دانلود کتاب Novel Algorithms for Fast Statistical Analysis of Scaled Circuits

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Introduction
Background and Motivation
Major Contributions
SiLVR: Nonlinear Response Surface Modeling and Dimensionality Reduction
Fast Monte Carlo Simulation Using Quasi-Monte Carlo
Statistical Blockade: Estimating Rare Event Statistics, with Application to High Replication Circuits
Preliminaries
Organization
Contents
SiLVR: Projection Pursuit for Response Surface Modeling
Motivation
Prevailing Response Surface Models
Linear Model
Quadratic Model
PROjection Based Extraction (PROBE): A Reduced-Rank Quadratic Model
Latent Variables and Ridge Functions
Latent Variable Regression
Ridge Functions and Projection Pursuit Regression
Approximation Using Ridge Functions: Density and Degree of Approximation
Density: What Can Ridge Functions Approximate?
Degree of Approximation: How Good Are Ridge Functions?
Projection Pursuit Regression
Smoothing and the Bias-Variance Tradeoff
Convergence of Projection Pursuit Regression
SiLVR
The Model
Model Complexity
On the Convergence of SiLVR
Interpreting the SiLVR Model
Relative Global Sensitivity
Input-Referred Correlation
Training SiLVR
Initialization Using Spearman\'s Rank Correlation
The Levenberg-Marquardt Algorithm
Bayesian Regularization
Modified 5-Fold Cross-validation
Experimental Results
Master-Slave Flip-Flop with Scan Chain
Two-Stage RC-Compensated Opamp
Sub-1 V CMOS Bandgap Voltage Reference
Training Time
Future Work
Quasi-Monte Carlo for Fast Statistical Simulation of Circuits
Motivation
Standard Monte Carlo
The Problem: Bridging Computational Finance and Circuit Design
Pricing an Asian Option
Estimating Circuit Yield
The Canonical Problem
Monte Carlo for Numerical Integration: Some Convergence Results
Discrepancy: Uniformity and Integration Error
Variation in the Sense of Hardy and Krause
Low-Discrepancy Sequences
(t,m,s)-Nets and (t,s)-Sequences in Base b
Constructing Low-Discrepancy Sequences: The Digital Method
The Van der Corput Sequence: A Building Block
The Digital Method, Digital Nets and Digital Sequences
Comparing (t,s)-Sequences and Choosing One
The Sobol\' Sequence
Choosing Primitive Polynomials for Good Sobol\' Sequences
Choosing Initial Direction Numbers for Good Sobol\' Sequences
Gray Code Construction
Latin Hypercube Sampling
Construction
Variance (and Integration Error) Reduction
LHS Sample Is a Scrambled (t,m,s)-Net
Quasi-Monte Carlo in High Dimensions
Effective Dimension of the Integrand
Why Is Quasi-Monte Carlo (Sobol\' Points) Better Than Latin Hypercube Sampling?
Quasi-Monte Carlo for Circuits
The Proposed Flow
Estimating Integration Error
Estimating Monte Carlo Error
Estimating QMC Error with Scrambled Sequences
Scrambled Digital (t,m,s)-Nets and (t,s)-Sequences
Owen\'s Scrambling
Linear Matrix Scrambling: A Simpler Scheme
Scrambling Sobol\' Sequences with Linear Matrix Scrambling
Experimental Results
Comparing LHS and QMC (Sobol\' Points)
LHS (Almost) Exactly Removes One Dimensional Variance Contribution
Sobol\' Points Are Better Than LHS for Functions with Significant Higher Dimensional Components
Experiments on Circuit Benchmarks
Analysis of Results
Future Work
Statistical Blockade: Estimating Rare Event Statistics
Motivation
Modeling Rare Event Statistics
The Problem
Extreme Value Theory: Tail Distributions
Tail Regularity Conditions Required for F MDA(Hxi)
Estimating the Tail: Fitting the GPD to Data
Maximum Likelihood Estimation
Moment Matching
Probability-Weighted Moment Matching
Statistical Blockade
Classification
Support Vector Classifier
The Statistical Blockade Algorithm
Note on Choosing and Unbiasing the Classifier
Experimental Results
6T SRAM Cell
64-Bit SRAM Column
Master-Slave Flip-Flop with Scan Chain
Making Statistical Blockade Practical
Conditionals and Disjoint Tail Regions
The Problem
The Solution
Extremely Rare Events and Statistics
Extremely Rare Events
The Reason for Error in the MSFF Tail Model
The Problem
A Recursive Formulation of Statistical Blockade
Experimental Results
Future Work
Concluding Observations
Appendix A Derivations of Variance Values for Test Functions in Sect. 2.6.1
Variance of fc
One Dimensional Variance of fs
References
Index