Neural network for Turing equation

[ghost]

Hello. I am able to run the Tutorial example with the Turing equation correctly. Now I am trying to extend that example by developing a neural network (nn) for the Turing equation, but I am getting error at the integration stage before training with any numerical data. Based on a tutorial example to create a nn, I am using the following to create a nn for the Turing equation:

# Run untrained neural net model

model_nn = models.PseudoLinearModel(equation, grid, 
                                    num_time_steps=4,  
                                    stencil_size=3, kernel_size=(3, 1), 
                                    num_layers=4, filters=32,
                                    constrained_accuracy_order=1, 
                                    learned_keys = {'A', 'B'}, 
                                    activation='relu')

tf.random.set_random_seed(0)

integrated_untrained = integrate.integrate_steps(model_nn, initial_state, time_steps)

I am getting the following error at the integrate.integrate_steps() step above.

anaconda2/envs/data-driven-pdes/lib/python3.6/site-packages/tensorflow/python/ops/nn_ops.py", line 1029, in __init__
    "input tensor must have rank %d" % (num_spatial_dims + 2))
ValueError: input tensor must have rank 4

I would appreciate your help in resolving the above error.

[JiaweiZhuang]

Could you print the shapes of your input tensors by [v.shape for v in initial_state.values()] ? They should all have 4 dimensions.

[ghost]

Hello, @JiaweiZhuang
The ouput of [v.shape for v in initial_state.values()] is as follows:

[TensorShape([Dimension(100), Dimension(1)]),
 TensorShape([Dimension(100), Dimension(1)]),
 TensorShape([Dimension(100), Dimension(1)])]

[JiaweiZhuang]

So there are only 2 dimensions (x, y). Adding a batch dimension to make it (batch, x, y)

[ghost]

Yes, there are 2 dimensions, but effectively 1D. I am sorry, but I did not get what you mean by 'adding a batch dimension to make it (batch, x, y)'. Can you please elaborate what you mean by that?

[JiaweiZhuang]

The integrator "vectorizes" over multiple samples. If you just have one sample in the input data, you can add a leading "1" dimension. Something like

correct_initial_state = {k: tf.expand_dims(v, 0) for k, v in initial_state.items()}

[ghost]

@JiaweiZhuang : thank you for your cooperation in helping me resolve this issue. I might not be familiar with many of the low-level things used in this code from tensorflow, so please bear with me. Your suggestion to correct the initial state did get rid of the earlier error related to input tensor rank, so the integrate.integrate_steps() did work. However, the next step of wrapping the result as an xarray is giving error, possibly due to not recognizing the key x as shown below:

anaconda2/envs/data-driven-pdes/lib/python3.6/site-packages/xarray/core/dataarray.py", line 101, in _infer_coords_and_dims
    if s != sizes[d]:

KeyError: 'x'

This is the code I am using:

def wrap_as_xarray(integrated, times, x_mesh):
  dr = xarray.DataArray(integrated['A'].numpy().squeeze(), 
                        dims = ('time', 'sample', 'x'), 
                        coords = {'time': times, 'x': x_mesh.squeeze()})
  return dr


equation = TuringEquation(alpha=-0.0001, beta=10, D_A=1, D_B=30)
NX = 100
NY = 1 # 1D can be obtained by haveing a y dimension of size 1
LX = 200
grid = grids.Grid(size_x=NX, size_y=NY, step=LX/NX)
x_mesh, _ = grid.get_mesh()

initial_state = equation.random_state(grid=grid, seed=12345)
times = equation._timestep*np.arange(0, 1000, 20)
time_steps = np.arange(0, 50)
model = pde.core.models.FiniteDifferenceModel(equation, grid)
res = pde.core.integrate.integrate_steps(model=model, state=initial_state, steps=time_steps, axis=0)

# Run untrained neural net model
correct_initial_state = {k: tf.expand_dims(v, 0) for k, v in initial_state.items()}
model_nn = models.PseudoLinearModel(equation, grid, 
                                    num_time_steps=4,  
                                    stencil_size=3, kernel_size=(3, 1), 
                                    num_layers=4, filters=32,
                                    constrained_accuracy_order=1, 
                                    learned_keys = {'A', 'B'},  
                                    activation='relu')

tf.random.set_random_seed(0)

integrated_untrained = integrate.integrate_steps(model_nn, correct_initial_state, time_steps)

wrap_as_xarray(integrated_untrained, times, x_mesh).isel(time=[0, 2, 10], sample=[4, 10, 16]).plot(col='sample', hue='time', ylim=[-0.2, 0.5])