def train(x_1, t):
N_epoch = 200
lr = 0.01
x_0 = np.array([0.0, 0.0]).reshape(-1, 1)
loss = []
plt.ion()
cnt = 0
for epoch in range(N_epoch):
x_1_prd = myode(f, x_0, t, is_full_state=False) #前向ode
a_1 = (x_1_prd - x_1) # dL/dx1
a_0 = myode(g, a_1, t[::-1], is_full_state=False) #反向ode
x_0 = x_0 - lr * a_0
ls = np.mean(a_1 * a_1)
loss.append(ls)
print('loss:', ls)
if epoch % (N_epoch // 10) == 0:
plt.cla()
trajectory_sample(x_0, t)
plt.plot(x_1[0], x_1[1], 'pm')
plt.plot(x_0[0], x_0[1], '*k')
plt.xlim(-1.5, 1.5)
plt.ylim(-1.5, 1.5)
plt.legend(['Trajectory', 'Target state', 'Initial state'], loc=4, fontsize=fontsize-4)
plt.xlabel('$x_1$', fontsize=fontsize)
plt.ylabel('$x_2$', fontsize=fontsize)
plt.savefig(main_image_path + "png_{}.png".format(cnt))
cnt += 1
plt.pause(0.1)
get_gif(cnt, gif_name='ode_init.gif')
plt.ioff()
plt.show()
return x_0
def train(x_1, t):
N_epoch = 350
lr = 0.01
x_0 = np.array([0.0, 0.0]).reshape(-1, 1)
A = np.random.uniform(-1, 1, size=(2, 2))
A_init = A.copy()
print('initial A:\n', A)
loss = []
x_0_list = [x_0.flatten()]
A_list = [A.flatten()]
plt.figure(figsize=(12, 5))
plt.ion()
cnt = 0
for epoch in range(N_epoch):
x_1_prd = myode(f, x_0, t, A, is_full_state=False) #前向ode
a_1 = (x_1_prd - x_1) # dL/dx1
x_0_back, a_0, A_grad = myode(h, [x_1_prd, a_1, np.zeros_like(A)], t[::-1], A, is_full_state=False) #反向ode
x_0 = x_0 - lr * a_0
A = A - lr * A_grad
x_0_list.append(x_0.flatten())
A_list.append(A.flatten())
ls = np.mean(a_1 * a_1)
loss.append(ls)
# print('loss:', ls)
if epoch % (N_epoch // 10) == 0:
plt.cla()
plt.subplot(1, 2, 1)
trajectory_sample(x_0, t, A)
plt.plot(x_1[0], x_1[1], 'pm')
plt.plot(x_0[0], x_0[1], '*k')
plt.xlim(-1.5, 1.5)
plt.ylim(-1.5, 1.5)
plt.legend(['Trajectory', 'Target state', 'Initial state'], loc=4, fontsize=fontsize-4)
plt.xlabel('$x_1$', fontsize=fontsize)
plt.ylabel('$x_2$', fontsize=fontsize)
plt.subplot(1, 2, 2)
# plt.cla()
tmp = np.array(A_list)
for i in range(len(A.flatten())):
plt.plot(tmp[:, i])
plt.legend(['$A_{11}$', '$A_{12}$', '$A_{21}$', '$A_{22}$'], loc=4, fontsize=fontsize-4)
plt.xlabel('Training steps', fontsize=fontsize)
plt.savefig(main_image_path + "png_{}.png".format(cnt))
cnt += 1
plt.pause(0.1)
get_gif(cnt, gif_name='ode_init_model.gif')
print('initial A:\n', A_init)
print('final A:\n', A)
print('x(0):\n', x_0)
plt.ioff()
plt.show()
return x_0
def train(_y, _t, method='euler_step'):
x_0 = np.array([2.0, 0.0]).reshape(1, -1)
A = np.random.uniform(-1, 1, size=(2, 2))
A_init = A.copy()
print('initial A:\n', A)
loss = []
x_0_list = [x_0.flatten()]
W1_list, W2_list = [], []
lr = LR
plt.figure(figsize=(18, 6))
plt.ion()
m_t_1, v_t_1 = np.zeros_like(ode_func.W1), np.zeros_like(ode_func.W1)
m_t_2, v_t_2 = np.zeros_like(ode_func.W2), np.zeros_like(ode_func.W2)
m_t_3, v_t_3 = np.zeros_like(ode_func.b1), np.zeros_like(ode_func.b1)
cnt = 0
for epoch in range(N_epoch):
batch_x_0, batch_t = get_batch()
batch_x_1 = myode(f,
batch_x_0,
batch_t,
method=method,
is_full_state=False) #前向ode
a_1, ls = dLdx1(batch_x_1) # dL/dx1
print('#' * 100)
print('batch_x_0 shape:', batch_x_0.shape)
print('batch_x_1 shape:', batch_x_1.shape)
print('a_1 shape:', a_1.shape)
x_0_back, a_0, W1_grad, W2_grad, b1_grad = myode(
h, [
batch_x_1, a_1,
np.zeros_like(ode_func.W1),
np.zeros_like(ode_func.W2),
np.zeros_like(ode_func.b1)
],
batch_t[::-1],
method=method,
is_full_state=False) #反向ode
# x_0 = x_0 - lr * a_0
# ode_func.W1 -= lr * W1_grad
# ode_func.W2 -= lr * W2_grad
ode_func.W1, m_t_1, v_t_1 = my_adam(theta=ode_func.W1,
g_t=W1_grad,
m_t=m_t_1,
v_t=v_t_1,
t=epoch + 1)
ode_func.W2, m_t_2, v_t_2 = my_adam(theta=ode_func.W2,
g_t=W2_grad,
m_t=m_t_2,
v_t=v_t_2,
t=epoch + 1)
