class ForwardSolverFHNDiff:
def __init__(self, point_cloud, diffusion_model, interpolated_spacing,
order_acc, fhn_model):
self.fhn_model = fhn_model
self.point_cloud = point_cloud
self.diffusion_model = diffusion_model
self.interpolated_spacing = interpolated_spacing
self.order_acc = order_acc
self.ut = Utils()
self.coeff_matrix_first_der = None
self.coeff_matrix_second_der = None
self.ut = Utils()
def solve(self, dt, duration):
assert self.diffusion_model.nn_u0.shape[
0] == 1, 'first axis of nn_u must be 1, indicating nn_u0'
assert self.diffusion_model.u0.shape[
0] == 1, 'first axis of u must be 1, indicating u0'
assert self.fhn_model.V0.shape[
0] == 1, 'first axis of u must be 1, indicating V0'
assert self.fhn_model.v0.shape[
0] == 1, 'first axis of u must be 1, indicating v0'
coeff_matrix_first_der = self.coeff_matrix_first_der.copy()
coeff_matrix_second_der = self.coeff_matrix_second_der.copy()
V = np.squeeze(self.fhn_model.V0).copy()
v = np.squeeze(self.fhn_model.v0).copy()
time_pt = np.linspace(0,
duration,
int(duration / dt) + 1,
endpoint=True,
dtype='float64')
V_update = []
v_update = []
V_update.append(V)
v_update.append(v)
for t in range(1, len(time_pt)):
print('time: {}'.format(t * dt))
# ==== FHN MODEL ====
fast_v = self.fhn_model.fast_variable(V, v)
slow_v = self.fhn_model.slow_variable(V, v)
applied_current = self.fhn_model.applied_current
# === DIFFUSION MODEL ===
deltaD_deltaV = self.diffusion_model.del_D_delV(V, self.interpolated_spacing, self.order_acc, \
coeff_matrix_first_der, coeff_matrix_second_der)
dVdt = deltaD_deltaV + fast_v + applied_current
dvdt = slow_v
next_time_pt_V = V + dt * dVdt
next_time_pt_v = v + dt * dvdt
if next_time_pt_V.size > 1:
assert sum(np.isnan(next_time_pt_V)
) == 0, 'at time {}, next_time_pt_V has nan'.format(
t * dt)
assert sum(np.isnan(next_time_pt_v)
) == 0, 'at time {}, next_time_pt_v has nan'.format(
t * dt)
assert next_time_pt_V.shape[0] == next_time_pt_v.shape[
0], 'V and v has different length'
elif next_time_pt_V.size == 1:
assert np.isnan(
next_time_pt_V
) == False, 'at time {}, next_time_pt_V has nan'.format(t * dt)
assert np.isnan(
next_time_pt_v
) == False, 'at time {}, next_time_pt_v has nan'.format(t * dt)
V = next_time_pt_V.copy()
v = next_time_pt_v.copy()
V_update.append(V)
v_update.append(v)
V_update = np.array(V_update, dtype='float64')
v_update = np.array(v_update, dtype='float64')
return V_update, v_update, time_pt
def generate_first_der_coeff_matrix(self):
coeff = self.ut.OA_coeff(self.order_acc)
input_length = np.shape(self.point_cloud.intp_coord_axis1)[1]
coeff_matrix_first_der = self.ut.coeff_matrix_first_order(
input_length, coeff)
self.coeff_matrix_first_der = coeff_matrix_first_der.copy()
return
def generate_second_der_coeff_matrix(self):
coeff = self.ut.OA_coeff(self.order_acc)
input_length2 = np.shape(
self.point_cloud.intp_coord_axis1)[1] - len(coeff) + 1
coeff_matrix_second_der = self.ut.coeff_matrix_first_order(
input_length2, coeff)
self.coeff_matrix_second_der = coeff_matrix_second_der.copy()
return
