast CUR Matrix Algorithms, Their Pre-Processing and Extensions
• High-Dimensional Uncertainty Quantification of Electronic and Photonic IC with Non-Gaussian Correlated Process Variations
• Prediction of multi-dimensional spatial variation data via Bayesian tensor completion
• Uncertainty Quantification of Electronic and Photonic ICs with Non-Gaussian Correlated Process Variations
• PASTA: A Parallel Sparse Tensor Algorithm Benchmark Suite