ode_func.b1, m_t_3, v_t_3 = my_adam(theta=ode_func.b1,
g_t=b1_grad,
m_t=m_t_3,
v_t=v_t_3,
t=epoch + 1)
W1_list.append(ode_func.W1.flatten())
W2_list.append(ode_func.W2.flatten())
x_0_list.append(x_0.flatten())
loss.append(ls)
print('loss:', ls)
if epoch % (N_epoch // 10) == 0:
lr *= 0.9
# lr *= 0.7
plt.clf()
plt.subplot(1, 3, 1)
plt.xlabel('epoch', fontsize=fontsize)
plt.ylabel('loss', fontsize=fontsize)
plt.plot(loss)
plt.subplot(1, 3, 2)
plt.plot(batch_x_0[:, 0], batch_x_0[:, 1], 'k*')
plt.xlabel('$x_1$', fontsize=fontsize)
plt.ylabel('$x_2$', fontsize=fontsize)
plt.subplot(1, 3, 3)
plt.plot(batch_x_1[:, 0], batch_x_1[:, 1], 'ro')
plt.xlabel('$x_1$', fontsize=fontsize)
plt.ylabel('$x_2$', fontsize=fontsize)
# trajectory_sample(f, x_0, _t, method=method)
# # plt.plot(x_1[0], x_1[1], 'pm')
#
# _A = np.array([[-0.1, 2.0], [-2.0, -0.1]])
# trajectory_sample(f_true, x_0, _t, method=method, xz='r--')
#
# plt.plot(x_0[:, 0], x_0[:, 1], '*k')
#
# scale = 2.5
# plt.xlim(-scale, scale)
# plt.ylim(-scale, scale)
#
# plt.legend(['Trajectory', 'True Trajectory', 'Initial state'], loc=4)
# plt.subplot(2, 2, 2)
# tmp1 = np.array(W1_list)
# for i in range(len(ode_func.W1.flatten())):
# plt.plot(tmp1[:, i])
# plt.ylabel('$W_1$')
#
# plt.subplot(2, 2, 4)
# tmp1 = np.array(W2_list)
# for i in range(len(ode_func.W2.flatten())):
# plt.plot(tmp1[:, i])
# # plt.legend(['$A_{11}$', '$A_{12}$', '$A_{21}$', '$A_{22}$'], loc=4)
# plt.xlabel('Training steps')
# plt.ylabel('$W_2$')
plt.savefig(main_image_path + "png_{}.png".format(cnt))
cnt += 1
plt.pause(0.1)
get_gif(cnt, gif_name=gif_name)
# print('initial A:\n', A_init)
# print('final A:\n', A)
# print('True A:\n', _A)
# print('x(0):\n', x_0)
print('lr final:', lr)
plt.ioff()
return x_0
def train(_y, _t):
N_epoch = 1000
lr = 0.1
x_0 = np.array([2.0, 0.0]).reshape(1, -1)
A = np.random.uniform(-1, 1, size=(2, 2))
A_init = A.copy()
print('initial A:\n', A)
loss = []
x_0_list = [x_0.flatten()]
A_list = [A.flatten()]
plt.figure(figsize=(13, 6))
plt.ion()
cnt = 0
for epoch in range(N_epoch):
batch_x0, batch_t, batch_x = get_batch(_y, _t)
batch_x_prd = myode(f, batch_x0, batch_t, A,
is_full_state=True) #前向ode
# print('batch_x0 shape:', batch_x0.shape)
# print('batch_x shape:', batch_x.shape)
# print('batch_x_prd shape:', batch_x_prd.shape)
a_1 = (batch_x_prd - batch_x) # dL/dx1
x_0_back, a_0, A_grad = myode(
h, [batch_x_prd[::-1], a_1[::-1],
np.zeros_like(A)],
batch_t[::-1],
A,
is_full_state=False) #反向ode
# x_0 = x_0 - lr * a_0
A = A - lr * A_grad
x_0_list.append(x_0.flatten())
A_list.append(A.flatten())
ls = np.mean(a_1 * a_1)
loss.append(ls)
print('loss:', ls)
if epoch % (N_epoch // 10) == 0:
plt.clf()
plt.subplot(1, 2, 1)
trajectory_sample(x_0, _t, A, method='euler_step')
# plt.plot(x_1[0], x_1[1], 'pm')
_A = np.array([[-0.1, 2.0], [-2.0, -0.1]])
trajectory_sample(x_0, _t, _A, method='euler_step', xz='r--')
plt.plot(x_0[:, 0], x_0[:, 1], '*k')
scale = 2.5
plt.xlim(-scale, scale)
plt.ylim(-scale, scale)
plt.legend(['Trajectory', 'True Trajectory', 'Initial state'],
loc=4,
fontsize=fontsize - 4)
plt.xlabel('$x_1$', fontsize=fontsize)
plt.ylabel('$x_2$', fontsize=fontsize)
plt.subplot(1, 2, 2)
# plt.cla()
tmp = np.array(A_list)
for i in range(len(A.flatten())):
plt.plot(tmp[:, i])
plt.legend(['$A_{11}$', '$A_{12}$', '$A_{21}$', '$A_{22}$'],
loc=4,
fontsize=fontsize - 4)
plt.xlabel('Training steps', fontsize=fontsize)
plt.ylabel('$W_2$', fontsize=fontsize)
plt.savefig(main_image_path + "png_{}.png".format(cnt))
cnt += 1
plt.pause(0.1)
get_gif(cnt, gif_name='ode_model.gif')
print('initial A:\n', A_init)
print('final A:\n', A)
print('True A:\n', _A)
print('x(0):\n', x_0)
plt.ioff()
plt.show()
return x_0