def train(epoch):
startTime=time.time()
xRes=0
yRes=0
mRes=0
eU=0
eV=0
eP=0
for iteration, batch in enumerate(training_data_loader):
[JJInv,coord,xi,eta,J,Jinv,dxdxi,dydxi,dxdeta,dydeta]=to4DTensor(batch)
optimizer.zero_grad()
output=model(coord)
output_pad=udfpad(output)
outputV=output_pad[:,0,:,:].reshape(output_pad.shape[0],1,
output_pad.shape[2],
output_pad.shape[3])
for j in range(batchSize):
outputV[j,0,-padSingleSide:,padSingleSide:-padSingleSide]=0
outputV[j,0,:padSingleSide,padSingleSide:-padSingleSide]=1
outputV[j,0,padSingleSide:-padSingleSide,-padSingleSide:]=1
outputV[j,0,padSingleSide:-padSingleSide,0:padSingleSide]=1
outputV[j,0,0,0]=0.5*(outputV[j,0,0,1]+outputV[j,0,1,0])
outputV[j,0,0,-1]=0.5*(outputV[j,0,0,-2]+outputV[j,0,1,-1])
dvdx=dfdx(outputV,dydeta,dydxi,Jinv)
d2vdx2=dfdx(dvdx,dydeta,dydxi,Jinv)
dvdy=dfdy(outputV,dxdxi,dxdeta,Jinv)
d2vdy2=dfdy(dvdy,dxdxi,dxdeta,Jinv)
continuity=(d2vdy2+d2vdx2);
loss=criterion(continuity,continuity*0)
loss.backward()
optimizer.step()
loss_mass=criterion(continuity, continuity*0)
mRes+=loss_mass.item()
CNNVNumpy=outputV[0,0,:,:].cpu().detach().numpy()
eV=eV+np.sqrt(calMSE(OFV_sb,CNNVNumpy)/calMSE(OFV_sb,OFV_sb*0))
print('Epoch is ',epoch)
print("mRes Loss is", (mRes/len(training_data_loader)))
print("eV Loss is", (eV/len(training_data_loader)))
if epoch%5000==0 or epoch%nEpochs==0 or np.sqrt(calMSE(OFV_sb,CNNVNumpy)/calMSE(OFV_sb,OFV_sb*0))<0.1:
torch.save(model, str(epoch)+'.pth')
fig1=plt.figure()
ax=plt.subplot(1,2,1)
visualize2D(ax,coord[0,0,1:-1,1:-1].cpu().detach().numpy(),
coord[0,1,1:-1,1:-1].cpu().detach().numpy(),
outputV[0,0,1:-1,1:-1].cpu().detach().numpy(),'horizontal',[0,1])
setAxisLabel(ax,'p')
ax.set_title('CNN '+r'$T$')
ax.set_aspect('equal')
ax=plt.subplot(1,2,2)
visualize2D(ax,coord[0,0,1:-1,1:-1].cpu().detach().numpy(),
coord[0,1,1:-1,1:-1].cpu().detach().numpy(),
OFV_sb[1:-1,1:-1],'horizontal',[0,1])
setAxisLabel(ax,'p')
ax.set_aspect('equal')
ax.set_title('FV '+r'$T$')
fig1.tight_layout(pad=1)
fig1.savefig(str(epoch)+'T.pdf',bbox_inches='tight')
plt.close(fig1)
return (mRes/len(training_data_loader)),(eV/len(training_data_loader))
Vmag_ = torch.sqrt(output[0, 0, :, :]**2 + output[0, 1, :, :]**2)
VelocityMagnitudeErrorRecord.append(
torch.sqrt(
criterion(Vmag_True, Vmag_) / criterion(Vmag_True, Vmag_True * 0)))
PErrorRecord.append(
torch.sqrt(
criterion(Ptrue, output[0, 2, :, :]) /
criterion(Ptrue, Ptrue * 0)))
xylabelsize = 20
xytickssize = 20
titlesize = 20
fig1 = plt.figure()
ax = plt.subplot(2, 2, 1)
_, cbar = visualize2D(ax, coord[0, 0, 1:-1, 1:-1].cpu().detach().numpy(),
coord[0, 1, 1:-1, 1:-1].cpu().detach().numpy(),
Vmag_True.cpu().detach().numpy(), 'vertical', [
Vmag_True.cpu().detach().numpy().min() * 0,
