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utils.py
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import numpy as np
import torch
import torch.nn as nn
from torch.autograd import grad, Variable
import pandas as pd
from sklearn.preprocessing import StandardScaler
def data_preprocessing(data_name, data_dir, device):
df = pd.read_csv(data_dir+data_name+".csv")
time_column = df.columns[0]
data_column = df.columns[1:]
time_trace = df[data_column].to_numpy().T
scaled_trace = time_trace.copy()
ss = StandardScaler()
scaled_trace = ss.fit_transform(scaled_trace)
scaled_trace = torch.FloatTensor(scaled_trace).unsqueeze(1).to(device)
mean_scaled_trace = scaled_trace.mean(axis=0).unsqueeze(1)
time_trace = torch.FloatTensor(time_trace).unsqueeze(1).to(device)
obs_time = torch.FloatTensor(df[time_column].values).unsqueeze(1).to(device)
return obs_time, time_trace, scaled_trace, mean_scaled_trace
def kl_divergence(mu, log_var):
kl = torch.mean(- 0.5 * torch.sum(1+ log_var - mu.pow(2) - log_var.exp(), axis=2))
return kl
def cal_der(y, x, device) :
return grad(y, x, create_graph=True, grad_outputs=torch.ones(y.size()).to(device))[0]
def train(model, optimizer, loss_f, loss_kl, col_time, obs_time, time_trace, beta, device, s_min=0.5, s_max=2) :
obs = obs_time.repeat(model.data.size()[0],1,1)
col = col_time.repeat(model.data.size()[0],1,1)
t_v = Variable(col, requires_grad = True)
mu, log_var = model.encoder()
model.z = model.reparameterization(mu, log_var)
s, tilde_g, tilde_y = model(t_v)
if s_max == None:
s_penalty = (torch.abs(s-((beta)/s_min**2))).mean()
else:
s_penalty = (torch.abs(s-((1-beta)/s_max**2+beta/s_min**2))).mean()
lb, ld = model.pred_lmda()
pred_lb = lb.repeat(1,1,len(col_time))
pred_ld = ld.repeat(1,1,len(col_time))
y_t = cal_der(tilde_y, t_v, device)[:,:,0].view(tilde_y.size())
_, _, tilde_y_obs = model(obs)
optimizer.zero_grad()
physics_loss = loss_f(y_t, - pred_ld*tilde_y + pred_lb*tilde_g)
data_loss = loss_f(tilde_y_obs, time_trace)
reg_loss = loss_kl(mu, log_var)+s_penalty
loss = physics_loss+data_loss+reg_loss
loss.backward(retain_graph=True)
optimizer.step()
return physics_loss.item(), data_loss.item(), reg_loss.item()
class MDN(nn.Module):
def __init__(self, d, final_time, device, K = 4, h = 16, M=80, s_min = 0.5, s_max = 2):
super(MDN, self).__init__()
self.d = d
self.final_time = final_time
self.d = d
self.M = M
self.latent_dim = K
self.hidden_dim = h
self.s_min = s_min
self.s_max = s_max
self.enc_hidden1 = nn.Linear(self.d, self.hidden_dim)
self.enc_hidden2 = nn.Linear(self.hidden_dim, self.hidden_dim)
self.latent_mu = nn.Linear(self.hidden_dim, self.latent_dim)
self.latent_logvar = nn.Linear(self.hidden_dim, self.latent_dim)
self.decoder_hidden3_1 = nn.Linear(self.latent_dim, self.hidden_dim)
self.decoder_lb = nn.Linear(self.hidden_dim, 1)
self.decoder_hidden3_2 = nn.Linear(self.latent_dim, self.hidden_dim)
self.decoder_ld = nn.Linear(self.hidden_dim, 1)
self.decoder_hidden4 = nn.Linear(self.latent_dim, self.hidden_dim)
self.decoder_hidden5 = nn.Linear(self.hidden_dim, self.hidden_dim)
self.decoder_w = nn.Linear(self.hidden_dim, self.M)
self.decoder_hidden6 = nn.Linear(self.latent_dim, self.hidden_dim)
self.decoder_hidden7 = nn.Linear(self.hidden_dim, self.hidden_dim)
self.decoder_s = nn.Linear(self.hidden_dim, self.M)
self.nn_hidden8 = nn.Linear(self.M, self.M)
self.nn_wprime = nn.Linear(self.M, self.M)
self.ELU = nn.ELU()
self.Sigmoid = nn.Sigmoid()
self.Softmax = nn.Softmax(dim=2)
self.device = device
def encoder(self):
