Hello! If applicable, put your complete code example down below. Make sure that your code:

- is 100% self-contained — someone can copy-paste exactly what is here and run it to

reproduce the behaviour you are observing - includes comments

If you want help with diagnosing an error, please put the full error message below:

```
import numpy as np
import tensorflow as tf
import matplotlib.pyplot as plt
# Define the neural network model
class PINN(tf.keras.Model):
def __init__(self):
super(PINN, self).__init__()
self.dense1 = tf.keras.layers.Dense(20, activation='tanh')
self.dense2 = tf.keras.layers.Dense(20, activation='tanh')
self.dense3 = tf.keras.layers.Dense(20, activation='tanh')
self.dense4 = tf.keras.layers.Dense(3, activation='linear')
#def call(self, x):
# x = tf.expand_dims(x, axis=-1) # Add an extra dimension to make input 2D
# x = self.dense1(x)
# x = self.dense2(x)
# x = self.dense3(x)
# x = self.dense4(x)
# return x
def call(self, x):
x = tf.expand_dims(x, axis=-1) # Add an extra dimension to make input 2D
x = self.dense1(x)
x = self.dense2(x)
x = self.dense3(x)
x = self.dense4(x)
# Split the output into three values
R_p = x[:, 0:1] # Extract first column as R_p
R_m = x[:, 1:2] # Extract second column as R_m
T = x[:, 2:3] # Extract third column as T
return R_p, R_m, T # Return a tuple of three tensors
def g(x, k):
# Placeholder function for g(x, k). Replace with actual logic if needed.
return x * k # Example computation for g function
# Define loss function with physics-informed constraints
def loss_function(model, omega, n):
D = 1
rho = 1
omega_complex = tf.cast(omega, tf.complex128) # Ensure omega is treated as complex
k = (omega_complex**2 * rho / D)**(1/4)
M = np.array([1])
K = np.array([1])
v = np.array([1])
a = 1
xmi = np.zeros(n)
# Populate mialpbet and xmi
for ind in range(n):
mialpbet = ((1 / (M * omega_complex**2)) - (1 / (K - 1j * omega_complex * v)))**-1
xmi[ind] = -0.5 + ind * a
k3 = k**3
malf = (2 * D * k3) / mialpbet
deltaalfbet = np.eye(n)
Malfbet = np.zeros((n, n), dtype=complex)
for xalf in range(len(xmi)):
for xbet in range(len(xmi)):
Malfbet[xalf, xbet] = malf[xalf] * deltaalfbet[xalf, xbet] - g(xmi[xalf] - xmi[xbet], k[xalf])
Malfbet1 = np.linalg.inv(Malfbet)
with tf.GradientTape(persistent=True) as tape:
tape.watch(omega_complex) # Watch the complex omega
R_p, R_m, T = model(omega)
physics_loss_Rp = tf.cast(R_p, tf.complex128) - (1j / 2) * tf.reduce_sum([Malfbet1[xalf, xbet] * tf.exp(1j * k * (xmi[xalf] + xmi[xbet])) for xalf in range(len(xmi)) for xbet in range(len(xmi))])
physics_loss_Rm = tf.cast(R_m, tf.complex128) - (1j / 2) * tf.reduce_sum([Malfbet1[xalf, xbet] * tf.exp(-1j * k * (xmi[xalf] + xmi[xbet])) for xalf in range(len(xmi)) for xbet in range(len(xmi))])
physics_loss_T = tf.cast(T, tf.complex128) - (1 + (1j / 2) * tf.reduce_sum([Malfbet1[xalf, xbet] * tf.exp(1j * k * (xmi[xalf] - xmi[xbet])) for xalf in range(len(xmi)) for xbet in range(len(xmi))]))
total_loss = tf.reduce_mean(tf.square(tf.abs(physics_loss_Rp)) + tf.square(tf.abs(physics_loss_Rm)) + tf.square(tf.abs(physics_loss_T))) # Magnitude of the complex loss
return total_loss
# Training function
def train(model, omega, n, epochs, learning_rate):
optimizer = tf.keras.optimizers.Adam(learning_rate)
for epoch in range(epochs):
with tf.GradientTape() as tape:
loss = loss_function(model, omega, n)
gradients = tape.gradient(loss, model.trainable_variables)
optimizer.apply_gradients(zip(gradients, model.trainable_variables))
if epoch % 100 == 0:
print(f'Epoch {epoch}, Loss: {loss.numpy()}')
# Initialize PINN model
pinn_model = PINN()
# Training parameters
epochs = 1000
learning_rate = 0.001
Omega = tf.constant(np.arange(0, 100), dtype=tf.float64)
n = 1
# Train the PINN
train(pinn_model, Omega, n, epochs, learning_rate)
# Predict using the trained PINN model
predictions = pinn_model(Omega)
print(pinn_model(Omega))
R_p_pred, R_m_pred, T_pred = pinn_model(Omega) # Unpack the tuple directly
# Predictions and plotting can remain similar; just ensure proper handling of complex values.
plt.figure(1)
plt.plot(Omega, np.abs(R_m_pred.numpy()), label='|R_m| PINN') # Convert tensor to numpy array correctly
plt.plot(Omega, np.abs(T_pred.numpy()), '--', label='|T| PINN') # Properly display magnitudes
plt.xlabel('Omega')
plt.legend()
plt.title('PINN Prediction of |R_m| and |T| vs Omega')
plt.show()
```

# Put full error message here

```
WARNING:tensorflow:You are casting an input of type complex128 to an incompatible dtype float32. This will discard the imaginary part and may not be what you intended.
```

And, finally, make sure to include the versions of your packages. Specifically, show us the output of `qml.about()`

.