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TL;DR: 'self-benchmark' for optimization module is giving a wrong final answer, even though the benchmark was generated with the exact same model.

Hello, and thank you in advance!

I'm trying to use Comsol optimization to find a diffusion coefficient, so I made a simple self-benchmark case to make sure I'm using the software correctly. I defined a simple 2d geometry and used the coefficient form PDE solver to generate a 'baseline' where I diffuse a species for 1 day with an interdiffusion coefficient of 1e-13. I export this to excel, save it as a CSV, and then use it as an objective for a least squares function optimization over an area.

I'll review the settings below, but essentially optimization gives a diffusion coefficient of 1.7e-13, not 1e-13 (or if the baseline is changed, 2.7e-13 instead of 2e-13). It seems very consistent; I can't get the solution to change with different solvers, settings, meshes or geometries. Since the baseline was generated by the exact same model, I see no reason why it should not get within 0.1% or so of the real solution.

Assume defaults unless specified
-1 parameter, Dcoeff, 1e-13 baseline value. This is the only optimization variable.
-Tried starting values of 1e-12, 1e-14 and scales of 1e-13 and 1e-14. Upper limit 1e-8, lower 1e-17. All eventually converge on 1.7e-13
-Nedler-Mead and BOBYQA tried, both converge on 1.7e-13
-Remeshing changes things a little - all previous are on 'fine' quads, switching to 'fine' triangles gives 2.74e-13 instead of 2e-13.
-Turning up the optimality tolerance had no effect
-Objective function is only evaluated at t=86400 s (1 day)
-Geometry is 3 rectangles; two 200x200 um on top and a 400x200 one on bottom, to make a big square. Top left has starting concentration value of 0.5; others start at 0. Zero flux on outer boundaries.

Let me know if any other details or an upload of the model would explain further, thank you!!!