I want to minimize the error function, which I defined as the sum of the square distances between data points and a given numerical solution. My error function then solely depends on the ODE parameters. Which iterative optimization method should I use in order to minimize the error function in the parametric space? My ODEs are nonlinear. I would like a solution based on an open source software such as Octave.
You can use fmincon or lsqnonlin optimization toolbox from matlab which is the same as Octave.
good luck
A simple method is as follows.
You need to generate data with the with your system of ODEs in an excel sheet. l and use something like excel's solver to fit that data to the parameters. Use excel's solver to vary the parameters
see
http://www.google.co.uk/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0ahUKEwiZk6Xk27bOAhXoBcAKHYZKClAQFggoMAA&url=http%3A%2F%2Fpeople.chem.ucsb.edu%2Flaverman%2Fleroy%2FChem116%2FPDF116CL%2FSolver.pdf&usg=AFQjCNFriOOHaXoM4DFgFN08qhg8WVLchA
https://www.google.co.uk/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&cad=rja&uact=8&ved=0ahUKEwiZk6Xk27bOAhXoBcAKHYZKClAQtwIILTAB&url=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3D3Fd4ukzkxps&usg=AFQjCNH4OLvkibMBGrm7rf0Mc7U-70ARlg
Or you can use r to do the task. r is free and downloadable here
https://cran.r-project.org/
here is an example of how to use r for parameter estimation
http://www.google.co.uk/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&cad=rja&uact=8&ved=0ahUKEwiF04XT4bbOAhWpC8AKHUnLC_wQFggkMAE&url=http%3A%2F%2Fsherrytowers.com%2F2013%2F01%2F29%2Fneiu-lecture-vi-fitting-the-parameters-of-an-sir-model-to-influenza-data%2F&usg=AFQjCNFEPY8ueMTMLQNqxQKrX8l_-H1WKA
Hi,
it depends on the dimension of the parameter space, the regularity of the problem ($f$ Lipschitz continuous or of class C^k ?), the kind of data you have (noisy or not ?). Generally you also need Tikhonov regularization in order to return a robust estimation.
After that, you can use standard optimization toolboxes in Octave or Scilab
Hi!
I agree with the first answer, that you have to try the MATLAB optimization functions.
Regards
Jan SIkora
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I would like to thank you for the answers: Mohammed, Loopinder, Florian and Jan.
I have tried using lsqnonlin from Octave and in fact it did the job. Now I want to improve it.
I couldn't find fmincon as a function of Octave, even in the optim package.
Unfortunately, the excel-based solutions cannot be used in my case since I do not have an analytical solution of the ODE system. Although the answer involving Monte Carlo in R Software seems to be helpful, for the moment, however, I am looking for non-heuristic methods.
Regarding regularity, the only one issue in my case is I have a parameter (whose value is known) that suddenly is set to zero at t=T, where T is also a given value. As an extension, would be interesting to have a method also when such a parameter is not known before t=T.
For the data, I would like to consider two cases where I have a 95% confidence interval for each point or just the value of one measure (both in a given time). What would be a good reference for reading about these things and also Tikhonov regularization?
Final questions:
A) Regarding convergence, which method would be less depend on the initial guess?
B) Which method, if any, can the useful to sistematically determine a good initial guess?
Thank you!
Dear Florian De Vuyst and dear colleagues,
Now things have progressed and I have just started to use R programming to perform ODE parameter estimations. Regarding the subject, I do recommend the FME package of R (https://cran.r-project.org/web/packages/FME/index.html).
My secondary "question" is then the following:
What reference do you recommed for a first reading on Tikhonov regularization in the context of ODE parameter estimation?
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