Vmag_True.cpu().detach().numpy().max() * 0 + 0.5
])
ax.set_title('CFD Velocity', fontsize=titlesize)
cbar.set_ticks([0, 0.1, 0.2, 0.3, 0.4, 0.5])
ax.set_xticks([-0.5, 0.5])
ax.tick_params(axis='x', labelsize=xytickssize)
ax.tick_params(axis='y', labelsize=xytickssize)
cbar.ax.tick_params(labelsize=xytickssize)
ax.tick_params(axis='both',
which='both',
bottom=False,
left=False,
top=False,
labelbottom=False,
labelleft=False)
def train(epoch):
startTime = time.time()
xRes = 0
yRes = 0
mRes = 0
eU = 0
eV = 0
eP = 0
for iteration, batch in enumerate(training_data_loader):
[Para, coord, xi, eta, J, Jinv, dxdxi, dydxi, dxdeta, dydeta,
truth] = to4DTensor(batch)
optimizer.zero_grad()
output = model(Para)
output_pad = udfpad(output)
outputV = output_pad[:, 0, :, :].reshape(output_pad.shape[0], 1,
output_pad.shape[2],
output_pad.shape[3])
for j in range(batchSize):
#Impose BC
outputV[j, 0, -padSingleSide:, padSingleSide:-padSingleSide] = (
outputV[j, 0, 1:2, padSingleSide:-padSingleSide])
outputV[j, 0, :padSingleSide, padSingleSide:-padSingleSide] = (
outputV[j, 0, -2:-1, padSingleSide:-padSingleSide])
outputV[j, 0, :, -padSingleSide:] = 0
outputV[j, 0, :, 0:padSingleSide] = Para[j, 0, 0, 0]
dvdx = dfdx(outputV, dydeta, dydxi, Jinv)
d2vdx2 = dfdx(dvdx, dydeta, dydxi, Jinv)
dvdy = dfdy(outputV, dxdxi, dxdeta, Jinv)
d2vdy2 = dfdy(dvdy, dxdxi, dxdeta, Jinv)
continuity = (d2vdy2 + d2vdx2)
loss = criterion(continuity, continuity * 0)
loss.backward()
optimizer.step()
loss_mass = criterion(continuity, continuity * 0)
mRes += loss_mass.item()
eV = eV + torch.sqrt(
criterion(truth, outputV) / criterion(truth, truth * 0))
if epoch % 1000 == 0 or epoch % nEpochs == 0:
torch.save(model, str(epoch) + '.pth')
for j in range(batchSize):
fig1 = plt.figure()
ax = plt.subplot(1, 2, 1)
visualize2D(ax, coord[0, 0, :, :].cpu().detach().numpy(),
coord[0, 1, :, :].cpu().detach().numpy(),
outputV[j, 0, :, :].cpu().detach().numpy())
ax.set_aspect('equal')
setAxisLabel(ax, 'p')
ax.set_title('CNN ' + r'$T$')
ax = plt.subplot(1, 2, 2)
visualize2D(ax, coord[0, 0, :, :].cpu().detach().numpy(),
coord[0, 1, :, :].cpu().detach().numpy(),
truth[j, 0, :, :].cpu().detach().numpy())
ax.set_aspect('equal')
setAxisLabel(ax, 'p')
ax.set_title('FV ' + r'$T$')
fig1.tight_layout(pad=1)
fig1.savefig('Epoch' + str(epoch) + 'Para' + str(j) + 'T.pdf',
bbox_inches='tight')
#plt.show()
plt.close(fig1)
print('Epoch is ', epoch)
print("mRes Loss is", (mRes / len(training_data_loader)))
print("eV Loss is", (eV / len(training_data_loader)))
return (mRes / len(training_data_loader)), (eV / len(training_data_loader))
def train(epoch):
startTime = time.time()
xRes = 0
yRes = 0
mRes = 0
eU = 0
eV = 0
eP = 0
