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August 6, 2009 7:18am UTC

how to estimate the parameters in PDE/ODE equations

In my research, I have been dealing with mass transport processes in porous media. I used several coupled PDE/ODE equations to depict the physical process. The values of some critical parameters, such as diffusivities, are unknown to me. What I typically did was first assuming the values of those parameters, then using Comsol Multiphysics to solve the Equations and getting the profile of a variable with respect to time, then compare this model predicted profile with the experimental data. If these two can match, I accept the original assumptions, otherwise, I have to re-assume the values of those parameters, and repeat the above process till the model prediction well match the experimental results. We can imagine the above procedure is very tedious, time-consuming and low-efficient.

I was wondering whether this is a way to design an algorithm for auto-data fitting with Matlab to quickly figure out the values of those unknown parameters? Or please show me some of such examples if you know.

Thank you very much!

Jacky

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