Variation-aware behavioural modelling using support vector machines and affine arithmetic

Abstract

AGIAS Generalised Interval Arithmetic Simulator (AGIAS) is a specialised simulator which uses affine arithmetic to model parameter variations. It uses a specialised root-finding algorithm to simulate analogue circuits with parameter variations in one single simulation run. This is a significant speed-up compared to the multiple runs needed by industrialised solutions such as Monte-Carlo (MC) or Worst-Case Analysis (WCA). Currently, AGIAS can simulate analogue circuits only under very specific conditions. In many cases, circuits can only be simulated for certain operating points. If the circuits is to be evaluated in other operating points, the solver becomes numerically unstable and simulation fails. In these cases, interval widths approach infinity. Behavioural modelling of analogue circuits was introduced by researchers working around limitations of simulators. Most early approaches require expert knowledge and insight into the circuit which is modelled. In recent years, Machine Learning techniques for automatic generation of behavioural models have made their way into the field. This thesis combines Machine Learning techniques with affine arithmetic to include the effects of parameter variations into models. Support Vector Machines (SVMs) train two sets of parameters: one slope parameter and one offset parameter. These parameters are replaced by affine forms. Using these two parameters allows affine SVMs to model effects of parameter variations with varying widths. Training requires additional information about maximum and minimum values in addition to the nominal values in the data set. Based on these changes, affine ε Support Vector Machine (ε̂SVR) and ν Support Vector Machine (ν̂SVR) algorithms for regression are presented. To train the affine parameters directly and profit from the Sequential Minimal Optimisation algorithm (SMO)’s selectivity, the SMO is extended to handle the new, larger optimisation problems. The new affine SVMs are tested on analogue circuits that have been chosen based on whether they could be simulated with AGIAS and how strongly non-linear their characteristic function is.