One-Dimensional Deep Image Prior for Curve Fitting of S-Parameters from
  Electromagnetic Solvers
Sriram Ravula Varun Gorti Bo Deng Swagato Chakraborty James Pingenot Bhyrav Mutnury Doug Wallace Doug Winterberg Adam Klivans Alexandros G. Dimakis
A key problem when modeling signal integrity for passive filters and
interconnects in IC packages is the need for multiple S-parameter measurements
within a desired frequency band to obtain adequate resolution. These samples
are often computationally expensive to obtain using electromagnetic (EM) field
solvers. Therefore, a common approach is to select a small subset of the
necessary samples and use an appropriate fitting mechanism to recreate a
densely-sampled broadband representation. We present the first deep generative
model-based approach to fit S-parameters from EM solvers using one-dimensional
Deep Image Prior (DIP). DIP is a technique that optimizes the weights of a
randomly-initialized convolutional neural network to fit a signal from noisy or
under-determined measurements. We design a custom architecture and propose a
novel regularization inspired by smoothing splines that penalizes discontinuous
jumps. We experimentally compare DIP to publicly available and proprietary
industrial implementations of Vector Fitting (VF), the industry-standard tool
for fitting S-parameters. Relative to publicly available implementations of VF,
our method shows superior performance on nearly all test examples using only
5-15% of the frequency samples. Our method is also competitive to proprietary
VF tools and often outperforms them for challenging input instances.