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LV_model.py
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import os
import argparse
import time
import numpy as np
import torch
import torch.nn as nn
import torch.optim as optim
import matplotlib.pyplot as plt
import torch.nn.functional as F
parser = argparse.ArgumentParser('ODE demo')
parser.add_argument('--method', type=str, choices=['dopri5', 'adams'], default='dopri5')
parser.add_argument('--data_size', type=int, default=1000)
parser.add_argument('--batch_time', type=int, default=25)
parser.add_argument('--batch_size', type=int, default=100)
parser.add_argument('--niters', type=int, default=2000)
parser.add_argument('--test_freq', type=int, default=20)
parser.add_argument('--viz', action='store_true')
parser.add_argument('--gpu', type=int, default=0)
parser.add_argument('--adjoint', action='store_true')
args = parser.parse_args()
if args.adjoint:
from torchdiffeq import odeint_adjoint as odeint
else:
from torchdiffeq import odeint
device = torch.device('cuda:' + str(args.gpu) if torch.cuda.is_available() else 'cpu')
true_y0 = torch.tensor([[0.9, 1.8]]) # shape: 1 * 2
# true_y0 = torch.tensor([[0.1, 0.2]])
t = torch.linspace(0., 25., args.data_size) # shape: 1000
t = torch.linspace(-5., 5., args.data_size) # shape: 1000
# true_A = torch.tensor([[-0.1, 2.0], [-2.0, -0.1]]) # shape: 2 * 2
true_A = torch.tensor([[2.0/3, -4.0/3], [1, -1]])
# true_A = torch.tensor([[0, 1], [-1, 0.85]])
#
# true_A = torch.tensor([[0, 1], [-1, -0.45]])
class Lambda(nn.Module):
# In this code, row vector: y'^T = y^T A^T textbook format: column vector y' = A y
def forward(self, t, y):
# return F.leaky_relu(torch.mm(y**3, true_A))
# return F.tanh(torch.mm(y ** 3, true_A))
# return torch.mm(y ** 3, true_A)
# return torch.mm(y ** 3, true_A)
x = torch.tensor([[y[0, 0], y[0, 0] * y[0, 1]], [y[0, 0] * y[0, 1], y[0, 1]]])
y1 = torch.diag(torch.mm(x, true_A.t()))
# y1 = F.tanh(y1)
# result = y1/torch.sum(y1)
# result = F.normalize(y1)
# return torch.mm(y, true_A.t())
return y1
with torch.no_grad():
true_y = odeint(Lambda(), true_y0, t, method='dopri5') # shape: 1000 * 1 * 2
print(true_y.shape) # batchsize*1*2
# my = torch.mean(true_y[:,0,1])
# vy = torch.std(true_y[:,0,1])
# true_y[:,0,1] = (true_y[:,0,1] - my) / vy
#
# mx = torch.mean(true_y[:, 0, 0])
# vx = torch.std(true_y[:, 0, 0])
# true_y[:, 0, 1] = (true_y[:, 0, 1] - mx) / vx
# test ground truth
plt.plot(true_y[:,0,0].numpy(), true_y[:,0,1].numpy(), '-o')
plt.show()
def get_batch():
s = torch.from_numpy(np.random.choice(np.arange(args.data_size - args.batch_time, dtype=np.int64), args.batch_size, replace=False))
# s: 20
batch_y0 = true_y[s] # (M, D) 500*1*2
batch_y0 = batch_y0.squeeze() # 500 * 2
batch_t = t[:args.batch_time] # (T) 19
batch_y = torch.stack([true_y[s + i] for i in range(args.batch_time)], dim=0)
# (T, M, D) 19*500*1*2 from s and its following batch_time sample
batch_y = batch_y.squeeze() # 19 * 500 * 2
return batch_y0, batch_t, batch_y
def makedirs(dirname):
if not os.path.exists(dirname):
os.makedirs(dirname)
if args.viz:
makedirs('png')
import matplotlib.pyplot as plt
fig = plt.figure(figsize=(12, 4), facecolor='white')
ax_traj = fig.add_subplot(131, frameon=False)
ax_phase = fig.add_subplot(132, frameon=False)
ax_vecfield = fig.add_subplot(133, frameon=False)
fig.tight_layout()
# plt.show(block=False)
def visualize(true_y, pred_y, odefunc, itr):
if args.viz:
ax_traj.cla()
ax_traj.set_title('Trajectories')
ax_traj.set_xlabel('t')