for iteration, batch in enumerate(training_data_loader):
[JJInv,coord,xi,
eta,J,Jinv,
dxdxi,dydxi,
dxdeta,dydeta,
Utrue,Vtrue,Ptrue]=\
to4DTensor(batch)
solutionTruth = torch.cat([Utrue, Vtrue, Ptrue], axis=1)
optimizer.zero_grad()
output = model(coord)
output_pad = udfpad(output)
outputU = output_pad[:, 0, :, :].reshape(output_pad.shape[0], 1,
output_pad.shape[2],
output_pad.shape[3])
outputV = output_pad[:, 1, :, :].reshape(output_pad.shape[0], 1,
output_pad.shape[2],
output_pad.shape[3])
outputP = output_pad[:, 2, :, :].reshape(output_pad.shape[0], 1,
output_pad.shape[2],
output_pad.shape[3])
XR = torch.zeros([batchSize, 1, ny, nx]).to('cuda')
YR = torch.zeros([batchSize, 1, ny, nx]).to('cuda')
MR = torch.zeros([batchSize, 1, ny, nx]).to('cuda')
for j in range(batchSize):
outputU[j, 0, -padSingleSide:,
padSingleSide:-padSingleSide] = output[j, 0,
-1, :].reshape(
1, nx - 2 *
padSingleSide)
outputU[j, 0, :padSingleSide, padSingleSide:-padSingleSide] = 0
outputU[j, 0, padSingleSide:-padSingleSide, -padSingleSide:] = 0
outputU[j, 0, padSingleSide:-padSingleSide, 0:padSingleSide] = 0
outputU[j, 0, 0,
0] = 0.5 * (outputU[j, 0, 0, 1] + outputU[j, 0, 1, 0])
outputU[j, 0, 0,
-1] = 0.5 * (outputU[j, 0, 0, -2] + outputU[j, 0, 1, -1])
outputV[j, 0, -padSingleSide:,
padSingleSide:-padSingleSide] = output[j, 1,
-1, :].reshape(
1, nx - 2 *
padSingleSide)
outputV[j, 0, :padSingleSide, padSingleSide:-padSingleSide] = 0.4
outputV[j, 0, padSingleSide:-padSingleSide, -padSingleSide:] = 0
outputV[j, 0, padSingleSide:-padSingleSide, 0:padSingleSide] = 0
outputV[j, 0, 0,
0] = 0.5 * (outputV[j, 0, 0, 1] + outputV[j, 0, 1, 0])
outputV[j, 0, 0,
-1] = 0.5 * (outputV[j, 0, 0, -2] + outputV[j, 0, 1, -1])
outputP[j, 0, -padSingleSide:, padSingleSide:-padSingleSide] = 0
outputP[j, 0, :padSingleSide,
padSingleSide:-padSingleSide] = output[j, 2, 0, :].reshape(
1, nx - 2 * padSingleSide)
outputP[j, 0, padSingleSide:-padSingleSide,
-padSingleSide:] = output[j, 2, :, -1].reshape(
ny - 2 * padSingleSide, 1)
outputP[j, 0, padSingleSide:-padSingleSide,
0:padSingleSide] = output[j, 2, :, 0].reshape(
ny - 2 * padSingleSide, 1)
outputP[j, 0, 0,
0] = 0.5 * (outputP[j, 0, 0, 1] + outputP[j, 0, 1, 0])
outputP[j, 0, 0,
-1] = 0.5 * (outputP[j, 0, 0, -2] + outputP[j, 0, 1, -1])
dudx = dfdx(outputU, dydeta, dydxi, Jinv)
d2udx2 = dfdx(dudx, dydeta, dydxi, Jinv)
dudy = dfdy(outputU, dxdxi, dxdeta, Jinv)
d2udy2 = dfdy(dudy, dxdxi, dxdeta, Jinv)
dvdx = dfdx(outputV, dydeta, dydxi, Jinv)
d2vdx2 = dfdx(dvdx, dydeta, dydxi, Jinv)
dvdy = dfdy(outputV, dxdxi, dxdeta, Jinv)
d2vdy2 = dfdy(dvdy, dxdxi, dxdeta, Jinv)
dpdx = dfdx(outputP, dydeta, dydxi, Jinv)
d2pdx2 = dfdx(dpdx, dydeta, dydxi, Jinv)
dpdy = dfdy(outputP, dxdxi, dxdeta, Jinv)
