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TOuNN.py
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import numpy as np
import torch
import torch.optim as optim
import matplotlib.pyplot as plt
from matplotlib import colors
from network import TopNet
from projections import applyFourierMap, \
applyReflection, applyDensityProjection
from materialCoeffs import microStrs
import pickle
import scipy.io as sio
from scipy.ndimage import rotate
#-----------------------------#
def to_torch(x):
return torch.tensor(x).float()
#-----------------------------#
def to_np(x):
return x.detach().cpu().numpy()
#-----------------------------#
class TOuNN:
def __init__(self, mesh, material, FE, nnSettings, fourierMap, symMap, bc, optimizationMethod, overrideGPU= True):
self.device = self.setDevice(overrideGPU);
self.FE = FE(mesh, material, bc)
xy = self.FE.mesh.generatePoints()
self.xy = torch.tensor(xy, requires_grad = True).\
float().view(-1,2).to(self.device);
self.fourierMap = fourierMap
if(fourierMap['isOn']):
nnSettings['inputDim'] = 2*fourierMap['numTerms']
else:
nnSettings['inputDim'] = self.FE.mesh.meshSpec['elemSize']
self.topNet = TopNet(nnSettings).to(self.device)
# # densProj to generate 0-1 designs
self.densityProj = {'isOn':False, 'sharpness':5.}
self.symMap = symMap
self.mstrData = microStrs
self.optimizationMethod = optimizationMethod
#-----------------------------#
def setDevice(self, overrideGPU):
if(torch.cuda.is_available() and (overrideGPU == False) ):
device = torch.device("cuda:0");
print("GPU enabled")
else:
device = torch.device("cpu")
print("Running on CPU")
return device;
#-----------------------------#
def rotateCMatrix(self, C, theta):
c = torch.cos(theta)
s = torch.sin(theta)
Cprime = {}
Cprime['00'] = (1/C['00'])*c**2 + (1/C['11'])*s**2 #Taking the inverse first then doing rotation transformation
Cprime['11'] = (1/C['11'])*c**2 + (1/C['00'])*s**2 #As inv(rot*C*rot.T) = rot*inv(C)*rot.T
Cprime['01'] = (1/C['00'])*c*s - (1/C['11'])*c*s
Cprime['area'] = C['area']
Cprime['perim'] = C['perim']
return Cprime
# #-----------------------------#
def optimizeDesign(self, optParams, savedNet):
convgHistory = {'epoch':[], 'af':[], 'J':[]}
xyR, signsReflection = applyReflection(self.xy, self.symMap)
if(self.fourierMap['isOn']):
self.xyF = applyFourierMap(xyR, self.fourierMap)
else:
self.xyF = xyR
penal = 1
# C Matrix
def getCfromCPolynomial(sizePow, mstr):
C = {}
for c in ['00', '11', 'perim']: # init
C[c] = torch.zeros((self.FE.mesh.meshSpec['numElems']))
for c in ['00', '11', 'perim']: # c = Q0*a^0 + Q1*a^1 + ... + Qn*a^n
for pw in range(mstr['order']+1):
C[c] = C[c]+(mstr[c][str(pw)]*sizePow[str(pw)])
return C
def getCMatrix(mstrType, size, theta):
sizePow = {} # compute the powers once to avoid repeated calc
for pw in range(self.mstrData['squircle']['order']+1):# TODO: use the max order of all mstrs
sizePow[str(pw)] = size**pw
C = {}
for c in ['00', '11', 'area', 'perim']:
C[c] = torch.zeros((self.FE.mesh.meshSpec['numElems']))
for mstrCtr, mstr in enumerate(self.mstrData):
Cmstr = getCfromCPolynomial(sizePow, self.mstrData[mstr])
Cmstr['area'] = 1. - self.mstrData[mstr]['sizeCoeff']*sizePow[str(2)]
mstrPenal = mstrType[:,mstrCtr]**penal # now select mstrs
mstrWithoutPenal = mstrType[:,mstrCtr]
for c in ['00', '11']:
Cmstr[c] = (torch.maximum(to_torch(0), Cmstr[c])+1e-4)
C[c] = C[c] + (torch.einsum('i,i->i', mstrPenal, Cmstr[c]))
# C[c] = Cmstr[c]
for c in ['perim', 'area']:
Cmstr[c] = (torch.maximum(to_torch(0), Cmstr[c])+1e-4)
C[c] = C[c] + (torch.einsum('i,i->i', mstrWithoutPenal, Cmstr[c]))
