Failure during training

[motavini]

Hello, I am wondering if anyone could help figure out what is going wrong in my code. I'm attempting to solve the double pendulum problem, but it seems to failing in the training stage.

import deepxde as dde
from deepxde.backend import tf

theta1 = 0.0
theta2 = np.pi/32.0
theta1p = 0.0
theta2p = 0.0


def ode_system(x, y):
    m1 = 100000
    m2 = 0.1
    L1 = 1
    L2 = 1
    g = 9.81
   
    y1, y2, y3, y4 = y[:, 0], y[:, 1], y[:, 2], y[:, 3]
    dy1_x = dde.grad.jacobian(y, x, i=0)
    dy2_x = dde.grad.jacobian(y, x, i=1)
    dy3_x = dde.grad.jacobian(y, x, i=2)
    dy4_x = dde.grad.jacobian(y, x, i=3)
    eq1 = (-g*(2*m1+m2)*tf.sin(y1)-m2*g*tf.sin(y1-2*y2)-2*tf.sin(y1-y2)*m2*(L2*y4**2+L1*tf.cos(y1-y2)*y3**2))/(L1*(2*m1+m2-m2*tf.cos(2*y1-2*y2)))
    eq2 = (2*tf.sin(y1-y2)*(L1*(m1+m2)*y3**2+g*(m1+m2)*tf.cos(y1)+L2*m2*tf.cos(y1-y2)*y4**2))/(L2*(2*m1+m2-m2*tf.cos(2*y1-2*y2)))
    return [dy1_x - y3, dy2_x - y4, dy3_x - eq1, dy4_x - eq2]


def boundary(_, on_initial):
    return on_initial



geom = dde.geometry.TimeDomain(0, 10)
ic1 = dde.icbc.IC(geom, lambda x: theta1, boundary, component=0)
ic2 = dde.icbc.IC(geom, lambda x: theta2, boundary, component=1)
ic3 = dde.icbc.IC(geom, lambda x: theta1p, boundary, component=2)
ic4 = dde.icbc.IC(geom, lambda x: theta2p, boundary, component=3)
data = dde.data.PDE(geom, ode_system, [ic1, ic2, ic3, ic4], 10000, 2, num_test=10000)

layer_size = [1] + [16] * 3 + [4]
activation = "tanh"
initializer = "Glorot uniform"
net = dde.nn.FNN(layer_size, activation, initializer)

model = dde.Model(data, net)
model.compile("adam", lr=0.001, metrics=["l2 relative error"])

losshistory, train_state = model.train(iterations=10000)

dde.saveplot(losshistory, train_state, issave=True, isplot=True)


t = np.linspace(0, 10, 100)
t = t.reshape(100, 1)
sol_pred = model.predict(t)
x_pred = sol_pred[:, 0:1]
y_pred = sol_pred[:, 1:2]

plt.plot(t, x_pred, color="red", linestyle="dashed", label="x_pred")
plt.plot(t, y_pred, color="orange", linestyle="dashed", label="y_pred")
plt.legend()
plt.show()

The error message shown is the following:

TypeError                                 Traceback (most recent call last)
<ipython-input-8-a56f429e3a1d> in <module>
     40 model.compile("adam", lr=0.001, metrics=["l2 relative error"])
     41 
---> 42 losshistory, train_state = model.train(iterations=1000)
     43 
     44 dde.saveplot(losshistory, train_state, issave=True, isplot=True)

4 frames
/usr/local/lib/python3.8/dist-packages/deepxde/utils/internal.py in wrapper(*args, **kwargs)
     20     def wrapper(*args, **kwargs):
     21         ts = timeit.default_timer()
---> 22         result = f(*args, **kwargs)
     23         te = timeit.default_timer()
     24         print("%r took %f s\n" % (f.__name__, te - ts))

/usr/local/lib/python3.8/dist-packages/deepxde/model.py in train(self, iterations, batch_size, display_every, disregard_previous_best, callbacks, model_restore_path, model_save_path, epochs)
    603         self.train_state.set_data_train(*self.data.train_next_batch(self.batch_size))
    604         self.train_state.set_data_test(*self.data.test())
--> 605         self._test()
    606         self.callbacks.on_train_begin()
    607         if optimizers.is_external_optimizer(self.opt_name):

/usr/local/lib/python3.8/dist-packages/deepxde/model.py in _test(self)
    810             ]
    811         else:
--> 812             self.train_state.metrics_test = [
    813                 m(self.train_state.y_test, self.train_state.y_pred_test)
    814                 for m in self.metrics

/usr/local/lib/python3.8/dist-packages/deepxde/model.py in <listcomp>(.0)
    811         else:
    812             self.train_state.metrics_test = [
--> 813                 m(self.train_state.y_test, self.train_state.y_pred_test)
    814                 for m in self.metrics
    815             ]

/usr/local/lib/python3.8/dist-packages/deepxde/metrics.py in l2_relative_error(y_true, y_pred)
     10 
     11 def l2_relative_error(y_true, y_pred):
---> 12     return np.linalg.norm(y_true - y_pred) / np.linalg.norm(y_true)
     13 
     14 

TypeError: unsupported operand type(s) for -: 'NoneType' and 'float'

I am running this code on google collab.

[ghost]

You did not provide a exact solution in dde.data.PDE. Use

data = dde.data.PDE(geom, ode_system, [ic1, ic2, ic3, ic4], 10000, 2)
...
model.compile("adam", lr=0.001)