I managed to implement a WENO scheme for the 2D compressible Euler equations which works pretty well, but, by trying to run training the following error is thrown:

ValueError: You cannot pass a dictionary as model target.

It is due to the fact that the output is a dict of arrays regarding each of the learned keys (in this case, the conservative variables: 'density', 'x_momentum', 'y_momentum', 'energy').

How can I overcome this?

Thank you in advance,

P.S.: Passing the dict values as a list does not work neither and throws
AttributeError: 'NoneType' object has no attribute 'dtype'

https://github.com/googleprivate/pde-superresolution-2d/blob/6981ff1ee8a1bc99275d34d5f835213d02b174f8/pde_superresolution_2d/core/equations.py#L159-L161
@shoyer @JiaweiZhuang I think we might want to change the signature of equation.time_derivative to include the time:

 def time_derivative( 
     self, time, grid: grids.Grid, **inputs: tf.Tensor 
 ) -> Dict[str, tf.Tensor]:

For cases where the equation depends explicitly on time (e.g time-dependent forcing)

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.

I've been asking myself some questions whose answers might help me in implementing a finite-volume scheme for the 2D compressible Euler equations
(following Jameson et al. (1981)):

1. The definition of variables in staggered grids through the offset argument in states.StateDefinition instances is intended for flux computations.

How can I be sure, however, that its value equals the mean of the two edge-adjacent cells' values?

In other words, for the Advection problem, for instance, where is it defined that
concentration_edge_x [ i+1/2, j ] = ( concentration [ i, j ] + concentration [ i+1, j ] ) / 2 ?

2. By default, the Euler explicit method is used for time integration. However, I do need to implement a 4th order Runge-Kutta method which requires multi-step flux computing
(I suppose I might define a new method called 'take_time_step' within the class definition).

Does the staggered 'x_momentum_edge_x' variable get automatically updated once I compute one step for 'x_momentum'?

It is necessary, since I need updated values in order to compute fluxes for each step.

Thank you in advance,

I am getting errors while running the advection_1d example given in this python notebook. The version I have for tensorflow is same as the version shown in that example:

tf.__version__, tf.keras.__version__
('1.13.1', '2.2.4-tf')

The error I am getting is at the following line, just before neural network is trained with the data:

model_nn.compile(optimizer=tf.keras.optimizers.Adam(0.001 * 1), loss='mae', metrics=[tf.keras.metrics.RootMeanSquaredError()])

AttributeError: module 'tensorflow._api.v1.keras.metrics' has no attribute 'RootMeanSquaredError'

I checked the class tf.keras.metrics and it does not have any function called RootMeanSquaredError, which is the reason for error. After some search, I modified the metrics in above line throwing the error as metrics=["RootMeanSquaredError"], which helps get rid of that particular error, but I get another error on the next line as follows:

history = model_nn.fit(train_input, train_output, epochs=80, batch_size=32, verbose=1, shuffle=True)

ValueError: When running a model in eager execution, the optimizer must be an instance of tf.train.Optimizer. Received: <tensorflow.python.keras.optimizers.Adam object at 0x7f0c885da400>

The above error does not go away whether I enable the eager execution or not. I was curious how the example in that notebook ran with the exact same version of tensorflow that I am also using with Python 3.6. I would appreciate your help with this.

For any discretization stencil size , k > 3 (In above case k = 7), I get the following error. I am trying to analyze the solution accuracy for larger stencil sizes and I am getting the above error for any stencil with k>3.
My apologies if I am making some silly error, but it seems to me like a problem in the extract_patches_2d function but I do not understand how it would cause me to be unable to use k>3.
Thanks in Advance.

Error message:

/data-driven-pdes-master/datadrivenpdes/core/equations.py in _validate_keys(self)
77 """Validate the key_definitions, evolving_keys and constant_keys attributes.
78 """
---> 79 repeated_keys = self.evolving_keys & self.constant_keys
80 if repeated_keys:
81 raise ValueError('overlapping entries between evolving_keys and '

TypeError: unsupported operand type(s) for &: 'ellipsis' and 'ellipsis'

I didn't build any evolving key or constant key.

key_definitions = {
    'Phi': states.StateDefinition(name='Phi',     
                                  tensor_indices=(),          
                                  derivative_orders=(0,0,0),  
                                  offset=(0,0)),              
    'Phi_xx': states.StateDefinition(name='Phi',     
                                     tensor_indices=(X,),          
                                     derivative_orders=(2,0,0),  
                                     offset=(0,0)),              
    'Phi_yy': states.StateDefinition(name='Phi',       
                                     tensor_indices=(Y,),
                                     derivative_orders=(0, 2, 0),    
                                     offset=(0, 0)),             
}

def __init__(self, D, timestep=1e-4):
    self.D = D
    self._timestep = timestep
    super().__init__()

def time_derivative(
      self, grid, Phi_xx, Phi_yy):
    diff_X = self.D * Phi_xx
    diff_Y = self.D * Phi_yy
    return {diff_X + diff_Y}

I don't know what this ellipsis is?

