Least-Squares Estimation of Parameters in ODEs - Webinars - Maplesoft

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Least-Squares Estimation of Parameters in ODEs

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Date/Time: Tuesday, July 19, 2022 06:00 PM
Language: English
Duration: 1 hour

Least-Squares Estimation of Parameters in ODEs

If an initial-value problem or a boundary-value problem should contain parameters that can only be determined from observed data, can Maple solve the least-squares fitting problem that is implied?

This webinar provides an affirmative answer. It considers two IVPs and a BVP, each containing two parameters. One IVP and the BVP are solved exactly in terms of the parameters, so the parameters can be given specific values, and data points generated. The addition of random noise provides a set of "observations" from which estimates of the parameters are obtained by least squares. The other IVP contains a system of nonlinear first-order ODEs, and comes with a set of observations for one of the unknowns.

In principle, the least-squares fitting would start with a guess at the parameters, followed by a solution of that version of the problem. Data points would be generated and compared to the observations by a sum-of-squares-of deviations. This serves as a performance measure for the guess. Now subject the guessing process to a minimization algorithm in such a way that the tedium of this repetitive process is removed.

Perhaps the approach taken is naive, but that is all that was intended, namely, could the tools of Maple be marshaled to solve some such problems.

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