A POD-Enhanced Multi-PCE DNN for High-Dimensional Uncertainty Quantification of High-Speed Circuits

Uncertainty quantification (UQ) of high-speed circuits by Monte Carlo (MC) simulations is highly time-consuming, whereas surrogate-model-based UQ is much more efficient. In this article, a surrogate modeling framework based on proper orthogonal decomposition (POD), polynomial chaos expansion (PCE), and deep neural network (DNN) is proposed for the UQ of high-speed circuits, which is called POD-enhanced multi-PCE DNN (POD-MPCE-DNN). In the POD-MPCE-DNN model, the DNN block extracts low-dimensional features from high-dimensional uncertain parameters. These low-dimensional features are then fed into the multi-PCE (MPCE) blocks to predict the POD coefficients. The predicted POD coefficients are used to calculate circuit responses by the inverse POD (IPOD) block. The whole framework well addresses the challenges of high-dimensional inputs and outputs in surrogate-based UQ for high-speed circuits. Furthermore, analytical formulas for calculating the mean and variance of circuit responses are derived from the POD-MPCE-DNN model. Numerical examples of the UQ for radio frequency (RF) low-noise amplifier (LNA) circuits and high-speed links are provided to validate the POD-MPCE-DNN model. Compared with conventional surrogate models, the POD-MPCE-DNN model achieves the highest accuracy. Moreover, it realizes much higher efficiency than circuit MC simulations in the UQ of high-speed circuits.