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extend SpectralConv to n-dim #10
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23cb507
extend SpectralConv to n-dim
foldfelis 7b24c31
refactor
foldfelis 3549344
skip NavierStokes
foldfelis c2a9d22
darcy flow data
foldfelis 4a341b2
deal with n-dim m
foldfelis 8e6e4a5
fix wrong dim
foldfelis dc018ec
fix wrong dim on permutation and shrink test
foldfelis 58cf994
revise api
foldfelis c419e72
Apply suggestions from code review
foldfelis 483dfcb
Apply suggestions from code review
foldfelis 7225fe5
fix dims for shaped array
foldfelis 99d775d
update deps for doc
foldfelis 3e06c3a
update compat
foldfelis 01167c5
diversion
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
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@@ -2,6 +2,7 @@ module NeuralOperators | |
| using DataDeps | ||
| using Fetch | ||
| using MAT | ||
| using StatsBase | ||
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| using Flux | ||
| using FFTW | ||
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -1,53 +1,62 @@ | ||
| export | ||
| SpectralConv1d, | ||
| SpectralConv, | ||
| FourierOperator | ||
|
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| struct SpectralConv1d{T, S} | ||
| struct SpectralConv{N, T, S} | ||
| weight::T | ||
| in_channel::S | ||
| out_channel::S | ||
| modes::S | ||
| modes::NTuple{N, S} | ||
| ndim::S | ||
| σ | ||
| end | ||
|
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| c_glorot_uniform(dims...) = Flux.glorot_uniform(dims...) + Flux.glorot_uniform(dims...)*im | ||
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| function SpectralConv1d( | ||
| ch::Pair{<:Integer, <:Integer}, | ||
| modes::Integer, | ||
| function SpectralConv( | ||
| ch::Pair{S, S}, | ||
| modes::NTuple{N, S}, | ||
| σ=identity; | ||
| init=c_glorot_uniform, | ||
| T::DataType=ComplexF32 | ||
| ) | ||
| ) where {S<:Integer, N} | ||
| in_chs, out_chs = ch | ||
| scale = one(T) / (in_chs * out_chs) | ||
| weights = scale * init(out_chs, in_chs, modes) | ||
| weights = scale * init(out_chs, in_chs, prod(modes)) | ||
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| return SpectralConv1d(weights, in_chs, out_chs, modes, σ) | ||
| return SpectralConv(weights, in_chs, out_chs, modes, N, σ) | ||
| end | ||
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| Flux.@functor SpectralConv1d | ||
| Flux.@functor SpectralConv | ||
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| Base.ndims(::SpectralConv{N}) where {N} = N | ||
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| # [prod(m.modes), out_chs, batch] <- [prod(m.modes), in_chs, batch] * [out_chs, in_chs, prod(m.modes)] | ||
| spectral_conv(𝐱₁, 𝐱₂) = @tullio 𝐲[m, o, b] := 𝐱₁[m, i, b] * 𝐱₂[o, i, m] | ||
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| function (m::SpectralConv1d)(𝐱::AbstractArray) | ||
| 𝐱ᵀ = permutedims(Zygote.hook(real, 𝐱), (2, 1, 3)) # [x, in_chs, batch] <- [in_chs, x, batch] | ||
| 𝐱_fft = fft(𝐱ᵀ, 1) # [x, in_chs, batch] | ||
| function (m::SpectralConv)(𝐱::AbstractArray) | ||
| n_dims = ndims(𝐱) | ||
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| 𝐱ᵀ = permutedims(Zygote.hook(real, 𝐱), (ntuple(i->i+1, ndims(m))..., 1, ndims(m)+2)) # [x, in_chs, batch] <- [in_chs, x, batch] | ||
| 𝐱_fft = fft(𝐱ᵀ, 1:ndims(m)) # [x, in_chs, batch] | ||
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| 𝐱_flattened = reshape(view(𝐱_fft, map(d->1:d, m.modes)..., :, :), :, size(𝐱_fft, n_dims-1), size(𝐱_fft, n_dims)) | ||
| 𝐱_weighted = spectral_conv(𝐱_flattened, m.weight) # [prod(m.modes), out_chs, batch], only 3-dims | ||
| 𝐱_shaped = reshape(𝐱_weighted, m.modes..., size(𝐱_weighted, 2), size(𝐱_weighted, 3)) | ||
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| # [modes, out_chs, batch] <- [modes, in_chs, batch] * [out_chs, in_chs, modes] | ||
| 𝐱_weighted = spectral_conv(view(𝐱_fft, 1:m.modes, :, :), m.weight) | ||
| # [x, out_chs, batch] <- [modes, out_chs, batch] | ||
| 𝐱_padded = cat(𝐱_weighted, zeros(ComplexF32, size(𝐱_fft, 1)-m.modes, Base.tail(size(𝐱_weighted))...), dims=1) | ||
