Beyond Low-Order Statistical Response Surfaces: Latent Variable Regression for Efficient, Highly Nonlinear Fitting

The number and magnitude of process variation sources are increasing as we scale further into the nano regime. Today's most successful response surface methods limit us to low-order forms - linear, quadratic -- to make the fitting tractable. Unfortunately, not all variational scenarios are well modeled with low-order surfaces. We show how to exploit latent variable regression ideas to support efficient extraction of arbitrarily nonlinear statistical response surfaces. An implementation of these ideas called SiLVR, applied to a range of analog and digital circuits, in technologies from 90 to 45 nm, shows significant improvements in prediction, with errors reduced by up to 2IX, with very reasonable runtime costs.