We consider the use of a numerical optimization technique to solve an inverse problem for Burger’s equation with a periodic forcing term. The solution depends on the initial data profile. The goal is to obtain an optimal continuous linear initial profile which generates the fixed target solution using a numerical optimization technique. Because Burger’s equation is time dependent, the cost function measures the difference between the target and the computed solution at a fixed final time. The optimization algorithm utilizes BFGS updates without computing Hessians and a line search is applied as a globalization. Burger’s equation is solved by a generalized Lax-Friedrichs scheme. This problem is motivated by flow matching problems in optimal design of nozzles and 1-dimensional ducts (see [1]).

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