Periodic Adjoint Sensitivity Analysis

TL;DR

The paper tackles the high computational cost of sensitivity analysis for the steady-state response of time-periodic nonlinear circuits. It combines adjoint sensitivity analysis (ASA) with a periodic Parareal method (PP-PC) to solve periodic problems without full transient simulations, and derives a periodic ASA formulation by restricting the sensitivity integral to a single period and enforcing periodic boundary states. The approach yields a modified transient ASA suitable for periodic systems and demonstrates substantial speedups on a buck converter example, with good agreement to reference DSA for certain parameters. This work enables efficient, parallel-in-time sensitivity analysis of nonlinear periodic circuits, offering practical impact for design optimization when long transients precede steady-state oscillations.

Abstract

This paper proposes the utilization of a periodic Parareal with a periodic coarse problem to efficiently perform adjoint sensitivity analysis for the steady state of time-periodic nonlinear circuits. In order to implement this method, a modified formulation for adjoint sensitivity analysis based on the transient approach is derived.

Figures (3)

• Figure 1: Schematic of the DCDC buck-converter circuit. Example taken from sarpe:gyselinckDCDC.
• Figure 2: Output voltage $V_\mathrm{out}$ of the DCDC-Converter (Fig. \ref{['sarpe:fig_dcdcSchematic']}) plotted as a function of time.
• Figure 3: Sensitivity $\mathrm{d}V_\mathrm{out}/\mathrm{d}R$ (left) and sensitivity $\mathrm{d}V_\mathrm{out}/\mathrm{d}C$ (right) of the DCDC-converter plotted as a function of time. Calculated using Xyce DSA sarpe:XyceSensitivityAnalysis.