Cprime = self.rotateCMatrix(C, theta)
Cprime['perim'] *= self.FE.mesh.meshSpec['elemSize'][0] # perim generated assuming elemsize of 1... scale by element size
return Cprime
self.getCMatrix = getCMatrix
#--------------------------#
def saveTopologyNetwork(self, fileName):
torch.save(self.topNet.state_dict(), fileName)
#--------------------------#
def loadTopologyNetwork(self, fileName):
self.topNet.load_state_dict(torch.load(fileName))
#--------------------------#
# optimizer
if(self.optimizationMethod == 'adam'):
optParams['epochSnapShot'] = 20
muVar = 0; # lagrange multiplier
self.optimizer = optim.Adam(self.topNet.parameters(), amsgrad=True,lr=optParams['learningRate']);
else:
optParams['lossMethod']['alpha0'] = 10 # start
optParams['lossMethod']['delAlpha'] = 0.15
optParams['epochSnapShot'] = 1
muVar = 0;
self.optimizer = optim.LBFGS(self.topNet.parameters(),
line_search_fn = 'strong_wolfe')
#--------------------------#
def computeLoss(objective, constraints):
if(optParams['lossMethod']['type'] == 'penalty'):
alpha = min(100.,optParams['lossMethod']['alpha0'] + \
self.epoch*optParams['lossMethod']['delAlpha']) # penalty method
loss = objective
for c in constraints:
loss = loss + alpha*c**2
if(optParams['lossMethod']['type'] == 'logBarrier'):
t = optParams['lossMethod']['t0']* \
optParams['lossMethod']['mu']**self.epoch
loss = objective
for c in constraints:
if(c < (-1/t**2)):
loss = loss - torch.log(-c)/t
else:
loss = loss + t*c - torch.log(1/t**2)/t + 1./t
if(optParams['lossMethod']['type'] == 'augLag'):
alpha = min(100, optParams['lossMethod']['alpha0'] + \
optParams['lossMethod']['delAlpha']); # Augumented Lagrangian
# for c in constraints:
loss = objective
for c in constraints:
loss = loss + alpha*c**2 + muVar*c
return loss, alpha
#--------------------------#
def closure():
convgHistory = {'epoch':[], 'af':[], 'J':[]}
self.optimizer.zero_grad()
self.mstrType, self.size, self.theta = self.topNet(self.xyF)
# self.size = applyDensityProjection(self.size, self.densityProj)
self.theta = torch.einsum('i,i->i', self.theta, signsReflection['X'])
self.theta = torch.einsum('i,i->i', self.theta, signsReflection['Y']) #(180 - theta) and not -theta
self.C = getCMatrix(self.mstrType, 0.01+self.size, self.theta)
areaCons = (torch.mean(self.C['area'])/optParams['desiredAreaFraction'])- 1.
perimCons = 1. - (torch.sum(self.C['perim'])/optParams['desiredPerimeter'])
self.J, self.Uvel, self.Vvel,self.Pressure = self.FE.objectiveHandle(self.C)
if(self.epoch == 0 or self.epoch == 10):
self.J0 = self.J.item()
self.constraints = [perimCons] #areaCons , perimCons
loss, self.alpha = computeLoss(self.J/self.J0, self.constraints)
loss.backward(retain_graph = True);
return loss# , areaCons , perimCons
#--------------------------#
loss_old = 100.
loss = 0.
for self.epoch in range(optParams['maxEpochs']):
if abs(loss-loss_old)<0.00001:
break
loss_old = loss
print(loss)
penal = min(8.0, 1. + self.epoch*0.02)
loss = closure()
if(self.optimizationMethod == 'adam'):
self.optimizer.step()
else:
self.optimizer.step(closure)
for c in self.constraints:
muVar = muVar + self.alpha*2*c.item()
self.mstrType, self.size, self.theta = self.topNet(self.xyF)
# self.size = applyDensityProjection(self.size, self.densityProj)
self.theta = torch.einsum('i,i->i', self.theta, signsReflection['X'])
self.theta = torch.einsum('i,i->i', self.theta, signsReflection['Y']) #(180 - theta) and not -theta
self.C = getCMatrix(self.mstrType, 0.01+self.size, self.theta)
areaCons = (torch.mean(self.C['area'])/optParams['desiredAreaFraction'])- 1.
