Bayesian ODE with Julia

Question

I have been trying to implement Bayesian ODE. In Oil industry, we use the following equation to fit production data then forecasting : $u(t)=u_0 (1+n\times K t)^{(-1/n)}$

The ODE equation is described as :

$\frac{du}{dt}=K\times u^{n+1}$

where 0<n<1, n and K are parameters defined by fitting the raw production data, in my case K is 0.17, n = 0.87.

My initial code :

using DiffEqFlux, OrdinaryDiffEq, Flux, Optim, Plots, AdvancedHMC
    
function Arps!(du,u,p,t)
    y = u
    K,n = p
    du  = (y * K * y^n)
end

tspan=(1.0,200.0)
tsteps = range(1, 200, length = 200)
u0 = [5505.99]
p=[0.17,0.87]
prob1 = ODEProblem(Arps!,u0,tspan)
sol_ode = solve(prob1,Vern7(),saveat = tsteps)

Not sure how to solve this issue :

MethodError: no method matching iterate(::DiffEqBase.NullParameters)

score 3 · Answer 1 · answered Jan 05 '21 at 15:43

3

You didn't pass any parameters into your ODE. prob1 = ODEProblem(Arps!,u0,tspan,p).

For the Bayesian part, look at the tutorial:

https://turing.ml/dev/tutorials/10-bayesiandiffeq/

answered Jan 05 '21 at 15:43

Chris Rackauckas

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Oh I forgot to include the p parameter, but once i did it : prob1 = ODEProblem(Arps!,u0,tspan,p) sol_ode = solve(prob1,Tsit5(),saveat = tsteps) I recieve this error : MethodError: no method matching ^(::Array{Float64,1}, ::Float64) – Minou92 Jan 05 '21 at 15:57
1

`y` is an array. `y = u[1]` and `du[1] = (y * K * y^n)`. – Chris Rackauckas Jan 05 '21 at 16:09

Bayesian ODE with Julia

1 Answers1