Neural ordinary differential equation models for circuits

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Electrical & Computer Engr

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2022

Author dc:creator

• Xiong, Jie

Contributors dc:contributor

• Rosenbaum, Elyse
• Raginsky, Maxim
• Schutt-Ainé, José E.
• Zhou, Jin

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

Statement dc:rights

• Copyright 2022 Jie Xiong

Language dc:language

en, eng

Handle dc:identifier

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

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F116242