class InverseSolverFHNDiff:
def __init__(self, fhn_dl_model, diff_dl_model, order_acc):
self.fhn_dl_model = fhn_dl_model
self.diff_dl_model = diff_dl_model
self.order_acc = order_acc
self.ut = Utils()
self.tf_coeff_matrix_first_der = None
self.tf_coeff_matrix_second_der = None
return
def solve(self, num_epochs, batch_size, tf_loss, tf_optimizer):
duration = self.fhn_dl_model.t[-1]
dt = self.fhn_dl_model.t[1] - self.fhn_dl_model.t[0]
tf_V = self.fhn_dl_model.tf_V.__copy__()
tf_v = self.fhn_dl_model.tf_v.__copy__()
tf_dVdt = self.fhn_dl_model.tf_dVdt.__copy__()
tf_dvdt = self.fhn_dl_model.tf_dvdt.__copy__()
tf_intp_V_axis1 = self.diff_dl_model.tf_intp_u_axis1.__copy__()
tf_intp_V_axis2 = self.diff_dl_model.tf_intp_u_axis2.__copy__()
tf_coeff_matrix_first_der = self.tf_coeff_matrix_first_der.__copy__()
tf_coeff_matrix_second_der = self.tf_coeff_matrix_second_der.__copy__()
n_training_epoch = []
training_loss = []
batch_iteration = int(int(duration / dt) / batch_size)
lowest_loss_value = 1e9
for epoch in range(num_epochs):
loss_value = 0
# loss_value_dVdt = 0
# loss_value_dvdt = 0
for iteration in range(batch_iteration):
begin = [iteration * batch_size, 0, 0]
size = [(iteration + 1) * batch_size, tf_intp_V_axis1.shape[1],
tf_intp_V_axis1.shape[2]]
tf_intp_V_axis1_tmp = tf.slice(tf_intp_V_axis1, begin, size)
tf_intp_V_axis2_tmp = tf.slice(tf_intp_V_axis2, begin, size)
begin = [iteration * batch_size, 0, 0]
size = [(iteration + 1) * batch_size, tf_dVdt.shape[1],
tf_dVdt.shape[2]]
tf_V_tmp = tf.slice(tf_V, begin, size)
tf_v_tmp = tf.slice(tf_v, begin, size)
tf_dVdt_tmp = tf.slice(tf_dVdt, begin, size)
tf_dvdt_tmp = tf.slice(tf_dvdt, begin, size)
with tf.GradientTape(persistent=True) as tape:
tf_diffusion_term = self.diff_dl_model.call_dl_model(
tf_intp_V_axis1_tmp, tf_intp_V_axis2_tmp,
tf_coeff_matrix_first_der, tf_coeff_matrix_second_der,
self.order_acc)
tf_fast_variable = self.fhn_dl_model.fast_variable(
tf_V_tmp, tf_v_tmp)
tf_slow_variable = self.fhn_dl_model.slow_variable(
tf_V_tmp, tf_v_tmp)
tf_dVdt_pred = tf_diffusion_term + tf_fast_variable + self.fhn_dl_model.tf_weight_current
tf_dvdt_pred = tf_slow_variable
pred = tf_dVdt_pred + tf_dvdt_pred
true = tf_dVdt_tmp + tf_dvdt_tmp
loss_value += tf_loss(true, pred)
# == calculate gradient and update variables =====
grads_diff = tape.gradient(
loss_value, self.diff_dl_model.trainable_weights)
tf_optimizer.apply_gradients(
zip(grads_diff, self.diff_dl_model.trainable_weights))
grads_fhn = tape.gradient(loss_value,
self.fhn_dl_model.trainable_weights)
tf_optimizer.apply_gradients(
zip(grads_fhn, self.fhn_dl_model.trainable_weights))
del tape
average_loss = loss_value.numpy() / batch_iteration
lowest_loss_value = self.check_if_avg_loss_lower_than_lowest_loss_value(
lowest_loss_value, average_loss)
n_training_epoch.append(epoch)
training_loss.append(average_loss)
if epoch % 1 == 0:
print('epoch {}/{}: loss{}'.format(epoch, num_epochs,
average_loss))
print('avg_weight_D: {0:0.4f}'.format(
tf.reduce_mean(self.diff_dl_model.tf_weight_D).numpy()))
