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Parameter estimation - Results which yield physically meaningful information

Posted Mar 10, 2026, 7:06 a.m. EDT Chemical, Chemical Reaction Engineering, Modeling Tools & Definitions, Optimization, Modeling Workflow Version 6.4 0 Replies

Thomas Ferriday

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Hi COMSOL community!

I have an issue I am sure several others have experienced, where I use COMSOL to model a physical system, though the numerical output does not necessarily make any sense.

Specifically, I use the PDE interface to define my equations and the parameter estimation option to model my experimental data. This is a diffusion problem, where I have time dependent diffusion data (loss/gain of concentration [mol/m^3] over time [s]) for several temperatures. I can model this data with Fick's second law, with the diffusion coefficient as the fitting variable, though it will naturally change with temperature.

My goal is to model these data sets simultaneously, with a global objective function describing the Arrhenius relationship between the diffusion coefficient and the temperature. This way, all the individual diffusion coefficients will change such that they change linearly based on the temperature change. My current model only allows to do one temperature at a time, after which I must change settings to another temperature, and so on. This can yield odd diffusion coefficients, which do not necessarily follow the expected Arrhenius behaviour, hence my wish to circumvent the issue.

A main issue is that I cannot seem to "access" the final value of the diffusion coefficient (from the parameter estimation). I cannot say e.g.: D_trend = [sol1.conpar10 sol2.conpar10 sol3.conpar10]; %where conpar10 is a name for the diffusion coefficient

and that this vector should change linearly with temperature.

This issue is also applicable to other issues, such as heat conduction, structural or fluid mechanics, or any problem where several fitting results should follow a trend with respect to either a temperature, pressure, or any other parameter.

Thank you for any and all input.

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