d2pdy2 = dfdy(dpdy, dxdxi, dxdeta, Jinv)
continuity = dudx + dvdy
momentumX = outputU * dudx + outputV * dudy
forceX = -dpdx + nu * (d2udx2 + d2udy2)
Xresidual = momentumX - forceX
momentumY = outputU * dvdx + outputV * dvdy
forceY = -dpdy + nu * (d2vdx2 + d2vdy2)
Yresidual = momentumY - forceY
loss=(criterion(Xresidual,Xresidual*0)+\
criterion(Yresidual,Yresidual*0)+\
criterion(continuity,continuity*0))
loss.backward()
optimizer.step()
loss_xm = criterion(Xresidual, Xresidual * 0)
loss_ym = criterion(Yresidual, Yresidual * 0)
loss_mass = criterion(continuity, continuity * 0)
xRes += loss_xm.item()
yRes += loss_ym.item()
mRes += loss_mass.item()
eU = eU + torch.sqrt(
criterion(Utrue, output[:, 0:1, :, :]) /
criterion(Utrue, Utrue * 0))
eV = eV + torch.sqrt(
criterion(Vtrue, output[:, 1:2, :, :]) /
criterion(Vtrue, Vtrue * 0))
eP = eP + torch.sqrt(
criterion(Ptrue, output[:, 2:3, :, :]) /
criterion(Ptrue, Ptrue * 0))
if epoch % 5000 == 0 or epoch % nEpochs == 0:
torch.save(model, str(epoch) + '.pth')
for j in range(batchSize):
fig1 = plt.figure()
ax = plt.subplot(2, 3, 1)
visualize2D(ax, coord[j, 0, 1:-1, 1:-1].cpu().detach().numpy(),
coord[j, 1, 1:-1, 1:-1].cpu().detach().numpy(),
Utrue[j, :, :, :].cpu().detach().numpy())
setAxisLabel(ax, 'p')
ax.set_title('Physics Domain ' + 'U FV')
ax.set_xticks([-0.25, 0.25])
ax = plt.subplot(2, 3, 2)
visualize2D(ax, coord[j, 0, 1:-1, 1:-1].cpu().detach().numpy(),
coord[j, 1, 1:-1, 1:-1].cpu().detach().numpy(),
Vtrue[j, :, :, :].cpu().detach().numpy())
setAxisLabel(ax, 'p')
ax.set_title('Physics Domain ' + 'V FV')
ax.set_xticks([-0.25, 0.25])
ax = plt.subplot(2, 3, 3)
visualize2D(ax, coord[j, 0, 1:-1, 1:-1].cpu().detach().numpy(),
coord[j, 1, 1:-1, 1:-1].cpu().detach().numpy(),
Ptrue[j, :, :, :].cpu().detach().numpy())
setAxisLabel(ax, 'p')
ax.set_title('Physics Domain ' + 'P FV')
ax.set_xticks([-0.25, 0.25])
ax = plt.subplot(2, 3, 4)
visualize2D(ax, coord[j, 0, 1:-1, 1:-1].cpu().detach().numpy(),
coord[j, 1, 1:-1, 1:-1].cpu().detach().numpy(),
outputU[j, 0, 1:-1, 1:-1].cpu().detach().numpy())
setAxisLabel(ax, 'p')
ax.set_title('U CNN')
ax.set_xticks([-0.25, 0.25])
ax = plt.subplot(2, 3, 5)
visualize2D(ax, coord[j, 0, 1:-1, 1:-1].cpu().detach().numpy(),
coord[j, 1, 1:-1, 1:-1].cpu().detach().numpy(),
outputV[j, 0, 1:-1, 1:-1].cpu().detach().numpy())
setAxisLabel(ax, 'p')
ax.set_title('V CNN')
ax.set_xticks([-0.25, 0.25])
ax = plt.subplot(2, 3, 6)
visualize2D(ax, coord[j, 0, 1:-1, 1:-1].cpu().detach().numpy(),
coord[j, 1, 1:-1, 1:-1].cpu().detach().numpy(),
outputP[j, 0, 1:-1, 1:-1].cpu().detach().numpy())
setAxisLabel(ax, 'p')
ax.set_title('P CNN')
ax.set_xticks([-0.25, 0.25])
fig1.tight_layout(pad=1)
fig1.savefig('epoch' + str(epoch) + 'Para' + str(j) +
