Sensitivity Analysis for Active Sampling, with Applications to the Simulation of Analog Circuits

TL;DR

This work tackles the challenge of high-dimensional parametric variation in analog circuit simulations where Monte Carlo sampling is prohibitively expensive. It introduces an active sampling flow that jointly performs sensitivity-analysis–driven dimensionality reduction and Bayesian surrogate modeling (Gaussian Processes) to guide sample selection, iterating from an initial budget to a final budget. The methodology is complemented by a theoretically grounded feature-selection component based on Chatterjee’s CvM indices and a conjectured behavior for noisy-feature detection, with empirical validation on a synthetic Sobol' G-function and real HSOTA and FIRC circuit datasets. The results demonstrate that the proposed flow can substantially outperform MC-based exploration, offering a practical pathway to efficient design-space exploration in modern, high-dimensional analog circuits.

Abstract

We propose an active sampling flow, with the use-case of simulating the impact of combined variations on analog circuits. In such a context, given the large number of parameters, it is difficult to fit a surrogate model and to efficiently explore the space of design features. By combining a drastic dimension reduction using sensitivity analysis and Bayesian surrogate modeling, we obtain a flexible active sampling flow. On synthetic and real datasets, this flow outperforms the usual Monte-Carlo sampling which often forms the foundation of design space exploration.

Figures (6)

• Figure 1: Diagram of our active sampling flow.
• Figure 2: Given $N_{\mathrm{max}} = 10000$, $k=100$ and $P = 500$, we generate $N_{\mathrm{max}} \times P$ i.i.d. realisations of mutually independent random variables $\left(X^{(1)}, \dots, X^{(k)}, Y\right)$, so that we have $P$ batches of $N_{\mathrm{max}}$ samples. On each of these batches, we use the $N_{\mathrm{max}}$ samples to compute $\widehat{\xi}_{\mathrm{max}}(N,(1,\dots, k))$ for $N \le N_{\mathrm{max}}$. Thus, we obtain $P$ independent realisations of $\gamma(N, k)$ depending on $N<N_{\mathrm{max}}$, what we plot in blue.
• Figure 3: Given $N=10\ 000$, $k_{\mathrm{max}}$ and $P = 500$, we generate $N \times P$ i.i.d. realisations of mutually independent random variables $\left(X^{(1)}, \dots, X^{(k_{\mathrm{max}})}, Y\right)$, so that we have $P$ batches of $N$ samples. On each of these batches, we use the $N$ samples to compute $\widehat{\xi}_{\mathrm{max}}(N,(1,\dots, k))$ for $k \le k_{\mathrm{max}}$. Thus, we obtain $P$ independent realisations of $\gamma(N, k)$ depending on $k<k_{\mathrm{max}}$, what we plot in blue.
• Figure 4: We perform an (OLS) linear regression to estimate the slope $-\alpha_1$ in Equation \ref{['eq:log_xi_max_assumption']}. We obtain a confidence interval for $\alpha_1$ of $[0.498 \ , \ 0.501 ]$ with risk level at $95\%$.
• Figure 5: We perform an (OLS) linear regression to estimate the slope $\beta_1$ in Equation \ref{['eq:log_xi_max_assumption']}. We obtain a confidence interval of $[0.497 \ ; \ 0.504]$ with risk level at $95\%$.

Theorems & Definitions (2)

• Theorem 3.1: 2.2 from chatterjee2021new
• Conjecture 3.2