Improved LSQ Optimization Problems
An LSQ fit of a number of COMSOL Multiphysics parameters to real-world measurements can be formulated as a least-squares optimization problem. For these problems, the parameters to fit are the so-called control variables, and the objective is a least-squares sum of the deviations between values taken from the model and the measurement values. In more mathematical terms, these problems are called inverse problems, which function to determine the actual model from observations. COMSOL Multiphysics version 5.2 has special interfaces and solvers for such problems.
For LSQ optimization problems, the data files are read by the core code. In earlier versions of the software, it was only possible to read and use these files from the gradient-based solvers (e.g., SNOPT, Levenberg-Marquardt, and MMA). In COMSOL Multiphysics version 5.2, these files are parsed for their times and/or parameter values, which are stored in the solver nodes for inspection, but not modification. These values are also automatically added and used in the case of derivative-free optimization solvers. The new functionality automatically adds a Parametric Solver node for cases in which there are no user-added parameters to the study.