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Note that the estimate can be computed in a distributed manner using the adjoint network of [15].
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The partial derivatives required for the implementation of the training algorithm are calculated using the adjoint model approach, adapted to the fuzzy network's architecture exercised here.
The partial derivatives required by the learning algorithms are derived using the adjoint model approach, adapted to the architecture of the networks being used.
Using the adjoint framework, we develop and apply an adaptive strategy in a French drinking water network that provides the optimal placement from 1 sensor to 6 sensors.
The optimization problem is analyzed using the adjoint method to obtain the adjoint sensitivity.
The corresponding sensitivity number is derived using the adjoint method.
Sensitivities are evaluated by using the adjoint method.
Implementation of the discrete adjoint method is validated by comparing sensitivity derivatives obtained using the adjoint technique with results obtained using direct-differentiation and finite-difference methods.
The dependence of the objective function on the design variables is incorporated using the adjoint technique.
We also present a rigorous method of computing the Fréchet derivative using the adjoint operators.
Sensitivity analysis of the general displacement functional is derived using the adjoint method.
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