Page 1. Model Order Reduction of Nonlinear Dynamical Systems by Chenjie Gu A dissertation submitt... more Page 1. Model Order Reduction of Nonlinear Dynamical Systems by Chenjie Gu A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Engineering – Electrical Engineering and Computer Science in the Graduate Division of the University of California, Berkeley Committee in charge: Professor Jaijeet Roychowdhury, Chair Professor Robert Brayton Professor Jon Wilkening Fall 2011 Page 2. Model Order Reduction of Nonlinear Dynamical Systems Copyright 2011 by Chenjie Gu Page 3.
Abstract We present a new manifold construction and parameterization algorithm for model reductio... more Abstract We present a new manifold construction and parameterization algorithm for model reduction approaches based on projection on manifolds.
Abstract Oscillations and rhythmic activity are seen in natural and man-made systems. Dynamics of... more Abstract Oscillations and rhythmic activity are seen in natural and man-made systems. Dynamics of oscillators can be compactly described by phase domain models. Phase equations for periodic, single-frequency oscillators have been developed and utilized in analyzing oscillation phenomena that arise in electronic systems, circadian clocks, and the nervous system.
In scientific computing, we often need to compute derivatives in various numerical methods. Autom... more In scientific computing, we often need to compute derivatives in various numerical methods. Automatic differentiation [1] is a method to automatically generate a program that computes derivatives, from the code that evaluates the function value. With that, people can focus on the core of their scientific problems, and avoid manually writing the code for derivative evaluations which is a tedious and time-consuming job.
Abstract We extend the concept of timing/phase macromodels, previously established rigorously onl... more Abstract We extend the concept of timing/phase macromodels, previously established rigorously only for oscillators, to apply to general systems, both non-oscillatory and oscillatory. We do so by first establishing a solid foundation for the timing/phase response of any nonlinear dynamical system, then deriving a timing/phase macromodel via nonlinear perturbation analysis. The macromodel that emerges is a scalar, nonlinear time-varying equation that accurately characterizes the system's phase/timing responses.
Abstract The design of a communications system is typically most effective only when each of its ... more Abstract The design of a communications system is typically most effective only when each of its components can be accurately represented by a discrete, symbolic behavioural abstraction. Such abstractions, in addition to providing valuable design intuition, also enable highly efficient and scalable system-level simulation. However, given a SPICE-level description for a subsystem such as a latch, it is a challenge to come up with a discrete, symbol-level abstraction that accurately captures its continuous-time dynamics.
Page 1. Model Order Reduction of Nonlinear Dynamical Systems by Chenjie Gu A dissertation submitt... more Page 1. Model Order Reduction of Nonlinear Dynamical Systems by Chenjie Gu A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Engineering – Electrical Engineering and Computer Science in the Graduate Division of the University of California, Berkeley Committee in charge: Professor Jaijeet Roychowdhury, Chair Professor Robert Brayton Professor Jon Wilkening Fall 2011 Page 2. Model Order Reduction of Nonlinear Dynamical Systems Copyright 2011 by Chenjie Gu Page 3.
Abstract We present a new manifold construction and parameterization algorithm for model reductio... more Abstract We present a new manifold construction and parameterization algorithm for model reduction approaches based on projection on manifolds.
Abstract Oscillations and rhythmic activity are seen in natural and man-made systems. Dynamics of... more Abstract Oscillations and rhythmic activity are seen in natural and man-made systems. Dynamics of oscillators can be compactly described by phase domain models. Phase equations for periodic, single-frequency oscillators have been developed and utilized in analyzing oscillation phenomena that arise in electronic systems, circadian clocks, and the nervous system.
In scientific computing, we often need to compute derivatives in various numerical methods. Autom... more In scientific computing, we often need to compute derivatives in various numerical methods. Automatic differentiation [1] is a method to automatically generate a program that computes derivatives, from the code that evaluates the function value. With that, people can focus on the core of their scientific problems, and avoid manually writing the code for derivative evaluations which is a tedious and time-consuming job.
Abstract We extend the concept of timing/phase macromodels, previously established rigorously onl... more Abstract We extend the concept of timing/phase macromodels, previously established rigorously only for oscillators, to apply to general systems, both non-oscillatory and oscillatory. We do so by first establishing a solid foundation for the timing/phase response of any nonlinear dynamical system, then deriving a timing/phase macromodel via nonlinear perturbation analysis. The macromodel that emerges is a scalar, nonlinear time-varying equation that accurately characterizes the system's phase/timing responses.
Abstract The design of a communications system is typically most effective only when each of its ... more Abstract The design of a communications system is typically most effective only when each of its components can be accurately represented by a discrete, symbolic behavioural abstraction. Such abstractions, in addition to providing valuable design intuition, also enable highly efficient and scalable system-level simulation. However, given a SPICE-level description for a subsystem such as a latch, it is a challenge to come up with a discrete, symbol-level abstraction that accurately captures its continuous-time dynamics.
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