HFMV: hybridizing formal methods and machine learning for verification of analog and mixed-signal circuits

With increasing design complexity and robustness requirement, analog and mixed-signal (AMS) verification manifests itself as a key bottleneck. While formal methods and machine learning have been proposed for AMS verification, these two techniques suffer from their own limitations, with the former being specifically limited by scalability and the latter by the inherent uncertainty in learning-based models. We present a new direction in AMS verification by proposing a hybrid formal/machine-learning verification technique (HFMV) to combine the best of the two worlds. HFMV adds formalism on the top of a probabilistic learning model while providing a sense of coverage for extremely rare failure detection. HFMV intelligently and iteratively reduces uncertainty of the learning model by a proposed formally-guided active learning strategy and discovers potential rare failure regions in complex high-dimensional parameter spaces. It leads to reliable failure prediction in the case of a failing circuit, or a high-confidence pass decision in the case of a good circuit. We demonstrate that HFMV is able to employ a modest amount of data to identify hard-to-find rare failures which are completely missed by state-of-the-art sampling methods even with high volume sampling data.