# Multivariate parameter optimization in "3-states differential equations" where two of the states have measured data and one state lacks data.

#1

I have three differential equations in the form of:
$$\frac{dx}{dt}=ax+y+z$$
$$\frac{dy}{dt}=x+by+z$$
$$\frac{dz}{dt}=x+y+cz$$

I have measured data:
$$x=[2+5randn(100)]$$
$$y=[0.5+2 randn(100)]$$
I do not have data for $$z$$

The initial parameters are $$a,b,c=3,4,5$$

How do I optimize this parameter only knowing the measured value of 2 states only? Thanks in advance.

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#2

If you use save_idxs = 1:2, then saveat will only save the values of [x,y] at each time point, and then the parameter estimation routines will compare against two dimensional data.

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