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closure.jl
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closure.jl
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"""
wrappedclosure(m, setup)
Wrap closure model and parameters so that it can be used in the solver.
"""
function wrappedclosure(m, setup)
(; dimension, Iu) = setup.grid
D = dimension()
# function neuralclosure(u)
# u = stack(ntuple(α -> u[α][Iu[α]], D))
# u = reshape(u, size(u)..., 1) # One sample
# mu = m(u, θ)
# mu = pad_circular(mu, 1)
# sz..., _ = size(mu)
# i = ntuple(Returns(:), D)
# mu = ntuple(α -> mu[i..., α, 1], D)
# end
neuralclosure(u, θ) =
if D == 2
u = cat(u[1][Iu[1]], u[2][Iu[2]]; dims = 3)
u = reshape(u, size(u)..., 1) # One sample
mu = m(u, θ)
mu = pad_circular(mu, 1)
mu = (mu[:, :, 1, 1], mu[:, :, 2, 1])
elseif D == 3
u = cat(u[1][Iu[1]], u[2][Iu[2]], u[3][Iu[3]]; dims = 4)
u = reshape(u, size(u)..., 1) # One sample
mu = m(u, θ)
mu = pad_circular(mu, 1)
mu = (mu[:, :, :, 1, 1], mu[:, :, :, 2, 1], mu[:, :, :, 3, 1])
end
end
"""
create_closure(layers...; rng)
Create neural closure model from layers.
"""
function create_closure(layers...; rng)
chain = Chain(layers...)
# Create parameter vector (empty state)
params, state = Lux.setup(rng, chain)
θ = ComponentArray(params)
# Compute closure term for given parameters
closure(u, θ) = first(chain(u, θ, state))
closure, θ
end
"""
create_tensorclosure(layers...; setup, rng)
Create tensor basis closure.
"""
function create_tensorclosure(layers...; setup, rng)
D = setup.grid.dimension()
cnn, θ = create_closure(layers...; rng)
function closure(u, θ)
B, V = tensorbasis(u, setup)
V = stack(V)
α = cnn(V, θ)
τ = sum(k -> α[ntuple(Returns(:), D)..., k] .* B[k], 1:length(B))
end
end
"""
collocate(u)
Interpolate velocity components to volume centers.
"""
function collocate(u)
sz..., D, _ = size(u)
# for α = 1:D
# v = selectdim(u, D + 1, α)
# v = (v + circshift(v, ntuple(β -> α == β ? -1 : 0, D + 1))) / 2
# end
if D == 2
a = selectdim(u, 3, 1)
b = selectdim(u, 3, 2)
a = (a .+ circshift(a, (-1, 0, 0))) ./ 2
b = (b .+ circshift(b, (0, -1, 0))) ./ 2
a = reshape(a, sz..., 1, :)
b = reshape(b, sz..., 1, :)
cat(a, b; dims = 3)
elseif D == 3
a = selectdim(u, 4, 1)
b = selectdim(u, 4, 2)
c = selectdim(u, 4, 3)
a = (a .+ circshift(a, (-1, 0, 0, 0))) ./ 2
b = (b .+ circshift(b, (0, -1, 0, 0))) ./ 2
c = (c .+ circshift(c, (0, 0, -1, 0))) ./ 2
a = reshape(a, sz..., 1, :)
b = reshape(b, sz..., 1, :)
c = reshape(c, sz..., 1, :)
cat(a, b, c; dims = 4)
end
end
"""
decollocate(u)
Interpolate closure force from volume centers to volume faces.
"""
function decollocate(u)
sz..., D, _ = size(u)
# for α = 1:D
# v = selectdim(u, D + 1, α)
# v = (v + circshift(v, ntuple(β -> α == β ? -1 : 0, D + 1))) / 2
# end
if D == 2
a = selectdim(u, 3, 1)
b = selectdim(u, 3, 2)
a = (a .+ circshift(a, (1, 0, 0))) ./ 2
b = (b .+ circshift(b, (0, 1, 0))) ./ 2
# a = circshift(a, (1, 0, 0)) .- a
# b = circshift(b, (0, 1, 0)) .- b
a = reshape(a, sz..., 1, :)
b = reshape(b, sz..., 1, :)
cat(a, b; dims = 3)
elseif D == 3
a = selectdim(u, 4, 1)
b = selectdim(u, 4, 2)
c = selectdim(u, 4, 3)
a = (a .+ circshift(a, (1, 0, 0, 0))) ./ 2
b = (b .+ circshift(b, (0, 1, 0, 0))) ./ 2
c = (c .+ circshift(c, (0, 0, 1, 0))) ./ 2
# a = circshift(a, (1, 0, 0, 0)) .- a
# b = circshift(b, (0, 1, 0, 0)) .- b
# c = circshift(c, (0, 0, 1, 0)) .- c
a = reshape(a, sz..., 1, :)
b = reshape(b, sz..., 1, :)
c = reshape(c, sz..., 1, :)
cat(a, b, c; dims = 4)
end
end