minimization fmincon with ode

Hello, I am using fmincon to fit my model to data.

I have a set of differential equations that give me the model results:

dy/dt=f(x,y,t)

where y are the points I want to compare to experimental points, x are my decision variables and t is time.

My objective function objfun is the sum of the squares of the residuals (y-data)^2

I profiled my code and I saw that it spends the most time solving the ode. I wanted to know if there is a way, numerically, to use my set of ODE dy/dt to determine the gradient dobjfun/dx so I can give it to fmincon beforehand instead of it using finite differences to determine it.

Thank you,

Answer 1

[Torsten]

To get dobjectfun/dx numerically, you had to solve even more ODEs:

https://de.mathworks.com/help/optim/ug/optimizing-a-simulation-or-ordinary-differential-equation.html

Section: Use a Gradient Evaluation Function.

I wouldn't advice you to do so.

Best wishes

Torsten.

[AM]

I see, thank you!

Does that mean that if all the other aspects of my code were optimized (which isn't the case yet), there is nothing else that can be done regarding this bottleneck to improve overall efficiency? I can't provide an anlytical expression of the gradient so I wanted to see if it could be done numerically.

[Torsten]

You can use derivative-free optimization methods, e.g. fminsearch.

For methods that need the Jacobian, nothing can be done.