In Order To Calculate The Sensitivity Matrix Of A PDE By Adjoint Method, The System Equations Need To Be Solved Many Times
Posted Oct 10, 2020, 11:02 PM EDT Version 5.5 2 Replies
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Recently, I established an optimized simulation model based on the Aquifer Characterization case (http://cn.comsol.com/model/aquifer-characterization-4410). The optimization method is Levenberg-Marquardt. The supposed measurement values and predictive values are fitted by the Optimization Module -> Least-Squares Objective. When the number of supposed measurement points increases, the optimization calculation becomes slower. We noticed "The adjoint method solves for the derivatives of a single scalar objective function, requiring only one single additional linear system solution." in the Optimization Module User’s Guide. Does this mean that for each additional supposed measurement point in the Optimization Module -> Least-Squares Objective, an additional solving the system equation will be required? Can the Adjoint Method in the Optimization Module calculate the sensitivity matrix by solving the system equation only once, in other words, how can I calculate the derivative of the supposed measurement value vector (supposed measurement values at multiple points) to the control variable vector (all control variables) by solving the system equation only once?
Thanks in advance for the help