enc = self.ELU(self.enc_hidden1(self.data))
enc = self.ELU(self.enc_hidden2(enc))
mean = self.latent_mu(enc)
logvar = self.latent_logvar(enc)
return mean, logvar
def reparameterization(self, mean, logvar):
var = torch.exp(0.5 * logvar)
epsilon = torch.randn_like(var) # sampling epsilon
z = mean + var*epsilon # reparameterization trick
return z
def pred_lmda(self):
lb = self.ELU(self.decoder_hidden3_1(self.z))
lb = self.ELU(self.decoder_lb(lb))+1
ld = self.ELU(self.decoder_hidden3_2(self.z))
ld = self.ELU(self.decoder_ld(ld))+1
return lb, ld # return lambda_b, lambda_d
def reconstruct(self):
w = self.ELU(self.decoder_hidden4(self.z))
w = self.ELU(self.decoder_hidden5(w))
#w = self.Softmax(self.decoder_w(w))
w = self.ELU(self.decoder_w(w))+1 # You can also use self.Softmax instead of ELU+1
w = w/(w.sum(axis=2).unsqueeze(1)) # You can also use self.Softmax instead of ELU+1
s = self.ELU(self.decoder_hidden6(self.z))
s = self.ELU(self.decoder_hidden7(s))
s = self.decoder_s(s)
s = (1/self.s_min**2-1/self.s_max**2)*self.Sigmoid(s)+1/self.s_max**2
wprime = self.ELU(self.nn_hidden8(w))
wprime = self.ELU(self.nn_wprime(wprime))+1
return s, w, wprime
def Rayleigh(self, t, w, mu, s): # mixture of CDF Rayleigh distributions
MDN = -1*torch.max(torch.zeros_like(mu),1.1*s*(t-mu)-(1-torch.exp(-s*((t-mu)**2)/2)))
MDN += torch.max(torch.zeros_like(t), 1.1*s*(t-mu))
return (w*MDN).sum(axis=2).unsqueeze(1)
def forward(self, t):
s, w, wprime = self.reconstruct() # scale factor is square-inversed for a computational convenience.
s = s.repeat(1,t.size()[1],1)
w = w.repeat(1,t.size()[1],1)
wprime = wprime.repeat(1,t.size()[1],1)
t = t.repeat(1,1,self.M)
mu_g = torch.linspace(0,int(self.final_time),self.M).repeat(w.size()[0],w.size()[1],1).to(self.device)
mu_y = torch.linspace(0,int(self.final_time),self.M).repeat(wprime.size()[0],wprime.size()[1],1).to(self.device)
tilde_g = self.Rayleigh(t,w,mu_g,s)
tilde_y = self.Rayleigh(t,wprime,mu_y,s)
return s, tilde_g, tilde_y
def mean_w(model, mean_scaled_trace, time_trace, n_sample_traj=1000, is_scale = True):
model.data = mean_scaled_trace.repeat(n_sample_traj,1,1)
mu, log_var = model.encoder()
model.z = model.reparameterization(mu, log_var)
s, w, _ = model.reconstruct()
model.data = time_trace
if is_scale:
w_mean = ten_to_npy(w*torch.sqrt(s)).mean(axis=0).reshape(-1)
w_std = ten_to_npy(w*torch.sqrt(s)).std(axis=0).reshape(-1)
else:
w_mean = ten_to_npy(w).mean(axis=0).reshape(-1)
w_std = ten_to_npy(w).std(axis=0).reshape(-1)
return w_mean, w_std
def derivative_penalty(obs_y, target_size):
target_size
interpol_size = 1
der_y = torch.zeros_like(obs_y)
for k in range(len(obs_y)):
der_y[k] = moving_average(obs_y[k],7).view(1,-1)
der_y = torch.gradient(der_y, axis=2)[0]
der_y[torch.where(der_y < 0)] = 0
der_y = torch.abs(der_y)
while obs_y.size()[-1]*interpol_size <= target_size:
interpol_size +=1
der_penalty = (der_y-der_y.min(axis=2).values.unsqueeze(1))/(der_y.max(axis=2).values.unsqueeze(1)-der_y.min(axis=2).values.unsqueeze(1))
if interpol_size != 1:
der_diff = (der_penalty[:,:,1:]-der_penalty[:,:,:-1])/interpol_size
der_penalty = der_penalty.repeat_interleave(interpol_size, dim=2)
return der_penalty[:,:,:target_size]
def ten_to_npy(x):
return x.detach().cpu().numpy()
def moving_average(x, n):
x_roll = x.clone()
x_tmp = torch.zeros_like(x)
for k in range(-n+1,n):
x_tmp += torch.roll(x,k, dims=0)
x_tmp = x_tmp/(2*(n-1)+1)
x_roll[n:-n] = x_tmp[n:-n]
for k in range(1,n):
x_roll[0][-k] = x[0][-n-k:-k].mean()
return x_roll