'UVPCFD.pdf',
bbox_inches='tight')
plt.close(fig1)
print('Epoch is ', epoch)
print("xRes Loss is", (xRes / len(training_data_loader)))
print("yRes Loss is", (yRes / len(training_data_loader)))
print("mRes Loss is", (mRes / len(training_data_loader)))
print("eU Loss is", (eU / len(training_data_loader)))
print("eV Loss is", (eV / len(training_data_loader)))
print("eP Loss is", (eP / len(training_data_loader)))
return (xRes/len(training_data_loader)), (yRes/len(training_data_loader)),\
(mRes/len(training_data_loader)), (eU.item()/len(training_data_loader)),\
(eV.item()/len(training_data_loader)), (eP.item()/len(training_data_loader))
GT=OFGT*0
FI=OFFI*0
KL=OFKL*0
for i in range(nx):
for j in range(ny):
dist=(myMesh.x[j,i]-OFX)**2+(myMesh.y[j,i]-OFY)**2
idx_min=np.where(dist == dist.min())
GT[j,i,:]=OFGT[idx_min[0][0],idx_min[1][0],:]
FI[j,i,:]=OFFI[idx_min[0][0],idx_min[1][0],:]
KL[j,i,:]=OFKL[idx_min[0][0],idx_min[1][0],:]
Fontsize=20
for i in range(10):
fig0=plt.figure()
ax=plt.subplot(1,1,1)
_,cbar=visualize2D(ax,myMesh.x,
myMesh.y,
KL[:,:,i],'vertical')
ax.set_aspect('equal')
setAxisLabel(ax,'p')
ax.tick_params(axis='x',labelsize=Fontsize)
ax.tick_params(axis='y',labelsize=Fontsize)
cbar.ax.tick_params(labelsize=Fontsize)
ax.set_title('mode '+str(i+1),fontsize=Fontsize)
ax.set_xlabel(xlabel=r'$x$',fontsize=Fontsize)
ax.set_ylabel(ylabel=r'$y$',fontsize=Fontsize)
fig0.tight_layout(pad=0.5)
plt.savefig('test/KLMode'+str(i+1)+'.png',bbox_inches='tight')
plt.close(fig0)
trainSize=1000
batchSize=1
NvarInput=1
d2vdx2 = dfdx(dvdx, dydeta, dydxi, Jinv)
dvdy = dfdy(outputV, dxdxi, dxdeta, Jinv)
d2vdy2 = dfdy(dvdy, dxdxi, dxdeta, Jinv)
#Calculate PDE Residual
continuity = (d2vdy2 + d2vdx2)
loss = criterion(continuity, continuity * 0)
VelocityMagnitudeErrorRecord.append(
torch.sqrt(criterion(truth, outputV) / criterion(truth, truth * 0)))
fig1 = plt.figure()
xylabelsize = 20
xytickssize = 20
titlesize = 20
ax = plt.subplot(1, 2, 1)
_, cbar = visualize2D(ax, coord[0, 0, :, :].cpu().detach().numpy(),
coord[0, 1, :, :].cpu().detach().numpy(),
outputV[0, 0, :, :].cpu().detach().numpy(),
'horizontal', [0, max(ParaList)])
ax.set_aspect('equal')
setAxisLabel(ax, 'p')
ax.set_title('PhyGeoNet ' + r'$T$', fontsize=titlesize)
ax.set_xlabel(xlabel=r'$x$', fontsize=xylabelsize)
ax.set_ylabel(ylabel=r'$y$', fontsize=xylabelsize)
ax.set_xticks([-1, 0, 1])
ax.set_yticks([-1, 0, 1])
ax.tick_params(axis='x', labelsize=xytickssize)
ax.tick_params(axis='y', labelsize=xytickssize)
cbar.set_ticks([0, 1, 2, 3, 4, 5, 6, 7])
cbar.ax.tick_params(labelsize=xytickssize)
ax = plt.subplot(1, 2, 2)
_, cbar = visualize2D(ax, coord[0, 0, :, :].cpu().detach().numpy(),
coord[0, 1, :, :].cpu().detach().numpy(),
