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A time-unrolling method to compute sensitivity of dynamic systems

Sensitivities of the dynamic system responses with respect to the system parameters are highly valuable, with broad applications such as system tuning and uncertainty quantification. Compared to the direct methods, adjoint methods are much more efficient when the number of parameters is large. In this paper, we present a time-unrolling method to compute adjoint sensitivities. Instead of explicitly constructing the adjoint system, which quite often is nontrivial, our time-unrolling method implicitly retrace the response trajectory by utilizing the fitting polynomial of the integration methods. This paper provides theoretical foundation of the method as well as experimental demonstrations of its effectiveness.