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Anonymous 12/07/22(Sun)00:02 No. 158

Hi /calc/.

I'm working on estimating parameters of a system of nonlinear differential equations using experimental data. The best algorithm I could come up with was to define a cost function as solving the system numerically the data points and taking the squares of the error, then using a built-in Matlab tool to minimize that as a function of the parameters and initial conditions.

I'm worried that it's going to be very slow to solve a bunch of systems of DEs over and over again. Is there a better algorithm, either for solving the system repeatedly when I know the structure, or for parameter estimation in general?

>>	Anonymous 12/07/26(Thu)03:01 No. 159 this might be a dumb question, but can't you just solve the DE's with the parameters as arbitrary constants?

>>	Anonymous 12/07/26(Thu)19:49 No. 160 >>159 I could, but they are arbitrary, large, and nonlinear, so it would be a lot of work, both to program it up and to compute it. Parsing the input strings is already kind of a headache, so if that's the best way to optimize it, I'll leave it for future work.

>>	Anonymous 12/07/26(Thu)22:36 No. 161 Actually, is there an algorithm for analytically solving any system of ODEs?

>>	Anonymous 12/08/11(Sat)11:55 No. 172 Have you checked if any Laplace transforms fit your setup? Make them all linear then, solve out the system in terms of the transform, then try to invert the transforms?

>>	Anonymous 12/08/12(Sun)23:48 No. 174 >>172 I actually have never used multidimensional Laplace transforms. Do they generalize pretty intuitively?

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