Neural ODE for dynamic systems with input signals
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Mathworks provided a nice example here for modeling dynamic systems through neural ODE.
Is it possible to consider input signals in training? That is, to define the differential equation to be:
where is the input signal.
However, dlode45 will not allow the ODE function to be with more than three inputs.
So is there any other possible approach to incorporate the input signal?
Thanks a lot!
Ben on 25 Jan 2022
You should be able to create a new ODE function that has only three inputs as required. Let me show a few cases.
Case 1 -
In this case you can define . Assuming you have f as a function handle you can define g in code with:
g = @(t,x,theta) f(t,x,theta,e(t))
Then solve using g in dlode45.
Case 2 -
This is a special case of case 1:
g = @(t,x,theta) f(t,x,theta) + e(t)
Call dlode45 with g.
Case 3 - for
In this case you have an extra hyperparameter i which you just have to select a specific value for. For example let and . You could write this in code as:
e = @(t,i) cos(i*t);
f = @(t,x,A,i) A*x + e(t,i);
x0 = dlarray(randn());
tspan = [0,1];
A = dlarray(randn());
i = 3;
x = dlode45(@(t,x,A) f(t,x,A,i), tspan, x0, A, DataFormat="CB");
Note that in this case you can loop over the values you want for i.
Hope that helps,
More Answers (1)
David Willingham on 24 Jan 2022
Thanks for the feedback on our neural ode example! For your request, can you elloborate on what type of signal e(t) might be and what use cases you're looking to apply neural ode's to?