ax_traj.set_ylabel('x,y')
ax_traj.plot(t.numpy(), true_y.numpy()[:, 0, 0], t.numpy(), true_y.numpy()[:, 0, 1], 'g-')
ax_traj.plot(t.numpy(), pred_y.numpy()[:, 0, 0], '--', t.numpy(), pred_y.numpy()[:, 0, 1], 'b--')
ax_traj.set_xlim(t.min(), t.max())
ax_traj.set_ylim(-2, 5)
# ax_traj.legend()
# plt.show()
ax_phase.cla()
ax_phase.set_title('Phase Portrait')
ax_phase.set_xlabel('x')
ax_phase.set_ylabel('y')
ax_phase.plot(true_y.numpy()[:, 0, 0], true_y.numpy()[:, 0, 1], 'g-')
ax_phase.plot(pred_y.numpy()[:, 0, 0], pred_y.numpy()[:, 0, 1], 'b--')
ax_phase.set_xlim(-2, 5)
ax_phase.set_ylim(-2, 5)
# plt.show()
ax_vecfield.cla()
ax_vecfield.set_title('Learned Vector Field')
ax_vecfield.set_xlabel('x')
ax_vecfield.set_ylabel('y')
y, x = np.mgrid[-2:2:21j, -2:2:21j]
dydt = odefunc(0, torch.Tensor(np.stack([x, y], -1).reshape(21 * 21, 2))).cpu().detach().numpy()
mag = np.sqrt(dydt[:, 0]**2 + dydt[:, 1]**2).reshape(-1, 1)
dydt = (dydt / mag)
dydt = dydt.reshape(21, 21, 2)
ax_vecfield.streamplot(x, y, dydt[:, :, 0], dydt[:, :, 1], color="black")
ax_vecfield.set_xlim(-2, 5)
ax_vecfield.set_ylim(-2, 5)
plt.show()
fig.savefig('png/{:03d}'.format(itr))
plt.draw()
plt.pause(0.001)
class ODEFunc(nn.Module):
def __init__(self):
super(ODEFunc, self).__init__()
# self.net = nn.Sequential(
# nn.Linear(2, 10),
# #nn.BatchNorm1d(10),
# nn.Tanh(), # nn.ReLU(), #
# nn.Linear(10, 2) #,
# # nn.BatchNorm1d(2),
# )
self.net = nn.Sequential(
nn.Linear(2, 20),
nn.Tanh(),
nn.Linear(20, 2),
)
# self.scale = nn.Parameter(torch.FloatTensor([1])) # [0.01])) # np.random.rand(1) *
# self.bias = nn.Parameter(torch.FloatTensor([0]))
# for m in self.net.modules():
# if isinstance(m, nn.Linear):
# # nn.init.normal_(m.weight, mean=0, std=0.1)
# # nn.init.constant_(m.bias, val=0)
# nn.init.normal_(m.weight, mean=0, std=0.1)
# nn.init.normal_(m.bias, mean=1, std=1)
# # nn.init.constant_(m.bias, val=0)
def forward(self, t, y):
# z = y*1.0
# z[:,0,1] = y[:,0,0] * y[:,0,1]
# A = torch.tensor([[0.5, 0.5], [0.5, 0.5]])
result = self.net(y) #* self.scale + self.bias
return result #self.net(y) * self.scale + self.bias #*self.scale y = batchsize * 1 * 2
class RunningAverageMeter(object):
"""Computes and stores the average and current value"""
def __init__(self, momentum=0.99):
self.momentum = momentum
self.reset()
def reset(self):
self.val = None
self.avg = 0
def update(self, val):
if self.val is None:
self.avg = val
else:
self.avg = self.avg * self.momentum + val * (1 - self.momentum)
self.val = val
if __name__ == '__main__':
ii = 0
func = ODEFunc()
# optimizer = optim.RMSprop(func.parameters(), lr=1e-3)
optimizer = optim.Adam(func.parameters(), lr=1e-2, weight_decay=1e-3)
end = time.time()
time_meter = RunningAverageMeter(0.97)
loss_meter = RunningAverageMeter(0.97)
for itr in range(1, args.niters + 1):
optimizer.zero_grad()
batch_y0, batch_t, batch_y = get_batch() # batch_y0: 20*1*2 batch_t:10 batch_y: 10*20*1*2
# batch_y0 = true_y0
# batch_t = t
# batch_y = true_y
pred_y = odeint(func, batch_y0, batch_t, method='rk4' ) # 'dopri5'
# loss = torch.mean(torch.abs(pred_y - batch_y))
# loss = F.mse_loss(pred_y, batch_y)
loss = F.l1_loss(pred_y, batch_y)
loss.backward()
optimizer.step()
time_meter.update(time.time() - end)
loss_meter.update(loss.item())
if itr % args.test_freq == 0:
with torch.no_grad():
pred_y = odeint(func, true_y0, t)
loss = torch.mean(torch.abs(pred_y - true_y))
print('Iter {:04d} | Total Loss {:.6f}'.format(itr, loss.item()))
visualize(true_y, pred_y, func, ii)
ii += 1
end = time.time()