The proposed project aims to automatically synthesize robust high-performance circuits built upon unreliable nano devices and, eventually, to facilitate a bold move from silicon-chip towards nano-chip. To this end, the PI proposes to develop an efficient statistical regression (STAR) framework that facilitates large-scale modeling and optimization of integrated circuits containing 104~105 variables. STAR is derived from a new augmented maximum likelihood estimation (AMLE) scheme. Compared to the traditional least-squares fitting, STAR is expected to achieve 100~1000?e runtime speedup, thereby offering a fundamental infrastructure that enables large-scale statistical modeling and optimization. Both the theoretical aspects (e.g., optimality, convergence, etc.) and the practical implementations (e.g., fast solver, numerical stability, etc.) of STAR will be studied. In addition, the proposed framework will be applied to explore the trade-offs between performance, yield and cost for multiple circuit topologies and device structures of nano electronics.

The proposed project aims to initialize a paradigm shift in today¡¦s large-scale mixed-signal design and is expected to yield 2~5x performance improvement for advanced electrical circuits in a broad range of applications, from consumer electronics to aerospace controllers. It would also enable the circuit design community to efficiently and accurately explore the performance trade-offs of nano circuits built upon new devices (e.g., carbon nanotube) and, hence, provides the valuable information to guide future nano electronics research. For this reason, the proposed project would have an immediate impact on today¡¦s semiconductor industry and play an important role to enable American¡¦s leading position. Furthermore, the proposed statistical regression addresses a unique mathematical problem, and it would have fundamental impacts on applied statistics and machine learning. Finally, given the broad coverage over multiple science and engineering fields such as statistical learning, nonlinear optimization, nano electronics, etc., the proposed project offers an excellent opportunity to train the young generation of American researchers. It would substantially improve the American competitiveness by generating high-quality scientists and engineers in multiple areas.

Project Report

This project aims to develop a new statistical regression (STAR) framework to efficiently model and optimize nanoscale integrated circuits. Towards this goal, several efficient modeling algorithms have been developed to solve a large number of (e.g., 104~106) model parameters with extremely low computational cost. These algorithms are based on the observations that not all model parameters play an important role for a given circuit of interest. In other words, although there are a large number of unknown model parameters, many of these parameters are close to zero, rendering a unique sparse structure. Hence, we propose to apply statistical algorithms to automatically select the important model parameters such that the modeling cost can be significantly reduced. When tested by several industrial design examples, the proposed algorithms achieve more than 100x runtime speedup compared to other traditional techniques. In addition, the circuit models developed by this project have been used to determine the worst-case operation conditions for integrated circuits and provide valuable insights to understand the impact of various non-ideal effects. In particular, a new convex optimization formulation was derived for the proposed worst-case analysis. Taking advantage of the new optimization formulation, the worst-case condition for a given circuit can be found both efficiently (i.e., with low computational cost) and robustly (i.e., with high accuracy). Finally, the proposed algorithms have been further extended to efficiently model and analyze large-scale on-chip power grid networks for integrated circuits. The proposed method is based on the observation that a power grid network is often updated with local changes during circuit design. In these cases, the response of the power grid network also changes locally. In other words, the incremental "change" of the power grid voltage is almost zero at many internal nodes, resulting in a unique sparse pattern. In this case, an efficient numerical solver can be developed to find the underlying sparse solution with low computational cost. In summary, the research work developed in this project offers a fundamental infrastructure that enables large-scale modeling and optimization for a broad range of circuit applications. Without these proposed techniques, the aforementioned large-scale modeling and optimization problems were not computationally feasible in the past. The technique developed by this project has been successfully transferred to two major companies in the area of computer-aided design. Both companies investigated the proposed algorithms for commercial usage. While working on this project, the PI and the students have established a close collaboration with the industrial engineers at these two companies. Such a collaboration effort has provided a unique opportunity for the students to gain important industrial experience. The research conducted in this project has been integrated into two new graduate-level classes: (1) 18869A: Statistical IC Design, and (2) 18660: Numerical Methods for Engineering Design and Optimization. These two classes are taught at the Electrical & Computer Engineering (ECE) department of Carnegie Mellon University, and they are open to both graduate students and senior undergraduate students. These education activities made it possible to integrate the concept of large-scale circuit modeling and optimization into the ECE curriculum. On the other hand, the project funded several graduate assistants who have been working towards their PhD degree. Given the multidisciplinary nature of this project that covers statistical learning, numerical analysis, integrated circuits, etc., it offered a great opportunity for these graduate students to enhance their technical skills. The PI has also recruited several undergraduate students to work on circuit design and algorithm implementation for this project. Such an interaction with undergraduate students allows them to understand the practical applications of statistical algorithms and, hence, motivates their interest in related areas. Finally, the PI attended the 37th annual convention of the National Society of Black Engineers (http://convention.nsbe.org) held in St. Louis, MO in 2011. Thousands of minority engineering students throughout the country joined the event. The engineering college at CMU has continuously participated in the career and graduate-school fairs at this convention for the past 15 years. Hundreds of minority students (including both undergraduate and graduate students) visited the CMU booth every year. The PI presented this NSF project to the minority students to inspire their interests in science and engineering. He also discussed possible research projects for graduate school and explained the benefit of obtaining an advanced degree in engineering to these students.

Agency
National Science Foundation (NSF)
Institute
Division of Computer and Communication Foundations (CCF)
Application #
0811023
Program Officer
Sankar Basu
Project Start
Project End
Budget Start
2008-08-01
Budget End
2011-07-31
Support Year
Fiscal Year
2008
Total Cost
$268,432
Indirect Cost
Name
Carnegie-Mellon University
Department
Type
DUNS #
City
Pittsburgh
State
PA
Country
United States
Zip Code
15213