Parameter estimation - Results which yield physically meaningful information

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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.


2 Replies Last Post 2026年3月12日 GMT+8 19:09
Kristian Ejlebjærg Jensen COMSOL Employee

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Posted: 5 hours ago 2026年3月12日 GMT+8 16:14

Hi Thomas

It sounds like piecewise linear polynomials for the diffusion coefficient could suit your need. Have you thought about using a Control Function to discretize the diffusion coefficient?

Best regards,

Kristian E. Jensen

Technical Product Manager, Optimization

Hi Thomas It sounds like piecewise linear polynomials for the diffusion coefficient could suit your need. Have you thought about using a Control Function to discretize the diffusion coefficient? Best regards, Kristian E. Jensen Technical Product Manager, Optimization

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Posted: 2 hours ago 2026年3月12日 GMT+8 19:09

Hi Kristian!

Thank you for your reply. I actually came up with a somewhat simpler solution, where I formulated the diffusion coefficient as an activation energy, and solved multiple parameter estimations simultaneously w.r.t. the activation energy. The temperature was updated through the experimental conditions defined in each least squares objective under the parameter estimation.

One short-coming here is that the solution is an exact straight line (ref. an Arrhenius plot), thus the individual fits are lacking. I will solve this by adding some uncertainty function to account for the individual variances.

Best regards Thomas Ferriday

Hi Kristian! Thank you for your reply. I actually came up with a somewhat simpler solution, where I formulated the diffusion coefficient as an activation energy, and solved multiple parameter estimations simultaneously w.r.t. the activation energy. The temperature was updated through the experimental conditions defined in each least squares objective under the parameter estimation. One short-coming here is that the solution is an exact straight line (ref. an Arrhenius plot), thus the individual fits are lacking. I will solve this by adding some uncertainty function to account for the individual variances. Best regards Thomas Ferriday

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