Hello, I’m currently developing a package of a numerical solver to a certain kind of Stochastic PDE (Stochastic Neural Field Equations) in 1 and 2dimensional space in a DifferentialEquations.jl
fashion, i.e. with the user interface:
prob = probSNFE(inputs)
sol = solveSNFE(prob)
And I’m having a hard time to properly wrap my inputs in order to maintain a fairly simple user interface like the one I’ve mentioned.
Let me be more specific, the equation has the form:
where the functions I, K and S are given as inputs.
So, we can say that there are 3 types of inputs:

The equation’s parameters:
 α  Temporal decay
 v  Propagation velocity
 V0  Initial condition
 ϵ  Noise level
 ξ  Correlation parameter
 np  Number of trajectories

The functions:
 I, K and S

The domain’s parameters:
 L  Field’s length
 N  Number of nodes to discretise space
 T  Time span
 n  Number of nodes to discretise time
My first approach was to wrap the equation and domain’s parameters in 2 tuples and defining the 3 functions, in order to have the following:
using SNFE
prob = probSNFE(tupEqparam, tupDomain, I, K, S)
sol = solveSNFE(prob,saveat)
This approach is a bit messy when it comes to declare the parameters in the right order in the tuples. The probSNFE
signature is a bit too long and the most important, I’m not seeing any way to use multiple dispatch to distinguish 1D from 2D case.
To overcome some of these issues, I’ve decided to export 2 structures (for 1 and 2D) and use them as inputs to probSNFE
.
abstract type Problem end
abstract type OneDim <: Problem end
abstract type TwoDim <: Problem end
struct Input1D <: OneDim
α::Float64
v::Float64
# ...
I::Function
#...
end
struct Input2D <: TwoDim
#...
end
function probSNFE(in1d::Input1D)
# stuff
end
function probSNFE(in2d::Input2D)
# stuff
end
So, the user has to do something like this:
using SNFE #load the package
I(x,t)=...
K(x)=...
S(V)=...
in1d = Input1D(α,v,thresh,V0,L,N,T,n,I,K,S)
prob = probSNFE(in1d)
sol = solveSNFE(prob,saveat,[ϵ,ξ,np])
The only con I see here is the user has to know the order of the inputs to create the structure in1d
.
Am I approaching this in a good (“julian”) way? Is it bad to functions be fields of a structure? Any suggestions to improve?
Thank you,
Tiago