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PIRAMED Toolbox

Brief description

This Python PIRAMED toolbox provides an implementation of a novel Gaussian Process (GP) based framework for modeling complex-valued microwave S-parameters as a function of frequency and design variables. Unlike traditional macromodeling techniques such as vector fitting, this approach leverages a physics-informed kernel that captures the inherent Hermitian symmetry and holomorphic nature of S-parameters.

The framework is implemented using the GPyTorch library and supports multi-output Gaussian Processes (MOGP) to jointly model the real and imaginary parts of S-parameters, ensuring data efficiency and robust. It incorporates a composite kernel that combines the rational Szegő kernel with standard GP kernels, extended to handle multidimensional design spaces.

 

 

CVF

Key features

  • Physics-Informed Gaussian Process Modeling: captures the complex-valued nature and Hermitian symmetry of S-parameters.
  • Multi-Output Gaussian Processes (MOGP): jointly models the real and imaginary parts of frequency response data.
  • Parametric Macromodeling: incorporates design parameters directly into the model for design space exploration and optimization.
  • Frequency-scaling mechanism: accounts for compression and expansion effects along the frequency axis, significantly improving accuracy.
  • Composite Kernel Design: combines the rational Szegő kernel with Matérn kernels for multidimensional parameter spaces..

Download instructions

The code of the PIRAMED toolbox will be made available shortly.

Restrictions of use:

  • If the code is used in a scientific work, then reference should be made to the following two publications:
    1. Y. Lindemans, T. Ullrick, I. Couckuyt, D. Deschrijver, D. Vande Ginste, T. Dhaene, "Spectral Bayesian Optimization Using a Physics-Informed Rational Szegö Kernel for Microwave Design", IEEE Transactions on Components, Packaging and Manufacturing Technology, 2025.
    2. T. Ullrick, D. Deschrijver, W. Bogaerts, T. Dhaene, "Modeling Microwave S-parameters using Frequency-scaled Rational Gaussian Process Kernels", Proceedings of the IEEE 33rd Conference on Electrical Performance of Electronic Packaging and Systems (EPEPS), 4 pages, October 2024.