An Early-Stop Adjoint Transient Sensitivity Analysis Method for Objective Functions Associated with Many Time Points

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 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$O(N^{2})$</tex> for objective functions containing circuit states at <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N$</tex> time points. The computational complexity is too expensive for large <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N$</tex> , especially in time-frequency transform. This paper proposes a many-time-point sensitivity method to reduce the computational complexity to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$O(N)$</tex> 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.