Is a way to use differential equation as multiple variable function for regression?

New to Julia
,
1

I have a function: dx/dt = f(x, y) = (p1 + y) * x + p2 * sqrt(x)

where p1, p2 - parameter for optimization

Is a way to make solution like sol(t, y) for nonlinear model fitting? Can it be done with DifferentialEquations.jl?

2

Yes, it is possible to do parameter estimation using the DifferentialEquations.jl ecosystem. The docs describe how you can build an objective function from a DifferentialEquations.jl DEProblem that you can then pass to an optimization algorithm to do the fitting.

1 Like
3

Thank you! I noticed this method and it excelent works for parameters optimization when i have one dependent and one predictor (and any count of parameters) f(x, (p1, p2…pn)), but i have two predictors f(x,y, (p1, p2…pn)). Does it means that for each observation i have to build separate problem? And then optimize it?

4

Do a system of ODEs?

5

What is y? Do you have a differential equation for y, too? If yes, then you have a system of 2 differential equations.

Next, do you have observations? Do you have observations of x, or y, or both?

6

I have data like this (many observations):

time  y   x
1     0  0.2   
1     1  0.6
2     0  1.7
2     1  2.3
...

where dx/dt = (p1 + y) * x + p2 * sqrt(x)

and i have to find p1 and p2