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Signal Prediction for Digital Circuits by Sigmoidal Approximations using Neural Networks

Josef Salzmann, Ulrich Schmid

TL;DR

The paper addresses the inefficiency of traditional dynamic timing analysis by introducing sigmoidal waveform representations and neural-network–based transfer functions (TOM) to predict gate outputs from input transitions. By encoding waveforms as sums of parameterized sigmoids and learning the output parameters with ANNs, the authors demonstrate a prototype for NOR/inverter circuits that runs substantially faster than analog SPICE while achieving higher accuracy than digital simulators. The TOM framework accounts for rising and falling transitions with time-invariant transfer functions and mitigates error propagation via a concave-hull validity check. Experimental results show improved accuracy over ModelSim and significant speedups over Spectre, indicating strong potential for scalable, slope-aware dynamic timing analysis and guiding future analytic development.

Abstract

Investigating the temporal behavior of digital circuits is a crucial step in system design, usually done via analog or digital simulation. Analog simulators like SPICE iteratively solve the differential equations characterizing the circuits components numerically. Although unrivaled in accuracy, this is only feasible for small designs, due to the high computational effort even for short signal traces. Digital simulators use digital abstractions for predicting the timing behavior of a circuit. Besides static timing analysis, which performs corner-case analysis of critical path delays only, dynamic timing analysis provides per-transition timing information in signal traces. In this paper, we advocate a novel approach, which generalizes digital traces to traces consisting of sigmoids, each parameterized by threshold crossing time and slope. What is needed to compute the output trace of a gate is a transfer function, which determines the parameters of the output sigmoids given the parameters of the input sigmoids. Harnessing the power of artificial neural networks (ANN), we implement such transfer functions via ANNs. Using inverters and NOR as the elementary gates in a prototype implementation of a specifically tailored simulator, we demonstrate that our approach operates substantially faster than an analog simulator, while offering better accuracy than a digital simulator.

Signal Prediction for Digital Circuits by Sigmoidal Approximations using Neural Networks

TL;DR

The paper addresses the inefficiency of traditional dynamic timing analysis by introducing sigmoidal waveform representations and neural-network–based transfer functions (TOM) to predict gate outputs from input transitions. By encoding waveforms as sums of parameterized sigmoids and learning the output parameters with ANNs, the authors demonstrate a prototype for NOR/inverter circuits that runs substantially faster than analog SPICE while achieving higher accuracy than digital simulators. The TOM framework accounts for rising and falling transitions with time-invariant transfer functions and mitigates error propagation via a concave-hull validity check. Experimental results show improved accuracy over ModelSim and significant speedups over Spectre, indicating strong potential for scalable, slope-aware dynamic timing analysis and guiding future analytic development.

Abstract

Investigating the temporal behavior of digital circuits is a crucial step in system design, usually done via analog or digital simulation. Analog simulators like SPICE iteratively solve the differential equations characterizing the circuits components numerically. Although unrivaled in accuracy, this is only feasible for small designs, due to the high computational effort even for short signal traces. Digital simulators use digital abstractions for predicting the timing behavior of a circuit. Besides static timing analysis, which performs corner-case analysis of critical path delays only, dynamic timing analysis provides per-transition timing information in signal traces. In this paper, we advocate a novel approach, which generalizes digital traces to traces consisting of sigmoids, each parameterized by threshold crossing time and slope. What is needed to compute the output trace of a gate is a transfer function, which determines the parameters of the output sigmoids given the parameters of the input sigmoids. Harnessing the power of artificial neural networks (ANN), we implement such transfer functions via ANNs. Using inverters and NOR as the elementary gates in a prototype implementation of a specifically tailored simulator, we demonstrate that our approach operates substantially faster than an analog simulator, while offering better accuracy than a digital simulator.

Paper Structure

This paper contains 16 sections, 3 equations, 5 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction and Overview
  2. Our contributions
  3. Related work
  4. Paper organization
  5. Sigmoidal Approximations
  6. Waveform fitting
  7. Fitting improvements
  8. Third Order Model Basics
  9. Implementing Transfer Functions via ANNs
  10. Training data generation
  11. Valid region containment
  12. Experiments
  13. Prototype simulator
  14. Experimental setup
  15. Experimental results
  16. ...and 1 more sections

Figures (5)

  • Figure 1: SPICE waveform and fitting of two input transitions and two output transitions of an inverter, along with the parameters expressed in terms of the TOM transfer function.
  • Figure 2: Illustration of the ANN architecture used for each of the 4 transfer functions required for implementing the TOM for an inverter.
  • Figure 3: Example NOR chain, stimulated by systematically varied input pulses, for generating training data.
  • Figure 4: Heaviside input pulses and pulse-shaped input of the first gate $G_1$.
  • Figure 5: Example ModelSim and sigmoid prediction compared to the respective SPICE simulation.