perimCons = 1. - (torch.sum(self.C['perim'])/optParams['desiredPerimeter'])
self.J, self.Uvel, self.Vvel,self.Pressure = self.FE.objectiveHandle(self.C)
if(self.epoch == 0 or self.epoch == 10):
self.J0 = self.J.item()
self.constraints = [ perimCons]
loss, self.alpha = computeLoss(self.J/self.J0, self.constraints)
loss.backward(retain_graph = True);
if(self.epoch% optParams['epochSnapShot'] == 0):
convgHistory['epoch'].append(self.epoch)
convgHistory['J'].append(self.J.item())
areaf= torch.mean(self.C['area'])
convgHistory['af'].append(areaf.item())
exposed_perim = torch.sum(self.C['perim'])
status = 'epoch {:d} J \t {:.2E} areaf {:.2F} perim {:.2F}'.\
format(self.epoch, self.J, areaf, exposed_perim)
print(status)
if(self.epoch%30 == 0):
self.FE.mesh.plotField(to_torch(self.C['perim']), 'perimeter')
# self.FE.mesh.plotField(to_torch(self.C['area']), 'area')
# self.plotCompositeTopology(1) # comment this when not saving frames
# if(savedNet['isDump']):
# # saveTopologyNetwork(fileName)
self.plotVelocity(self.Uvel.detach().numpy(), self.Vvel.detach().numpy(), self.Pressure.detach().numpy())
self.FE.mesh.plotField(to_torch(self.C['area']), 'area')
NX = 1*int(np.ceil((self.FE.mesh.meshSpec['bb']['xmax']-\
self.FE.mesh.meshSpec['bb']['xmin'])/self.FE.mesh.meshSpec['elemSize'][0]))
NY = 1*int(np.ceil((self.FE.mesh.meshSpec['bb']['ymax']-\
self.FE.mesh.meshSpec['bb']['ymin'])/self.FE.mesh.meshSpec['elemSize'][1]))
plt.figure()
plt.imshow(self.size.detach().numpy().reshape((NX, NY)))
plt.title('size')
return convgHistory
#-----------------------#
def plotVelocity(self, uVelocity, vVelocity, Pressure):
plt.figure()
P =plt.imshow((Pressure).\
reshape((self.FE.mesh.meshSpec['nelx'], \
self.FE.mesh.meshSpec['nely'])).T, origin = 'lower', cmap ='rainbow')
v = np.linspace(np.amin(Pressure), np.amax(Pressure), 10, endpoint=True)
plt.colorbar(ticks=v)
plt.title('$Pressure$')
plt.axis('equal')
plt.figure()
a =plt.imshow(uVelocity.\
reshape((self.FE.mesh.meshSpec['nelx'], \
self.FE.mesh.meshSpec['nely'])).T, origin = 'lower', cmap ='rainbow')
plt.colorbar(a)
plt.title('$u_X$')
plt.axis('equal')
plt.figure()
b =plt.imshow(vVelocity.\
reshape((self.FE.mesh.meshSpec['nelx'], \
self.FE.mesh.meshSpec['nely'])).T, origin = 'lower', cmap ='rainbow')
plt.colorbar(b)
plt.title('$u_Y$')
plt.axis('equal')
plt.figure()
netV = np.sqrt(uVelocity**2 + vVelocity**2)
b =plt.imshow(netV.\
reshape((self.FE.mesh.meshSpec['nelx'], \
self.FE.mesh.meshSpec['nely'])).T, origin = 'lower', cmap ='rainbow')
plt.colorbar(b)
plt.title('||u||')
plt.axis('equal')
plt.show()
#-----------------------#
def plotCompositeTopology(self, res):
xy = self.FE.mesh.generatePoints(res)
xyR, signsReflection = applyReflection(to_torch(xy), self.symMap)
if(self.fourierMap['isOn']):
xyF = applyFourierMap(xyR, self.fourierMap)
else:
xyF = xyR
mstrType, size, theta = self.topNet(xyF)
C = self.getCMatrix(mstrType, 0.01+size, theta)
C['area'] = 1.-C['area']
theta = torch.einsum('i,i->i', theta, signsReflection['X'])
theta = torch.einsum('i,i->i', theta, signsReflection['Y'])