def train(epoch):
startTime = time.time()
xRes = 0
yRes = 0
mRes = 0
eU = 0
eV = 0
eP = 0
for iteration, batch in enumerate(training_data_loader):
[JJInv, coord, xi, eta, J, Jinv, dxdxi, dydxi, dxdeta,
dydeta] = to4DTensor(batch)
optimizer.zero_grad()
output = model(coord)
output_pad = udfpad(output)
outputU = output_pad[:, 0, :, :].reshape(output_pad.shape[0], 1,
output_pad.shape[2],
output_pad.shape[3])
outputV = output_pad[:, 1, :, :].reshape(output_pad.shape[0], 1,
output_pad.shape[2],
output_pad.shape[3])
outputP = output_pad[:, 2, :, :].reshape(output_pad.shape[0], 1,
output_pad.shape[2],
output_pad.shape[3])
XR = torch.zeros([batchSize, 1, ny, nx]).to('cuda')
YR = torch.zeros([batchSize, 1, ny, nx]).to('cuda')
MR = torch.zeros([batchSize, 1, ny, nx]).to('cuda')
for j in range(batchSize):
outputU[j, 0, -padSingleSide:,
padSingleSide:-padSingleSide] = output[j, 0,
-1, :].reshape(
1, nx - 2 *
padSingleSide)
outputU[j, 0, :padSingleSide, padSingleSide:-padSingleSide] = 0
outputU[j, 0, padSingleSide:-padSingleSide, -padSingleSide:] = 0
outputU[j, 0, padSingleSide:-padSingleSide, 0:padSingleSide] = 0
outputU[j, 0, 0, 0] = 1 * (outputU[j, 0, 0, 1])
outputU[j, 0, 0, -1] = 1 * (outputU[j, 0, 0, -2])
outputV[j, 0, -padSingleSide:,
padSingleSide:-padSingleSide] = output[j, 1,
-1, :].reshape(
1, nx - 2 *
padSingleSide)
outputV[j, 0, :padSingleSide, padSingleSide:-padSingleSide] = 1
outputV[j, 0, padSingleSide:-padSingleSide, -padSingleSide:] = 0
outputV[j, 0, padSingleSide:-padSingleSide, 0:padSingleSide] = 0
outputV[j, 0, 0, 0] = 1 * (outputV[j, 0, 0, 1])
outputV[j, 0, 0, -1] = 1 * (outputV[j, 0, 0, -2])
outputP[j, 0, -padSingleSide:, padSingleSide:-padSingleSide] = 0
outputP[j, 0, :padSingleSide,
padSingleSide:-padSingleSide] = output[j, 2, 0, :].reshape(
1, nx - 2 * padSingleSide)
outputP[j, 0, padSingleSide:-padSingleSide,
-padSingleSide:] = output[j, 2, :, -1].reshape(
ny - 2 * padSingleSide, 1)
outputP[j, 0, padSingleSide:-padSingleSide,
0:padSingleSide] = output[j, 2, :, 0].reshape(
ny - 2 * padSingleSide, 1)
outputP[j, 0, 0, 0] = 1 * (outputP[j, 0, 0, 1])
outputP[j, 0, 0, -1] = 1 * (outputP[j, 0, 0, -2])
dudx = dfdx(outputU, dydeta, dydxi, Jinv)
d2udx2 = dfdx(dudx, dydeta, dydxi, Jinv)
dudy = dfdy(outputU, dxdxi, dxdeta, Jinv)
d2udy2 = dfdy(dudy, dxdxi, dxdeta, Jinv)
dvdx = dfdx(outputV, dydeta, dydxi, Jinv)
d2vdx2 = dfdx(dvdx, dydeta, dydxi, Jinv)
dvdy = dfdy(outputV, dxdxi, dxdeta, Jinv)
d2vdy2 = dfdy(dvdy, dxdxi, dxdeta, Jinv)
dpdx = dfdx(outputP, dydeta, dydxi, Jinv)
d2pdx2 = dfdx(dpdx, dydeta, dydxi, Jinv)
dpdy = dfdy(outputP, dxdxi, dxdeta, Jinv)
d2pdy2 = dfdy(dpdy, dxdxi, dxdeta, Jinv)
continuity = dudx + dvdy
momentumX = outputU * dudx + outputV * dudy
