Analog Macromodeling using Kernel Methods

ABSTRACT

In this paper we explore the potential of using a general class offunctional representation techniques, kernel-based regression, inthe nonlinear model reduction problem. The kernel-based view-pointprovides a convenient computational framework for regression,unifying and extending the previously proposed polynomialand piecewise-linear reduction methods. Furthermore, as many familiarmethods for linear system manipulation can be leveraged ina nonlinear context, kernels provide insight into how new, morepowerful, nonlinear modeling strategies can be constructed. Wepresent an SVD-like technique for automatic compression of non-linearmodels that allows systematic identification of model redundanciesand rigorous control of approximation error.

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INDEX TERMS

Primary Classification:
  F. Theory of Computation
  F.3 LOGICS AND MEANINGS OF PROGRAMS
      F.3.3 Studies of Program Constructs
          Subjects: Functional constructs

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.0 General
          Subjects: Error analysis
      G.1.3 Numerical Linear Algebra
          Subjects: Linear systems (direct and iterative methods)

General Terms:
Algorithms, Design, Performance