print('avg_weight_a: {0:0.4f}'.format(
tf.reduce_mean(self.fhn_dl_model.tf_weight_a).numpy()))
print('avg_weight_epsilon: {0:0.4f}'.format(
tf.reduce_mean(
self.fhn_dl_model.tf_weight_epsilon).numpy()))
print('avg_weight_beta: {0:0.4f}'.format(
tf.reduce_mean(self.fhn_dl_model.tf_weight_beta).numpy()))
print('avg_weight_gamma: {0:0.4f}'.format(
tf.reduce_mean(self.fhn_dl_model.tf_weight_gamma).numpy()))
print('avg_weight_delta: {0:0.4f}'.format(
tf.reduce_mean(self.fhn_dl_model.tf_weight_delta).numpy()))
print('\n')
n_training_epoch = np.array(n_training_epoch)
training_loss = np.array(training_loss)
return n_training_epoch, training_loss
def check_if_avg_loss_lower_than_lowest_loss_value(
self, lowest_loss_value, current_epoch_loss_value):
print('current_loss = {} lowest_loss = {}'.format(
current_epoch_loss_value, lowest_loss_value))
if current_epoch_loss_value < lowest_loss_value:
print('assign_lowest_weight_D')
self.diff_dl_model.assign_tf_lowest_weight_D(
self.diff_dl_model.tf_weight_D)
self.fhn_dl_model.assign_tf_lowest_weight_a(
self.fhn_dl_model.tf_weight_a)
self.fhn_dl_model.assign_tf_lowest_weight_epsilon(
self.fhn_dl_model.tf_weight_epsilon)
self.fhn_dl_model.assign_tf_lowest_weight_beta(
self.fhn_dl_model.tf_weight_beta)
self.fhn_dl_model.assign_tf_lowest_weight_gamma(
self.fhn_dl_model.tf_weight_gamma)
self.fhn_dl_model.assign_tf_lowest_weight_delta(
self.fhn_dl_model.tf_weight_delta)
lowest_loss_value = current_epoch_loss_value.copy()
return lowest_loss_value
def generate_first_der_coeff_matrix(self):
coeff = self.ut.OA_coeff(self.order_acc)
input_length = np.shape(self.diff_dl_model.tf_intp_u_axis1.numpy())[-1]
coeff_matrix_first_der = self.ut.coeff_matrix_first_order(
input_length, coeff)
coeff_matrix_first_der = coeff_matrix_first_der.copy()
return coeff_matrix_first_der
def generate_second_der_coeff_matrix(self):
coeff = self.ut.OA_coeff(self.order_acc)
input_length2 = np.shape(
self.diff_dl_model.tf_intp_u_axis2.numpy())[-1] - len(coeff) + 1
coeff_matrix_second_der = self.ut.coeff_matrix_first_order(
input_length2, coeff)
coeff_matrix_second_der = coeff_matrix_second_der.copy()
return coeff_matrix_second_der
def convert_coeff_matrix_to_tensor_with_correct_shape(
self, coeff_matrix_first_der, coeff_matrix_second_der):
coeff_matrix_first_der = np.expand_dims(coeff_matrix_first_der,
axis=0) # shape(1, 5, 3)
coeff_matrix_second_der = np.expand_dims(coeff_matrix_second_der,
axis=0) # shape(1, 3, 1)
# coeff_matrix_first_der = np.expand_dims(coeff_matrix_first_der, axis=0) # shape(1, 1, 5, 3)
# coeff_matrix_second_der = np.expand_dims(coeff_matrix_second_der, axis=0) # shape(1, 1, 3, 1)
assert np.ndim(
coeff_matrix_first_der
) == 3, 'coeff_matrix_first_der must be 3D array (1, 5nn, 3)'
assert np.ndim(
coeff_matrix_first_der
) == 3, 'coeff_matrix_first_der must be 3D array (1, 3nn, 1)'
self.tf_coeff_matrix_first_der = tf.convert_to_tensor(
coeff_matrix_first_der, dtype=tf.float64)
self.tf_coeff_matrix_second_der = tf.convert_to_tensor(
coeff_matrix_second_der, dtype=tf.float64)
return