Bio

Research

Math Timeline

Sam Adams

Software

Theses

Publications

Talks

Computational Prototyping Group

MIT

Model Reduction Group

Bradley N. Bond

Keywords

modeling and simulation, nonlinear systems, model reduction, compact modeling, system stability, numerical simulation, system identification, nonlinear signal processing, interconnect modeling, analog circuit optimization, chemical kinetics

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Bio

I am currently living in Redwood City, California, where I work at a small biotech startup.

I received my Ph.D. in Electrical Engineering from MIT in February 2010, where I worked in the Computational Prototyping Group with professor Luca Daniel. I also received an SM in EE from MIT in Spring 2006, and my BS in Engineering Science and Mechanics from Penn State University in Spring 2004. Previously I have been a postdoc researcher at Sandia National Labs and at MIT, and a research intern at Cadence Research Labs, MIT Lincoln Labs, and Coventor.

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Research Interests

Broadly speaking, my reserach interests are in the modeling and simulation of dynamical systems. This includes efficient techniques for simulation of physics-based PDEs, methods for generating compact dynamical models from larger systems of equations or from input-output data, the qualitative analysis of nonlinear system properties such as stability, and efficient simulation techniques for nonlinear systems. Dynamical models describe the behavior of systems in all fields of engineering and science, and efficient modeling and simulation techniques may help facilitate, for instance, the design of analog circuits, or the analysis of biological systems.

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Math Timeline

In January 2010, when I was supposed to be writing my thesis, I decided to hang a 5 foot long piece of transparency film on my wall and draw a timeline of math history on it. Top to bottom increases chronologically, left to right corresponds to geographic location of their homes, and the colors roughly correspond to academic genealogy.

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Samuel Adams (the dog)

This is Samuel Adams, my faithful steed. He is named after the great American patriot, because they have similar personalities. I adopted him from a shelter when he was 9 months old.  Sammy was labeled as an "Australian Shepherd mix", and based on his giant brown triangular melon, I think he might be part copperhead. For more pictures, and Sammy's biography, go to the Sam page.

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Software

mmbasic: Basic Moment Matching Tools (Matlab, Octave)
A colleciton of matlab functions for model reduction of linear systems via moment matching. This is intended as a teaching tool to illustrate how moment matching works.

newton1d: Simple 1-D Newotn solver (Matlab, Octave)
A simple 1-dimensional Newton solver for Matlab. Plots each linearization as Newton progresses, a useful tool for teaching/learning about Newton's method and when it has trouble converging.

SMORES: Simulation and Model Order Reduction of Electrical Systems
A Matlab circuit simulator that reads spice-like netslists and performs several types of analysis.

STINS: Stable Identification of Nonlinear System via Semidefinite Programming
A Matlab tool for identifying compact stable dynamical models based on input-output data.

STPWL: Stabilized Trajectory PieceWise Linear model reduction
This is a collection of matlab stuff for generating trajectory piecewise linear reduced models for nonlinear systems. Contains functions for using the stabilzing projection method described one of the papers listed below ("Stable Reduced Models of Nonlinear...").

mems
A set of Matlab functions describing a dynamical system model of a MEMS switch.

Theses

Ph.D Thesis Stability-Preserving Model Reduction for Linear and Nonlinear Systems arising in Analog Circuit Applications

MS Thesis: Parameterized Model Order Reduction for Nonlinear Dynamical Systems

BS Thesis: Development of a Spin-Based Universal CNOT Gate for Quantum Computing

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Publications

A Stabilized Discrete Empirical Interpolation Method for Model Reduction of Electrical, Thermal, and Microelectromechanical Systems
Design Automation Conference (2011)
PDF

Automated Compact Dynamical Modeling: An Enabling Tool for Analog Designers
Design Automation Conference (2010): 415-420, Invited Paper
PDF

Compact Modeling of Nonlinear Analog Circuits using System Identification via Semi-Definite Programming and Incremental Stability Certification
IEEE Trans. on CAD of Integrated Circuits and Systems, 29(8): 1149-1162 (2010)
PDF

Passive Reduced Order Modeling of Multiport Interconnects via Semidefinite Programming
Design Automation and Test in Europe Conference (2010)
PDF

Stable Reduced Models of Nonlinear Descriptor Systems through Piecewise Linear Approximation and Projection
IEEE Trans. on CAD of Integrated Circuits and Systems 28(10): 1467-1480 (2009)
PDF

A Log-Frequency Approach to the Identification of the Wiener-Hammerstein Model
IEEE Signal Processing Letters 16(10): 889-892 (2009)
PDF

Guaranteed Stable Model Reduction for Indefinite and Unstable Linear Systems
IEEE/ACM International Conference on Computer Aided-Design 2008: 728-735
Recipient of the IEEE/ACM William J. McCalla ICCAD Best Paper Award
PDF

Stabilizing Schemes for Piecewise-linear Reduced Order Models via Projection and Weighting Functions
IEEE/ACM International Conference on Computer-Aided Design 2007: 860-866
Nominated for the IEEE/ACM William J. McCalla ICCAD Best Paper Award
PDF

A Piecewise-Linear Moment-Matching Approach to Parameterized Model-Order Reduction for Highly Nonlinear Systems
IEEE Trans. on CAD of Integrated Circuits and Systems 26(12): 2116-2129 (2007)
PDF

Parameterized Model Order Reduction of Nonlinear Dynamical Systems
IEEE/ACM International Conference on Computer-Aided Design 2005: 487-494
PDF

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Talks

Some slides available here, detailed list coming soon.

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