Optimisation of parameters in a PDE

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?

Answer 1

[Torsten]

https://de.mathworks.com/matlabcentral/answers/406938-fitting-the-numerical-solution-of-a-pde-with-one-parameter-to-some-data

Best wishes

Torsten.

[Matthew Hunt]

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]

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.