New Example: Parameter Identification from Non-Contiguous Measurements

[Peter230655]

I made some changes to parameter identification simulation. I deleted the old PR as it contained unwanted files, which I did not know how to remove.

[Peter230655]

removed instance constraints. They were not used, but I forgot to remove the code.

[moorepants]

I took the liberty to edit the example with the main thing being changing it to have different initial conditions for each measurement. I also removed the bias, as the identification will fail for large bias unless you add such a term in the model.

[moorepants]

You can see my edits here: 0961906

[moorepants]

If you are fine with my edits, I will merge it.

[moorepants]

You can do a "git pull origin parameter_identification" on that branch to bring my changes to your computer and then you can run it to see the result.

[Peter230655]

If you are fine with my edits, I will merge it.

It looks MUCH nicer!! Of course I am fine with these changes!
NB:
I REALLY appreciate these changes! Like this I will learn to write better, and better looking code!
So, the more you change my code, the better for me!

For example, tow days ago. you critiziced my convoluted way of reducing frames in an animation.
So I learned a much better way of doing it - and learned how to use slicing, too!
How else, atr my age, would I leanr to write better code?

[Peter230655]

I took the liberty to edit the example with the main thing being changing it to have different initial conditions for each measurement. I also removed the bias, as the identification will fail for large bias unless you add such a term in the model.

I wondered, that it worked with the bias. I gues it did because my 'biases' were centered around 0.
Would it be worth to make a model with bias?

the main thing being changing it to have different initial conditions for each measurement.
This is the reason, you integrated the complete system four times?
I am not sure I totally understand: The four differential equations are independent from each other?
When you write x0 = 4 * random(len(states)), are you not giving different initial conditions for each measurement, even if you integrate the system once only?
(of course, the code looks VERY elegant!)

[Peter230655]

There is a small typo. which I overlooked 50 times:

It should be estimate of the spring constant, the space is missing.

[moorepants]

Would it be worth to make a model with bias?

You could explore that if it interests you. When I was playing with the example I noticed that the identification would fail often if the bias was large relative to the measurements. There are biases in real experiment data, but I think you would need to identify the bias, i.e. include it as a parameter in the model, for things to work consistently.

[moorepants]

You simulate the same motion four times and changed the noise applied to the measurements. I'm simulating four times and change both the initial conditions and the noise. It is more typical, in my experience, that real measurements have arbitrary initial states. Only if you have a very controlled experiment is that not the case and I do most experiments with humans who cannot start in the same state.

[Peter230655]

I will play around with it, I have lots of time!

NB:
I think I told you that I added a force = F1sin(omegat)
and tried to get opty to find this unkown input trajectory.
No matter how many measurements I gave, I gave up to 50 or so, it would always get the trajectory to be 'Bang - Bang'.
(of course it would easily find F1 and omega as parameters)

Do you think, this is impossible in principle?
Or would one 'just' need a huge amount of measurements?

[moorepants]

Do you think, this is impossible in principle?

I don't know, I'd have to see how you are constructing the problem.

[Peter230655]

I will send you the program I wrote.
How would you prefer it:

• by email?
• as a PR?
• another way?

Thanks!