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Optimisation of parameters in a PDE

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Matthew Hunt
Matthew Hunt on 20 Sep 2018
Commented: Torsten on 24 Sep 2018
Hi,
Suppose I am dealing with the heat equation: ∂T/∂t=α∂^2T/∂x^2 and I have some data which I want to fit it to and determine the best value for α.
I can follow the general instructions for optimisation but how do I do it for a PDE such as this?

Answers (1)

Torsten
Torsten on 20 Sep 2018
https://de.mathworks.com/matlabcentral/answers/406938-fitting-the-numerical-solution-of-a-pde-with-one-parameter-to-some-data
Best wishes
Torsten.
  2 Comments
Matthew Hunt
Matthew Hunt on 20 Sep 2018
I'm not using pdepe to solve my equation. I have my own routine which takes in t,x, and alpha and spits out the profile. I understand what objective functions are in general. Do I have to put the data which I want to optimise against and the numerical solution in to the objective function?
Torsten
Torsten on 24 Sep 2018
Usually the sum of differences squared between experimental and simulated data is minimized with respect to a fitting parameter (in your case "alpha").
Best wishes
Torsten.

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