Running simulations over range of parameters

General Usage
1

Hi,
I am running a two differential equations over a range of parameters, and it works fine. I loop over two parameters (double loop). I would like to know the Julia way of doing this. Here is my code.

Run all α, β pairs

println(αs)
sols = Any
for α ∈ αs
for β ∈ βs
p1 = [α, β, 8., 5.] # α, β, D1, D2
println("α, β= ", α, β)
prob = ODEProblem(coupled!, u0, tspan, p1)
sol = solve(prob, Tsit5())
println("sol: ", size(sol))
append!(sols, [sol]) # <<< NOTICE
end
end
plot([sols[1]])

Notice the use of “append!”. “sol” is the output to “solve”, and I wish to concatenate the solutions into a Vector of four elements. To do this and properly access the variables, I had to enclose “sol” with brackets. If I do not do this, size(sols) returns 84 instead of 4. I do not quite understand why.

Next step, DiffEqFlux perhaps, which is my ultimate goal for now.

2

Please quote your code and provide an MWE.

1 Like
3

You can use the function map and map over the two ranges. This would automatically produce the output array for you.

map(as, bs) do a, b
   Body of for loop
end
1 Like
4

Thank you! Looks much nicer.

5

I will read the link. I did not think a MWE was necessary in this case since the code worked properly, and I was only asking for an alternative to the section I posted.
But I will do so next time.

6

By the way, inserting an element at the end of a vector is called push! . Append is for appending a vector to another.

7

The map solution does not work. If as=[1,2] and bs=[3,4], I expect to iterate over the combinations (1,3), (1,4), (2,3), (2,4). Your approach loops over (1,3) and (2,4).

8

Then you want Iterators.product(v1, v2) or perhaps CartesianIndices((v1, v2)) if both v1 and v2 are ranges.

9

Probably the OP has already considered this himself, and it also depends a bit on his particular purpose, but instead of creating simulations over a parameter grid, it may be more elegant and provide more insight to use a numerical continuation package.

(This is particularly true if you are interested in stability and destabilization of simple invariants such as stationary and periodic solutions.)

2 Likes
10

Right now, I am learning Julia, but I would be interested in a continuation package to study a system of reaction/diffusion equations. Could you point me to the latest stable resources? Thanks.

11

Although it overlaps with packages that I am familiar with (AUTO, MATCONT) or involved with (DDE-BIFTOOL), I think it is only fair to point you to PseudoArcLengthContinuation.jl for a project by @rveltz specifically in Julia. Hope, that helps, and enjoy the learning.

12

I indeed missed that map is elementwise by default. Note the additional requirement to destructure the argument tuple when using product

julia> map(Iterators.product(1:2, 3:4)) do (a,b)
                  (a,b)
       end
2×2 Array{Tuple{Int64,Int64},2}:
 (1, 3)  (1, 4)
 (2, 3)  (2, 4)

Notice the parenthesis in map(...) do (a,b)

13

You also have Bifurcations.jl for “small” systems