Bayesian Model Calibration for Deep-Learning-Based Indirect Test of Analog Circuits

Abstract

The indirect test offers a cost-effective alternative for the specification test of analog integrated circuits (ICs). It infers high-cost specifications from low-cost measurements through a mapping function. Deep learning provides an efficient means for modeling this mapping. However, batch-to-batch variations in IC manufacturing often lead to distribution shifts, which degrade the accuracy of such data-driven techniques. To address this, we propose a transfer learning-based framework—Bayesian model calibration (BMC)—for the indirect test. During testing, a deep neural network (DNN) is trained with early data for estimation. When a new-batch arrives, a small number of samples are conventionally tested to form a calibration set. The original estimator is updated with the new dataset via a Bayesian loss function. This loss function integrates a prior term (reflecting the early data) and a likelihood term (reflecting the new data), enabling a principled tradeoff between prior knowledge and new observations. The estimator thereby adapts its parameters to improve accuracy on the new batch. Moreover, by adjusting the relative weights of the prior and likelihood terms, the extent of model update can be controlled to match the degree of distribution shift, achieving optimal calibration. The proposed approach is evaluated on a simulated operational amplifier and two commercial IC datasets to demonstrate its advantage. The BMC can improve accuracy on new batches with minimal additional samples. Moreover, by flexibly integrating the prior knowledge and new data, it outperforms baseline methods such as direct data combination (DC) and simple fine-tuning (SFT).