EE6332: Modelling and Optimization in VLSI (Jan 2023)

• Janakiraman Viraraghavan (IITM)
• Dr. Rahul Rao (STSM IBM. India. Pvt. Ltd, Adjunct Faculty IITM)

ESB 129

Live session: K-slot - W (3:30 - 4:45 PM) and F(2:00 - 3:15 PM)

• Mid Term: 20%
• Project : 40%
• End Semester Exam: 40%

• Statistical Compact Model Extraction
• Gate Sizing via Geometric Programming
• Machine Learning in EDA

(What the students should be able to do after the course)

• Casting a problem in VLSI in a mathematical form.
• Formulating an optimization problem, proposing a suitable objective function and associated constraints.
• Solving the problem with commercial solvers.
• Interpreting the obtained solution and verifying correctness of the same.

• To set up the Linear Back Propagation of Variance problem.
• Employ importance sampling to estimate rare event failures in circuits
• To approximate the delay of a logic gate using the logical effort delay model.
• To set up and solve the path based timing problem.
• To set up the node based gate-sizing formulation as a Geometric Program.
• To solve the gate sizing problem using a commercial solver in Python.
• To obtain greedy approximations for the discrete gate sizes to the continuous solution.

• Review of Level-1 SPICE model - Definition of Idlin, Idsat, Vtlin and Vtsat
• Introduction to process variations

• Statistical Compact Model Extraction
• Forward and Back propagation of variance
• Modeling Ioff and Non-linear optimization

• Conventional Monte Carlo

• Importance Sampling

• Review of RC model of gate delay
• Logical effort model for delay
• Path delay optimization - Capacitance as variables

• Buffering Insertion
• Path delay optimization - Gate size as variables

• Power in Digital Circuits
• Introduction to Geometric Programming- Monomials and Posynomials

• Static Timing Analysis (STA)
• Minimum Area Gate Sizing Problem Formulation (Node Based)
• Gate sizing as a GP
• Circuit timing wall

• Alternate formulations including minimum area and power

• The continuous solution and convexity
• Discretizing the continuous solution
• Timing slack propagation
• Gate downsizing based on available slack

• Introdcution to Machine Learning- Linear Regression and Gradient Descent
• Overfitting, cross-validation
• Constrained K-Means Clustering

• Application of K-Means Clustering for Scan Chain Optimization
• Overview of reinforcement learning
• Ensemble techniques