Differential Learning of Interactions

[moradza]

Hi,

I was wondering if it is possible to combine NBodySimulator.jl with DiffEqFlux.jl to learn interaction parameters to reproduce a given RDF. loss is the distance euclidean distance between ground truth and current parameter RDFs to make it differentiable. I have done something similar for stochastic lotka_volterra.

Calculation of RDF is done through a function like this, where x's are radial distances of neighboring atoms.

rkMin = 0 # Ang
rkMax = 10 #Ang
nrk = 80
rk = LinRange(rkMin, rkMax, nrk)

function kernelHist(x, rk=rk)
dr = rk[2] - rk[1]
#x = reshape(x, (1, size(x)[2]size(x)[1]))
dx2 = .-(rk .- x).^2 ./ (2dr^2)
denUn = exp.(dx2 ./ (2dr^2))
denN = denUn ./ sum(denUn .+ 1e-16, dims=1)
totalDenUn = sum(denN, dims = 2)
totalDenUn ./= sum(totalDenUn . dr)
totalDenUn = reshape(totalDenUn, size(totalDenUn)[1])
#totalDenUn
totalDenUn
end