Neural ordinary differential equation models for circuits

Xiong, Jie

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https://hdl.handle.net/2142/116242 Copy

Description

Title

Neural ordinary differential equation models for circuits

Author(s)

Xiong, Jie

Issue Date

2022-07-14

Director of Research (if dissertation) or Advisor (if thesis)

• Rosenbaum, Elyse
• Raginsky, Maxim

Doctoral Committee Chair(s)

Rosenbaum, Elyse

Committee Member(s)

• Schutt-Ainé, José E.
• Zhou, Jin

Department of Study

Electrical & Computer Eng

Discipline

Electrical & Computer Engr

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• Nonlinear circuit
• behavioral modeling
• neural ordinary differential equation
• stability
• circuit aging
• process variation.

Abstract

Behavioral models are widely used for circuit simulation; examples include I/O Buffer Information Specification (IBIS) models, gate timing models, and neural networks. They are often preferred by circuit designers over physics-based models because they obscure intellectual property and are time-efficient to be simulated. In prior works, the recurrent neural network (RNN), a class of neural networks which features state feedback connections, was used to model the dynamic behavior of several types of circuits. This work advances the prior work in three aspects. First, the usual approximation of a discrete-time RNN by a continuous-time Verilog-A model introduces numerical error, which may not be negligible, especially for stiff systems. In this work, neural ordinary differential equations (ODEs) are proposed for circuit modeling, which facilitates the direct learning of continuous-time models including continuous-time RNNs. Second, an aging-aware model framework is proposed to incorporate circuit aging effects. It captures the varying degradation under different aging profiles and is applicable to various types of neural ODEs. A similar two-part model structure is proposed for modeling of process variations. Third, the stability of certain neural ODEs is investigated. A practical input-to-state stability constraint is applied to the training of neural ODE models, with and without aging effects. Finally, the system-level stability is analyzed for neural ODEs connected to generic source(s) and load(s), which may or may not be neural ODEs. Small-gain conditions for different feedback connections are derived, which can be used to identify suitable use conditions for neural ODE models, or to constrain the model parameters.

Graduation Semester

2022-08

Type of Resource

Thesis

Copyright and License Information

Copyright 2022 Jie Xiong

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