Calculation of Generalized Polynomial-Chaos Basis Functions and Gauss Quadrature Rules in Hierarchical Uncertainty Quantification

Stochastic spectral methods are efficient techniques for uncertainty quantification. Recently they have shown excellent performance in the statistical analysis of integrated circuits. In stochastic spectral methods, one needs to determine a set of orthonormal polynomials and a proper numerical quadrature rule. The former are used as the basis functions in a generalized polynomial chaos expansion. The latter is used to compute the integrals involved in stochastic spectral methods. Obtaining such information requires knowing the density function of the random input {\it a-priori}. However, individual system components are often described by surrogate models rather than density functions. In order to apply stochastic spectral methods in hierarchical uncertainty quantification, we first propose to construct physically consistent closed-form density functions by two monotone interpolation schemes. Then, by exploiting the special forms of the obtained density functions, we determine the generalized polynomial-chaos basis functions and the Gauss quadrature rules that are required by a stochastic spectral simulator. The effectiveness of our proposed algorithm is verified by both synthetic and practical circuit examples.Comment: Published by IEEE Trans CAD in May 201

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

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.Comment: 14 figures. Accepted by IEEE Trans. CAD of Integrated Circuits and System

Limits on Fundamental Limits to Computation

An indispensable part of our lives, computing has also become essential to industries and governments. Steady improvements in computer hardware have been supported by periodic doubling of transistor densities in integrated circuits over the last fifty years. Such Moore scaling now requires increasingly heroic efforts, stimulating research in alternative hardware and stirring controversy. To help evaluate emerging technologies and enrich our understanding of integrated-circuit scaling, we review fundamental limits to computation: in manufacturing, energy, physical space, design and verification effort, and algorithms. To outline what is achievable in principle and in practice, we recall how some limits were circumvented, compare loose and tight limits. We also point out that engineering difficulties encountered by emerging technologies may indicate yet-unknown limits.Comment: 15 pages, 4 figures, 1 tabl

Enhancing Power Efficient Design Techniques in Deep Submicron Era

Excessive power dissipation has been one of the major bottlenecks for design and manufacture in the past couple of decades. Power efficient design has become more and more challenging when technology scales down to the deep submicron era that features the dominance of leakage, the manufacture variation, the on-chip temperature variation and higher reliability requirements, among others. Most of the computer aided design (CAD) tools and algorithms currently used in industry were developed in the pre deep submicron era and did not consider the new features explicitly and adequately. Recent research advances in deep submicron design, such as the mechanisms of leakage, the source and characterization of manufacture variation, the cause and models of on-chip temperature variation, provide us the opportunity to incorporate these important issues in power efficient design. We explore this opportunity in this dissertation by demonstrating that significant power reduction can be achieved with only minor modification to the existing CAD tools and algorithms. First, we consider peak current, which has become critical for circuit's reliability in deep submicron design. Traditional low power design techniques focus on the reduction of average power. We propose to reduce peak current while keeping the overhead on average power as small as possible. Second, dual Vt technique and gate sizing have been used simultaneously for leakage savings. However, this approach becomes less effective in deep submicron design. We propose to use the newly developed process-induced mechanical stress to enhance its performance. Finally, in deep submicron design, the impact of on-chip temperature variation on leakage and performance becomes more and more significant. We propose a temperature-aware dual Vt approach to alleviate hot spots and achieve further leakage reduction. We also consider this leakage-temperature dependency in the dynamic voltage scaling approach and discover that a commonly accepted result is incorrect for the current technology. We conduct extensive experiments with popular design benchmarks, using the latest industry CAD tools and design libraries. The results show that our proposed enhancements are promising in power saving and are practical to solve the low power design challenges in deep submicron era

An investigation into adaptive power reduction techniques for neural hardware

In light of the growing applicability of Artificial Neural Network (ANN) in the signal processing field [1] and the present thrust of the semiconductor industry towards lowpower SOCs for mobile devices [2], the power consumption of ANN hardware has become a very important implementation issue. Adaptability is a powerful and useful feature of neural networks. All current approaches for low-power ANN hardware techniques are ‘non-adaptive’ with respect to the power consumption of the network (i.e. power-reduction is not an objective of the adaptation/learning process). In the research work presented in this thesis, investigations on possible adaptive power reduction techniques have been carried out, which attempt to exploit the adaptability of neural networks in order to reduce the power consumption. Three separate approaches for such adaptive power reduction are proposed: adaptation of size, adaptation of network weights and adaptation of calculation precision. Initial case studies exhibit promising results with significantpower reduction

Strategic Optimization Techniques For FRTU Deployment and Chip Physical Design

Combinatorial optimization is a complex engineering subject. Although formulation often depends on the nature of problems that differs from their setup, design, constraints, and implications, establishing a unifying framework is essential. This dissertation investigates the unique features of three important optimization problems that can span from small-scale design automation to large-scale power system planning: (1) Feeder remote terminal unit (FRTU) planning strategy by considering the cybersecurity of secondary distribution network in electrical distribution grid, (2) physical-level synthesis for microfluidic lab-on-a-chip, and (3) discrete gate sizing in very-large-scale integration (VLSI) circuit. First, an optimization technique by cross entropy is proposed to handle FRTU deployment in primary network considering cybersecurity of secondary distribution network. While it is constrained by monetary budget on the number of deployed FRTUs, the proposed algorithm identi?es pivotal locations of a distribution feeder to install the FRTUs in different time horizons. Then, multi-scale optimization techniques are proposed for digital micro?uidic lab-on-a-chip physical level synthesis. The proposed techniques handle the variation-aware lab-on-a-chip placement and routing co-design while satisfying all constraints, and considering contamination and defect. Last, the first fully polynomial time approximation scheme (FPTAS) is proposed for the delay driven discrete gate sizing problem, which explores the theoretical view since the existing works are heuristics with no performance guarantee. The intellectual contribution of the proposed methods establishes a novel paradigm bridging the gaps between professional communities