/
ode_demo.py
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/
ode_demo.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
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=10)
parser.add_argument('--batch_size', type=int, default=20)
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([[2., 0.]]).to(device)
t = torch.linspace(0., 25., args.data_size).to(device)
true_A = torch.tensor([[-0.1, 2.0], [-2.0, -0.1]]).to(device)
class Lambda(nn.Module):
def forward(self, t, y):
return torch.mm(y**3, true_A)
with torch.no_grad():
true_y = odeint(Lambda(), true_y0, t, method='dopri5')
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))
batch_y0 = true_y[s] # (M, D)
batch_t = t[:args.batch_time] # (T)
batch_y = torch.stack([true_y[s + i] for i in range(args.batch_time)], dim=0) # (T, M, D)
return batch_y0.to(device), batch_t.to(device), batch_y.to(device)
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)
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.cpu().numpy(), true_y.cpu().numpy()[:, 0, 0], t.cpu().numpy(), true_y.cpu().numpy()[:, 0, 1], 'g-')
ax_traj.plot(t.cpu().numpy(), pred_y.cpu().numpy()[:, 0, 0], '--', t.cpu().numpy(), pred_y.cpu().numpy()[:, 0, 1], 'b--')
ax_traj.set_xlim(t.cpu().min(), t.cpu().max())
ax_traj.set_ylim(-2, 2)
ax_traj.legend()
ax_phase.cla()
ax_phase.set_title('Phase Portrait')
ax_phase.set_xlabel('x')
ax_phase.set_ylabel('y')
ax_phase.plot(true_y.cpu().numpy()[:, 0, 0], true_y.cpu().numpy()[:, 0, 1], 'g-')
ax_phase.plot(pred_y.cpu().numpy()[:, 0, 0], pred_y.cpu().numpy()[:, 0, 1], 'b--')
ax_phase.set_xlim(-2, 2)
ax_phase.set_ylim(-2, 2)
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)).to(device)).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, 2)
ax_vecfield.set_ylim(-2, 2)
fig.tight_layout()
plt.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, 50),
nn.Tanh(),
nn.Linear(50, 2),
)
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)
def forward(self, t, y):
return self.net(y**3)
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().to(device)
optimizer = optim.RMSprop(func.parameters(), lr=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()
pred_y = odeint(func, batch_y0, batch_t).to(device)
loss = torch.mean(torch.abs(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()