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Multiple equations/systems of equations with Eureqa
holistic
September 2014
Hi
@all
,
I was wondering if it is possible to estimate parameters of multiple equations/ systems of equations (e.g. differential equations)?
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FelixMPereira
November 2016
Hi holistic, I uses eureqa to estimate parameters of a system of differential equations as follows.
For example:
dx/dt=f0(t,x,y)
dy/dt=f1(t,x,y)
on Eureqa you can uses the following function (for absolute error search):
0=(D(x,t,1)-f0(t,x,y))^2+(D(y,t,1)-f1(t,x,y))^2
other example, for growth kinetics (Monod model), substrate consumption and product prodution (Luedeking and Piret model):
dX/dt=vmax*S/(Ks+S) --> Monod
dP/dt=a*dX/dt+b*X --> Luedeking and Piret
dS/dt=-(1/Yxs)*dX/dt-(1/Yps)dP/dt-mX -->substrate consumption
to estimate the parameters vmax (f0), Ks (f1), a (f2), b (f3), Yxs (f4), Yps (f5) and m (f6) on Eureqa:
0=(D(X,t,1)-f0()*S/(f1()+S))^2+(D(P,t,1)-f2()*D(X,t,1)-f3()*X)^2+(D(S,t,1)+D(X,t,1)/f4()+D(P,t,1)/f5()+f(6)*X)^2
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