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I would like to optimize a differential equation's parameters. I have a dataset, which contains the measured values, and I would like to get similar results with help of differential equations. When I read Python pyswarm module's documentation, I didn't find any examples about minimization based on experimental data. I got examples only when it was minimized with functions and lower and upper bounds. Is it possible to do ODE minimization with PSO based on measured values, or must I give measured values as a function for the minimization?

dev1
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Of course you can do that. Your candidate solution encodes the vector of your missing parameters. One challenge is to determine the search space, i.e., the boundaries of your parameters. The fitness function would be some distance measure between the points in your datasets and the solution of your ODE system, using the putative parameterization. For a concrete example see, e.g., https://ieeexplore.ieee.org/abstract/document/8477873.

Marco S. Nobile
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