Sensitivity Analysis and Machine Learning and their Applications to Accelerate the Evaluation of Analog Performance in Semiconductor Circuits under Multiple Sources of Parametric Variations.

by Damien Remot

Thursday Jul 10, 2025, 10:00 AM → 1:00 PM Europe/Paris

Amphithéâtre Laurent Schwartz, bâtiment 1R3 (Institut de Mathématiques de Toulouse)

An integrated circuit is a collection of electronic circuits that combine various components, such as transistors, etched onto a semiconductor material chip, most commonly silicon. These circuits are found in a wide range of electronic devices — computers, smartphones, televisions — where they serve diverse functions, including information processing and storage. In sectors where safety is critical, such as the automotive industry, stringent performance control is essential. This necessitates a simulation process conducted upstream of production to ensure the circuits' reliability. Analog integrated circuits, which process continuous signals, are subject to numerous sources of variability that can impact their performance, thereby making simulations more complex and time-consuming.

This industrial Ph.D. project, conducted in collaboration with ANITI (Artificial and Natural Intelligence Toulouse Institute) and NXP Semiconductors, a company specialized in integrated circuit design, fits into this context. It aims to leverage machine learning techniques to accelerate simulations while maintaining a high level of confidence in the results. Thus, we explored an active sampling approach based on sequential selection of simulation points: each new point is chosen according to the information gained from previous simulations. To this end, we leveraged a Gaussian process model for the simulator outputs, which provides two key advantages: it enables the prediction of simulator outputs at unsimulated points and provides an associated measure of uncertainty with these predictions.

This approach is not well suited to high-dimensional spaces. In the field of integrated circuits, the number of parameters that can introduce variability into the final performance can easily reach several hundreds or even thousands. To overcome this challenge, global sensitivity analysis emerged as a valuable tool. By estimating sensitivity indices, we were able to identify the parameters with the most significant influence on performance. By combining this information with Gaussian processes, we optimized active sampling by focus simulation efforts where the influential parameters are most likely to induce significant variations. The use of global sensitivity analysis was greatly facilitated by recent advances in the estimation of sensitivity indices. In recent years, an estimator based on order statistics has emerged, offering several advantages, notably in terms of efficiency and flexibility in experimental design. Studying and adapting these estimators to our specific problem constituted a central part of this doctoral research.

In this context, we also investigated the possibility of establishing a functional convergence theorem, inspired by Donsker's theorem, for these estimators. Although our approach did not succeed in proving this result, it nonetheless led to progress for a simpler class of estimators, expressed as linear combinations of order statistics, also known as $L$-statistics.