In this paper, approaches to the numerical recovering of the initial condition in the inverse problem for a nonlinear singularly perturbed reaction–diffusion–advection equation are considered. The feature of the formulation of the inverse problem is the use of additional information about the value of the solution of the equation at the known position of a reaction front, measured experimentally with a delay relative to the initial moment of time. In this case, for the numerical solution of the inverse problem, the gradient method of minimizing the cost functional is applied. In the case when only the position of the reaction front is known, the method of deep machine learning is applied. Numerical experiments demonstrated the possibility of solving such kinds of considered inverse problems.
This article presents a computational approach for comparing various broadband monitoring strategies, taking into account the positive and negative effects associated with the correlation of thickness errors caused by the monitoring procedure. The approach is based on statistical estimates of the strength of the error self-compensation effect and the expected level of thickness errors. Its application is demonstrated by using a 50-layer, nonpolarizing edge filter. The presented approach is general and can be applied to verify the prospects of broadband monitoring for the production of various types of optical coatings.
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