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

**URL:** <https://discourse.julialang.org/t/multivariate-parameter-optimization-in-3-states-differential-equations-where-two-of-the-states-have-measured-data-and-one-state-lacks-data/23008>\
**Category:** General Usage\
**Tags:** diffeq, optim, optimization\
**Created:** [April 10, 2019, 5:03pm UTC](https://discourse.julialang.org/t/multivariate-parameter-optimization-in-3-states-differential-equations-where-two-of-the-states-have-measured-data-and-one-state-lacks-data/23008 "2019-04-10T17:03:25Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![pandeysudan27](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/pandeysudan27/32/8327_2.png) [@pandeysudan27](https://discourse.julialang.org/u/pandeysudan27)\
**Post date:** [April 10, 2019, 5:03pm UTC](https://discourse.julialang.org/t/multivariate-parameter-optimization-in-3-states-differential-equations-where-two-of-the-states-have-measured-data-and-one-state-lacks-data/23008/1 "2019-04-10T17:03:25Z")

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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:  
$$x=[2+5_randn(100)]$$  
$$y=[0.5+2_randn(100)]$$  
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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**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [April 11, 2019, 9:41am UTC](https://discourse.julialang.org/t/multivariate-parameter-optimization-in-3-states-differential-equations-where-two-of-the-states-have-measured-data-and-one-state-lacks-data/23008/2 "2019-04-11T09:41:25Z")

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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.