Constrained Gaussian Process for Signal Integrity applications using Variational Inference

Surrogate modeling with Gaussian Process is effective for problems where data is expensive to query. By construction, a vanilla Gaussian Process model use Gaussian likelihood whose support is R. This means the resulted model could generate non-physical values in certain cases. For instance, a negative-valued eye height in high-speed channel simulation can be generated. In this paper, a beta likelihood is used to enforce the non-negative constraints of the underlying mapping. Due to the non-Gaussian likelihood, the regression model is no longer analytical, the posterior is intractable and is approximated using variational Bayesian inference. A channel simulation example is used to demonstrate that the approximate Gaussian Process approach successfully avoids generating negative eye heights when used in a Monte-Carlo simulation.