fillColors = ['white', (0.5,0.5,0), (0,1,0), (0,0,1), (0,0,0),\
(1,0,1), (0.5,0,0.5), (0,0.5,0.5), (0,0,0.5), (0,0.5,0),\
(1,0,0), (0.5,0,0)]
microstrImages = to_torch(sio.loadmat('./data_generation/fluid/microStrImages.mat')['microstructures'])
NX = res*int(np.ceil((self.FE.mesh.meshSpec['bb']['xmax']-\
self.FE.mesh.meshSpec['bb']['xmin'])/self.FE.mesh.meshSpec['elemSize'][0]))
NY = res*int(np.ceil((self.FE.mesh.meshSpec['bb']['ymax']-\
self.FE.mesh.meshSpec['bb']['ymin'])/self.FE.mesh.meshSpec['elemSize'][1]))
nx, ny = microstrImages.shape[2], microstrImages.shape[3]
compositeImg = torch.zeros((NX*nx, NY*ny))
colorImg = torch.zeros((NX, NY))
densityImg = torch.zeros((NX, NY))
maxC = 0
step = 0.01 # THIS IS THE STEP USED WHEN GEN THE MSTR IMAGES! HC FOR NOW
cutOff = 10.98 # val above which its a dark square
cutOffLower = -0.0725
th = torch.zeros((theta.shape[0]))
dens_np = torch.zeros((size.shape[0]))
for elem in range(xy.shape[0]):
cx = int((res*xy[elem,0])/self.FE.mesh.meshSpec['elemSize'][0])
cy = int((res*xy[elem,1])/self.FE.mesh.meshSpec['elemSize'][1])
dens_np[elem] = int(100.*(C['area'][elem]))
densityImg[cx, cy] = dens_np[elem]
if(size[elem] > cutOff):
compositeImg[nx*cx:(cx+1)*nx, ny*cy:(cy+1)*ny] = torch.ones((nx, ny))
colorImg[cx, cy] = 1
elif(size[elem] < cutOffLower):
compositeImg[nx*cx:(cx+1)*nx, ny*cy:(cy+1)*ny] = torch.zeros((nx, ny))
colorImg[cx, cy] = 0
else:
mstrIdx = min(microstrImages.shape[1]-1, int((size[elem]//step)))
densityImg[cx, cy] = mstrIdx
mstrTypeIdx = torch.argmax(mstrType[elem,:])
mstrimg = to_torch(microstrImages[mstrTypeIdx, mstrIdx,:,:])
th[elem] = 90 + int(180*theta[elem]/torch.pi)
mstrimg = to_torch(rotate(mstrimg,th[elem],reshape = False, order = 0, mode = 'nearest'))
c = torch.argmax(mstrType[elem,:])+1
if(c > maxC):
maxC = c
compositeImg[nx*cx:(cx+1)*nx, ny*cy:(cy+1)*ny] = (1.-mstrimg)*c
colorImg[cx, cy] = c
plt.figure()
plt.imshow(compositeImg.T, cmap = colors.ListedColormap(fillColors[:maxC+1]),\
interpolation='none',vmin=0, vmax=maxC, origin = 'lower')
ax = plt.gca()
ax.axes.xaxis.set_ticks([])
ax.axes.yaxis.set_ticks([])
# plt.legend(['squircle', 'fishscale', 'fishscale_half', 'square', 'traingle', 'circle', 'ellipse', 'plus', 'mucosa10', 'mucosa20'])
plt.show()
plt.savefig(f'./frames/top_{self.epoch:d}.pdf', dpi=300)
plt.figure()
plt.imshow(colorImg.T, cmap = colors.ListedColormap(fillColors[:maxC+1]),\
interpolation='none',vmin=0, vmax=maxC, origin = 'lower')
ax = plt.gca()
ax.axes.xaxis.set_ticks([])
ax.axes.yaxis.set_ticks([])
plt.show()
plt.figure()
plt.imshow(100-densityImg.T, cmap = 'gray',\
interpolation='none', origin = 'lower')
plt.colorbar()
ax = plt.gca()
ax.axes.xaxis.set_ticks([])
ax.axes.yaxis.set_ticks([])
plt.show()
plt.figure()
xy = to_torch(xy)
a = plt.quiver(xy[:,0].reshape((NX, NY)),\
xy[:,1].reshape((NX, NY)), \
np.sin(np.pi*th/180.),\
np.cos(np.pi*th/180.),\
dens_np,\
cmap = 'rainbow', scale= 10, headwidth = 0.1)#plt.cm.gnuplot
plt.show()
plt.figure()
a = plt.imshow((th).reshape((NX,NY)).T, cmap = 'jet', origin = 'lower')
plt.title('orientation')
plt.colorbar(a)
plt.show()
#-----------------------#