forceX = -dpdx + nu * (d2udx2 + d2udy2)
Xresidual = momentumX - forceX
momentumY = outputU * dvdx + outputV * dvdy
forceY = -dpdy + nu * (d2vdx2 + d2vdy2)
Yresidual = momentumY - forceY
loss=(criterion(Xresidual,Xresidual*0)+\
criterion(Yresidual,Yresidual*0)+\
criterion(continuity,continuity*0))
#loss.backward()
optimizer.step()
loss_xm = criterion(Xresidual, Xresidual * 0)
loss_ym = criterion(Yresidual, Yresidual * 0)
loss_mass = criterion(continuity, continuity * 0)
xRes += loss_xm.item()
yRes += loss_ym.item()
mRes += loss_mass.item()
CNNUNumpy = outputU[0, 0, :, :].cpu().detach().numpy()
CNNVNumpy = outputV[0, 0, :, :].cpu().detach().numpy()
CNNPNumpy = outputP[0, 0, :, :].cpu().detach().numpy()
eU = eU + np.sqrt(
calMSE(OFU_sb, CNNUNumpy) / calMSE(OFU_sb, OFU_sb * 0))
eV = eV + np.sqrt(
calMSE(OFV_sb, CNNVNumpy) / calMSE(OFV_sb, OFV_sb * 0))
eP = eP + np.sqrt(
calMSE(OFP_sb, CNNPNumpy) / calMSE(OFP_sb, OFP_sb * 0))
eVmag = np.sqrt(
calMSE(np.sqrt(OFU_sb**2 + OFV_sb**2),
np.sqrt(CNNUNumpy**2 + CNNVNumpy**2)) /
calMSE(np.sqrt(OFU_sb**2 + OFV_sb**2),
np.sqrt(OFU_sb**2 + OFV_sb**2) * 0))
eVmag_FCNN = np.sqrt(
calMSE(np.sqrt(OFU_sb**2 + OFV_sb**2),
np.sqrt(fcnn_U**2 + fcnn_V**2)) /
calMSE(np.sqrt(OFU_sb**2 + OFV_sb**2),
np.sqrt(OFU_sb**2 + OFV_sb**2) * 0))
print('VelMagError_CNN=', eVmag)
print('VelMagError_FCNN=', eVmag_FCNN)
print('P_err_CNN=',
np.sqrt(calMSE(OFP_sb, CNNPNumpy) / calMSE(OFP_sb, OFP_sb * 0)))
print('P_err_FCNN=',
np.sqrt(calMSE(OFP_sb, fcnn_P) / calMSE(OFP_sb, OFP_sb * 0)))
print('Epoch is ', epoch)
print("xRes Loss is", (xRes / len(training_data_loader)))
print("yRes Loss is", (yRes / len(training_data_loader)))
print("mRes Loss is", (mRes / len(training_data_loader)))
print("eU Loss is", (eU / len(training_data_loader)))
print("eV Loss is", (eV / len(training_data_loader)))
print("eP Loss is", (eP / len(training_data_loader)))
if epoch % 5000 == 0 or epoch % nEpochs == 0:
torch.save(model, str(epoch) + '.pth')
fig0 = plt.figure()
ax = plt.subplot(2, 3, 1)
_,cbar=visualize2D(ax,coord[0,0,1:-1,1:-1].cpu().detach().numpy(),
coord[0,1,1:-1,1:-1].cpu().detach().numpy(),
np.sqrt(fcnn_U[1:-1,1:-1]**2+\
fcnn_V[1:-1,1:-1]**2),'vertical',[0,1.3])
cbar.set_ticks([0, 0.3, 0.6, 0.9, 1.3])
setAxisLabel(ax, 'p')
ax.set_title('FCNN ' + 'Velocity')
ax = plt.subplot(2, 3, 2)
_,cbar=visualize2D(ax,coord[0,0,1:-1,1:-1].cpu().detach().numpy(),
coord[0,1,1:-1,1:-1].cpu().detach().numpy(),
np.sqrt(outputU[0,0,1:-1,1:-1].cpu().detach().numpy()**2+\
outputV[0,0,1:-1,1:-1].cpu().detach().numpy()**2),'vertical',[0,1.3])
setAxisLabel(ax, 'p')
ax.set_title('PhyGeoNet ' + 'Velocity')
cbar.set_ticks([0, 0.3, 0.6, 0.9, 1.3])
ax = plt.subplot(2, 3, 3)
