@article{Hu2023, 
author = {Wenfei Hu and Sen Yin and Liang Wang and Chunxue Liu and Zhikai Wang and Zuochang Ye and Yan Wang},
title = {An Early-Stop Adjoint Transient Sensitivity Analysis Method for Objective Functions Associated with Many Time Points},
year = {2023},
journal = {Tsinghua Science and Technology},
volume = {28},
number = {3},
pages = {566-579},
keywords = {adjoint sensitivity, Fourier transformation, transient analysis, many time point sensitivity (MTPS), early-stop},
url = {https://www.sciopen.com/article/10.26599/TST.2022.9010024},
doi = {10.26599/TST.2022.9010024},
abstract = {Transient sensitivity analysis aims to obtain the gradients of objective functions (circuit performance) with respect to design or variation parameters in a simulator, which can be widely used in yield analysis and circuit optimization, among others. However, the traditional method has a computational complexity of  O⁢(N2) for objective functions containing circuit states at  N time points. The computational complexity is too expensive for large  N, especially in time-frequency transform. This paper proposes a many-time-point sensitivity method to reduce the computational complexity to  O⁢(N) in multiparameter many-time-point cases. The paper demonstrates a derivation process that improves efficiency by weighting the transfer chain and multiplexing the backpropagation process. We also proposed an early-stop method to improve efficiency further under the premise of ensuring accuracy. The algorithm enables sensitivity calculation of performances involving thousands of time points, such as signal-to-noise and distortion ratio and total harmonic distortion, with significant speed improvements.}
}