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Fix spectralConvolution3dLayer to include low negative frequencies. #22

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Fix spectralConvolution3dLayer to include low negative frequencies. #22

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130 changes: 90 additions & 40 deletions battery-module-cooling-analysis-with-fourier-neural-operator/spectralConvolution3dLayer.m
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Original file line number Diff line number Diff line change
Expand Up @@ -35,56 +35,106 @@
inChannels = ndl.Size( finddim(ndl,'C') );
outChannels = this.Cout;
numModes = this.NumModes;
M = 2*numModes - 1;

if isempty(this.Weights)
this.Cin = inChannels;
this.Weights = 1./(inChannels*outChannels).*( ...
rand([outChannels inChannels numModes numModes numModes]) + ...
1i.*rand([outChannels inChannels numModes numModes numModes]) );
rand([outChannels inChannels M M numModes]) + ...
1i.*rand([outChannels inChannels M M numModes]) );
end
end

function y = predict(this, x)

% Compute the 3d fft and retain only the low frequency modes as
% specified by NumModes.
x = real(x);
x = stripdims(x);
N = size(x, 1);
[N1,N2,N3] = size(x,[1,2,3]);
Nm = this.NumModes;
xft = fft(x, [], 1);
xft = xft(1:Nm,:,:,:,:);
xft = fft(xft, [], 2);
xft = xft(:,1:Nm,:,:,:);
xft = fft(xft, [], 3);
xft = xft(:,:,1:Nm,:,:);

% Multiply selected Fourier modes with the learnable weights.
xft = permute(xft, [4 5 1 2 3]);
yft = pagemtimes( this.Weights, xft );
yft = permute(yft, [3, 4, 5, 1, 2]);

% Make the frequency representation conjugate-symmetric such
% that the inverse Fourier transform is real-valued.
S = floor(N/2)+1 - this.NumModes;
idx = ceil(N/2):-1:2;
yft = cat(1, yft, zeros([S size(yft, 2:5)], 'like', yft));
yft = cat(1, yft, conj(yft(idx,:,:,:,:)));

yft = cat(2, yft, zeros([size(yft,1), S, size(yft,3:5)], like=yft));
yft = cat(2, yft, conj(yft(:,idx,:,:,:)));

yft = cat(3, yft, zeros([size(yft,[1,2]), S, size(yft,4:5)], like=yft));
yft = cat(3, yft, conj(yft(:,:,idx,:,:)));

% Return to physical space via 3d ifft
y = ifft(yft, [], 3, 'symmetric');
y = ifft(y,[],2, 'symmetric');
y = ifft(y,[],1, 'symmetric');

% Re-apply labels

x = fft(x,[],1);
x = fft(x,[],2);
x = fft(x,[],3);

% Retain the low frequency modes: DC, positive, and negative
% frequencies in dims 1 & 2; only non-negative in dim 3.
xFreq = union(1:Nm, N1-Nm+2:N1);
yFreq = union(1:Nm, N2-Nm+2:N2);
zFreq = 1:Nm;
x = x(xFreq, yFreq, zFreq, :, :);

% Multiply retained modes by learned weights.
x = permute(x, [4 5 1 2 3]);
W = this.Weights;
W = W(:,:,1:min(size(x,3),size(W,3)),1:min(size(x,4),size(W,4)),:);
x = pagemtimes(W, x);
x = permute(x, [3 4 5 1 2]);

% Place into full-size frequency grid.
y = zeros([N1, N2, N3, size(x,4), size(x,5)], 'like', x);
y(xFreq, yFreq, zFreq, :, :) = x;

% Enforce conjugate symmetry so that the ifft is real-valued.
[xPos,xNeg] = iPositiveAndNegativeFrequencies(N1);
[yPos,yNeg] = iPositiveAndNegativeFrequencies(N2);
[zPos,zNeg] = iPositiveAndNegativeFrequencies(N3);

% 2d symmetry on the k3=0 plane
y(xNeg,1,1,:,:) = conj(y(xPos,1,1,:,:));
y(1,yNeg,1,:,:) = conj(y(1,yPos,1,:,:));
y(xNeg,yNeg,1,:,:) = conj(y(xPos,yPos,1,:,:));
y(xPos,yNeg,1,:,:) = conj(y(xNeg,yPos,1,:,:));

% 1d symmetry on the k1=0,k2=0 line
y(1,1,zNeg,:,:) = conj(y(1,1,zPos,:,:));

% 2d symmetry on the k1=0 plane
y(1,yNeg,zNeg,:,:) = conj(y(1,yPos,zPos,:,:));
y(1,yPos,zNeg,:,:) = conj(y(1,yNeg,zPos,:,:));

% 2d symmetry on the k2=0 plane
y(xNeg,1,zNeg,:,:) = conj(y(xPos,1,zPos,:,:));
y(xPos,1,zNeg,:,:) = conj(y(xNeg,1,zPos,:,:));

% 3d symmetry for the interior octants
y(xNeg,yNeg,zNeg,:,:) = conj(y(xPos,yPos,zPos,:,:));
y(xPos,yNeg,zNeg,:,:) = conj(y(xNeg,yPos,zPos,:,:));
y(xNeg,yPos,zNeg,:,:) = conj(y(xPos,yNeg,zPos,:,:));
y(xPos,yPos,zNeg,:,:) = conj(y(xNeg,yNeg,zPos,:,:));

% DC and Nyquist frequencies must be real.
y(1,1,1,:,:) = real(y(1,1,1,:,:));
if mod(N1,2)==0
y(N1/2+1,1,1,:,:) = real(y(N1/2+1,1,1,:,:));
end
if mod(N2,2)==0
y(1,N2/2+1,1,:,:) = real(y(1,N2/2+1,1,:,:));
end
if mod(N3,2)==0
y(1,1,N3/2+1,:,:) = real(y(1,1,N3/2+1,:,:));
end
if mod(N1,2)==0 && mod(N2,2)==0
y(N1/2+1,N2/2+1,1,:,:) = real(y(N1/2+1,N2/2+1,1,:,:));
end
if mod(N1,2)==0 && mod(N3,2)==0
y(N1/2+1,1,N3/2+1,:,:) = real(y(N1/2+1,1,N3/2+1,:,:));
end
if mod(N2,2)==0 && mod(N3,2)==0
y(1,N2/2+1,N3/2+1,:,:) = real(y(1,N2/2+1,N3/2+1,:,:));
end
if mod(N1,2)==0 && mod(N2,2)==0 && mod(N3,2)==0
y(N1/2+1,N2/2+1,N3/2+1,:,:) = real(y(N1/2+1,N2/2+1,N3/2+1,:,:));
end

% Return to physical space.
y = ifft(y,[],3);
y = ifft(y,[],2);
y = ifft(y,[],1,'symmetric');
y = dlarray(y, 'SSSCB');
y = real(y);
end
end
end
end

function [pos,neg] = iPositiveAndNegativeFrequencies(N)
pos = 2:(floor(N/2)+1);
neg = N:-1:(ceil(N/2)+1);
end