Forward Sensitivity Analysis of the FitzHugh–Nagumo System: Parameter Estimation

Ahmed, Shady E.; San, Omer; Lakshmivarahan, S.

doi:10.1007/978-3-030-81170-9_9

Cited by 1 publication

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“…This is the first of the two advantages referred to in the title of this paper. The papers by Lewis et al [26,27] and Ahmed et al [28,29] contain several applications of this strategy.…”

Section: Introductionmentioning

confidence: 99%

On the dual advantage of placing observations through forward sensitivity analysis

et al. 2023

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The four-dimensional variational data assimilation methodology for assimilating noisy observations into a deterministic model has been the workhorse in forecasting centres for over three decades. While this method provides a computationally efficient framework for dynamic data assimilation, it is largely silent on the important question concerning the minimum number and placement of observations. To answer this question, we demonstrate the dual advantage of placing the observations where the square of the sensitivity of the model solution with respect to the unknown control variables, called forward sensitivities, attains its maximum. By following this approach, we can force the observability Gramian to be of full rank, which in turn guarantees efficient recovery of the optimal values of the control variables, which is the first of the two advantages of this strategy. We further show that the proposed strategy of placing observations has another inherent optimality: the square of the sensitivity of the optimal estimates of the control with respect to the observations (used to obtain these estimates) attains its minimum value, a second advantage that is a direct consequence of the above strategy for placing observations. Our analytical framework and numerical experiments on linear and nonlinear systems confirm the effectiveness of our proposed strategy.

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“…This is the first of the two advantages referred to in the title of this paper. The papers by Lewis et al [26,27] and Ahmed et al [28,29] contain several applications of this strategy.…”

Section: Introductionmentioning

confidence: 99%