Finding deterministic solution from underdetermined equation: Large-scale performance modeling by least angle regression

The aggressive scaling of IC technology results in high dimensional, strongly nonlinear performance variability that cannot be efficiently captured by traditional modeling techniques. In this paper, we adapt a novel L₁ norm regularization method to address this modeling challenge. Our goal is to solve a large number of (e.g., 10⁴~10⁶) model coefficients from a small set of (e.g., 10²~10³) sampling points without over-fitting. This is facilitated by exploiting the underlying sparsity of model coefficients. Namely, although numerous basis functions are needed to span the high dimensional, strongly nonlinear variation space, only a few of them play an important role for a given performance of interest. An efficient algorithm of least angle regression (LAR) is applied to automatically select these important basis functions based on a limited number of simulation samples. Several circuit examples designed in a commercial 65 nm process demonstrate that LAR achieves up to 25times speedup compared with the traditional least squares fitting.