| pad = zeros(ComplexF32, ntuple(i->size(𝐱_fft, i)-m.modes[i], ndims(m))..., size(𝐱_shaped, n_dims-1), size(𝐱_shaped, n_dims)) | ||
| 𝐱_padded = cat(𝐱_shaped, pad, dims=1:ndims(m)) | ||
|
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||
| 𝐱_out = ifft(𝐱_padded, 1) # [x, out_chs, batch] | ||
| 𝐱_outᵀ = permutedims(real(𝐱_out), (2, 1, 3)) # [out_chs, x, batch] <- [x, out_chs, batch] | ||
| 𝐱_out = ifft(𝐱_padded, 1:ndims(m)) # [x, out_chs, batch] | ||
| 𝐱_outᵀ = permutedims(real(𝐱_out), (ndims(m)+1, 1:ndims(m)..., ndims(m)+2)) # [out_chs, x, batch] <- [x, out_chs, batch] | ||
|
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||
| return m.σ.(𝐱_outᵀ) | ||
| end | ||
|
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||
| function FourierOperator(ch::Pair{<:Integer, <:Integer}, modes::Integer, σ=identity) | ||
| function FourierOperator(ch::Pair{S, S}, modes::NTuple{N, S}, σ=identity) where {S<:Integer, N} | ||
| return Chain( | ||
| Parallel(+, Dense(ch.first, ch.second), SpectralConv1d(ch, modes)), | ||
| Parallel(+, Dense(ch.first, ch.second), SpectralConv(ch, modes)), | ||
| x -> σ.(x) | ||
| ) | ||
| end | ||
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -1,34 +1,69 @@ | ||
| @testset "SpectralConv1d" begin | ||
| modes = 16 | ||
| modes = (16, ) | ||
| ch = 64 => 64 | ||
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| m = Chain( | ||
| Dense(2, 64), | ||
| SpectralConv1d(ch, modes) | ||
| SpectralConv(ch, modes) | ||
| ) | ||
| @test ndims(SpectralConv(ch, modes)) == 1 | ||
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| 𝐱, _ = get_burgers_data(n=1000) | ||
| @test size(m(𝐱)) == (64, 1024, 1000) | ||
| 𝐱, _ = get_burgers_data(n=5) | ||
| @test size(m(𝐱)) == (64, 1024, 5) | ||
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| T = Float32 | ||
| loss(x, y) = Flux.mse(m(x), y) | ||
| data = [(T.(𝐱[:, :, 1:5]), rand(T, 64, 1024, 5))] | ||
| data = [(𝐱, rand(Float32, 64, 1024, 5))] | ||
| Flux.train!(loss, params(m), data, Flux.ADAM()) | ||
| end | ||
|
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| @testset "FourierOperator" begin | ||
| modes = 16 | ||
| @testset "FourierOperator1d" begin | ||
| modes = (16, ) | ||
| ch = 64 => 64 | ||
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| m = Chain( | ||
| Dense(2, 64), | ||
| FourierOperator(ch, modes) | ||
| ) | ||
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| 𝐱, _ = get_burgers_data(n=1000) | ||
| @test size(m(𝐱)) == (64, 1024, 1000) | ||
| 𝐱, _ = get_burgers_data(n=5) | ||
| @test size(m(𝐱)) == (64, 1024, 5) | ||
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| loss(x, y) = Flux.mse(m(x), y) | ||
| data = [(Float32.(𝐱[:, :, 1:5]), rand(Float32, 64, 1024, 5))] | ||
| data = [(𝐱, rand(Float32, 64, 1024, 5))] | ||
| Flux.train!(loss, params(m), data, Flux.ADAM()) | ||
| end | ||
|
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| @testset "SpectralConv2d" begin | ||
| modes = (16, 16) | ||
| ch = 64 => 64 | ||
|
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| m = Chain( | ||
| Dense(1, 64), | ||
| SpectralConv(ch, modes) | ||
| ) | ||
| @test ndims(SpectralConv(ch, modes)) == 2 | ||
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| 𝐱, _, _, _ = get_darcy_flow_data(n=5, Δsamples=20) | ||
| @test size(m(𝐱)) == (64, 22, 22, 5) | ||
|
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| loss(x, y) = Flux.mse(m(x), y) | ||
| data = [(𝐱, rand(Float32, 64, 22, 22, 5))] | ||
| Flux.train!(loss, params(m), data, Flux.ADAM()) | ||
| end | ||
|
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| @testset "FourierOperator2d" begin | ||
| modes = (16, 16) | ||
| ch = 64 => 64 | ||
|
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| m = Chain( | ||
| Dense(1, 64), | ||
| FourierOperator(ch, modes) | ||
| ) | ||
|
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| 𝐱, _, _, _ = get_darcy_flow_data(n=5, Δsamples=20) | ||
| @test size(m(𝐱)) == (64, 22, 22, 5) | ||
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| loss(x, y) = Flux.mse(m(x), y) | ||
| data = [(𝐱, rand(Float32, 64, 22, 22, 5))] | ||
| Flux.train!(loss, params(m), data, Flux.ADAM()) | ||
| end |
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