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I'm not a user yet but CasADi seems very interesting for my purposes. I'm doing parameter estimation of ODEs through non-linear optimization via the least-squares approach, approximating the Jacobian with difference quotients (forward difference). My problem is that it's taking too long when there are many parameters (due to the numerical approximation of the Jacobian, I believe).
I've been searching for AD tools and this one seems very appropriate since it's already integrated with a good ODE solver. However, I'm not sure how it would be possible to get the sensitivity analysis of the output function with respect to the parameters (supposing the output is a nonlinear function of the states and inputs).
I think maybe I could use a quadrature function for this, defining it as g = (output_function(y, u, t) - experimental_output)², so its integration would be a continuous least-squares, and I could get the gradient d_g/d_pi to be exploited by the optimizer I'm using.
Does this make sense? Do any of you see a better other approach?
Thanks a lot,
State University of Campinas, Brazil.
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