_,cbar=visualize2D(ax,coord[0,0,1:-1,1:-1].cpu().detach().numpy(),
coord[0,1,1:-1,1:-1].cpu().detach().numpy(),
np.sqrt(OFU_sb[1:-1,1:-1]**2+\
OFV_sb[1:-1,1:-1]**2),'vertical',[0,1.3])
cbar.set_ticks([0, 0.3, 0.6, 0.9, 1.3])
setAxisLabel(ax, 'p')
ax.set_title('CFD ' + 'Velocity')
ax = plt.subplot(2, 3, 4)
visualize2D(ax, coord[0, 0, 1:-1, 1:-1].cpu().detach().numpy(),
coord[0, 1, 1:-1, 1:-1].cpu().detach().numpy(),
fcnn_P[1:-1, 1:-1], 'vertical', [0, 1.5])
setAxisLabel(ax, 'p')
ax.set_title('FCNN ' + 'Pressure')
ax = plt.subplot(2, 3, 5)
visualize2D(ax, coord[0, 0, 1:-1, 1:-1].cpu().detach().numpy(),
coord[0, 1, 1:-1, 1:-1].cpu().detach().numpy(),
outputP[0, 0, 1:-1,
1:-1].cpu().detach().numpy(), 'vertical', [0, 1.5])
setAxisLabel(ax, 'p')
ax.set_title('PhyGeoNet ' + 'Pressure')
ax = plt.subplot(2, 3, 6)
visualize2D(ax, coord[0, 0, 1:-1, 1:-1].cpu().detach().numpy(),
coord[0, 1, 1:-1, 1:-1].cpu().detach().numpy(),
OFP_sb[1:-1, 1:-1], 'vertical', [0, 1.5])
setAxisLabel(ax, 'p')
ax.set_title('CFD ' + 'Pressure')
fig0.tight_layout(pad=1)
fig0.savefig(str(epoch) + 'VelMagAndPressureFCNN.pdf',
bbox_inches='tight')
plt.close(fig0)
fig0 = plt.figure()
ax = plt.subplot(2, 2, 1)
_,cbar=visualize2D(ax,coord[0,0,1:-1,1:-1].cpu().detach().numpy(),
coord[0,1,1:-1,1:-1].cpu().detach().numpy(),
np.sqrt(outputU[0,0,1:-1,1:-1].cpu().detach().numpy()**2+\
outputV[0,0,1:-1,1:-1].cpu().detach().numpy()**2),'vertical',[0,1.3])
setAxisLabel(ax, 'p')
ax.set_title('PhyGeoNet ' + 'Velocity')
ax.set_aspect(1.3)
cbar.set_ticks([0, 0.3, 0.6, 0.9, 1.3])
ax = plt.subplot(2, 2, 2)
visualize2D(ax, coord[0, 0, 1:-1, 1:-1].cpu().detach().numpy(),
coord[0, 1, 1:-1, 1:-1].cpu().detach().numpy(),
outputP[0, 0, 1:-1,
1:-1].cpu().detach().numpy(), 'vertical', [0, 1.5])
setAxisLabel(ax, 'p')
ax.set_title('PhyGeoNet ' + 'Pressure')
ax.set_aspect(1.3)
ax = plt.subplot(2, 2, 3)
_,cbar=visualize2D(ax,coord[0,0,1:-1,1:-1].cpu().detach().numpy(),
coord[0,1,1:-1,1:-1].cpu().detach().numpy(),
np.sqrt(OFU_sb[1:-1,1:-1]**2+\
OFV_sb[1:-1,1:-1]**2),'vertical',[0,1.3])
setAxisLabel(ax, 'p')
ax.set_title('CFD ' + 'Velocity')
ax.set_aspect(1.3)
cbar.set_ticks([0, 0.3, 0.6, 0.9, 1.3])
ax = plt.subplot(2, 2, 4)
visualize2D(ax, coord[0, 0, 1:-1, 1:-1].cpu().detach().numpy(),
coord[0, 1, 1:-1, 1:-1].cpu().detach().numpy(),
OFP_sb[1:-1, 1:-1], 'vertical', [0, 1.5])
setAxisLabel(ax, 'p')
ax.set_title('CFD ' + 'Pressure')
ax.set_aspect(1.3)
fig0.tight_layout(pad=1)
fig0.savefig(str(epoch) + 'VelMagAndPressureCNN.pdf',
bbox_inches='tight')
plt.close(fig0)
return (xRes/len(training_data_loader)), (yRes/len(training_data_loader)),\
(mRes/len(training_data_loader)), (eU/len(training_data_loader)),\
(eV/len(training_data_loader)), (eP/len(training_data_loader))