Hello!

How can I use it for a system of equations?

Hi,
When trying to run the tutorial code, I get an error in the line:

results = pde.core.integrate.integrate_times(
model=pde.core.models.FiniteDifferenceModel(equation,grid),
state=initial_state,
times=times, axis=0)

The error that I get is (I will also send it to the AutoGraph team as they requested) :

W0717 14:24:34.494019 140735880733568 ag_logging.py:145] Entity <function integrate_steps..advance_until_saved_step at 0xb4026f378> could not be transformed and will be executed as-is. Please report this to the AutgoGraph team. When filing the bug, set the verbosity to 10 (on Linux, export AUTOGRAPH_VERBOSITY=10) and attach the full output. Cause: converting <function integrate_steps..advance_until_saved_step at 0xb4026f378>: ValueError: inconsistent nodes: None (NoneType) and None (NoneType)
WARNING: Entity <function integrate_steps..advance_until_saved_step at 0xb4026f378> could not be transformed and will be executed as-is. Please report this to the AutgoGraph team. When filing the bug, set the verbosity to 10 (on Linux, export AUTOGRAPH_VERBOSITY=10) and attach the full output. Cause: converting <function integrate_steps..advance_until_saved_step at 0xb4026f378>: ValueError: inconsistent nodes: None (NoneType) and None (NoneType)

TypeError Traceback (most recent call last)
in
1 time_step = equation.get_time_step(grid)
2 times = time_step*np.arange(400)
----> 3 results = pde.core.integrate.integrate_times(model=pde.core.models.FiniteDifferenceModel(equation,grid), state=initial_state,times=times, axis=0)

~/Dropbox/MIT/projects/burgers_theta_updated/pde_superresolution_2d/datadrivenpdes/core/integrate.py in integrate_times(model, state, times, initial_time, axis, xla_compile)
133 'time step {}: {}'.format(times, dt, approx_steps))
134
--> 135 return integrate_steps(model, state, steps, initial_time, axis, xla_compile)

~/Dropbox/MIT/projects/burgers_theta_updated/pde_superresolution_2d/datadrivenpdes/core/integrate.py in integrate_steps(failed resolving arguments)
88 starts = tf.concat([[0], steps[:-1]], axis=0)
89 integrated = tf.scan(advance_until_saved_step, [starts, steps],
---> 90 initializer=evolving_state)
91
92 integrated_constants = nest.map_structure(

~/anaconda3/envs/pde_TF/lib/python3.7/site-packages/tensorflow/python/ops/functional_ops.py in scan(fn, elems, initializer, parallel_iterations, back_prop, swap_memory, infer_shape, reverse, name)
503 back_prop=back_prop,
504 swap_memory=swap_memory,
--> 505 maximum_iterations=n)
506
507 results_flat = [r.stack() for r in r_a]

~/anaconda3/envs/pde_TF/lib/python3.7/site-packages/tensorflow/python/ops/control_flow_ops.py in while_loop(cond, body, loop_vars, shape_invariants, parallel_iterations, back_prop, swap_memory, name, maximum_iterations, return_same_structure)
3461
3462 while cond(*loop_vars):
-> 3463 loop_vars = body(*loop_vars)
3464 if try_to_pack and not isinstance(loop_vars, (list, _basetuple)):
3465 packed = True

~/anaconda3/envs/pde_TF/lib/python3.7/site-packages/tensorflow/python/ops/control_flow_ops.py in (i, lv)
3454 cond = lambda i, lv: ( # pylint: disable=g-long-lambda
3455 math_ops.logical_and(i < maximum_iterations, orig_cond(*lv)))
-> 3456 body = lambda i, lv: (i + 1, orig_body(*lv))
3457
3458 if executing_eagerly:

~/anaconda3/envs/pde_TF/lib/python3.7/site-packages/tensorflow/python/ops/functional_ops.py in compute(i, a_flat, tas)
480 packed_elems = input_pack([elem_ta.read(i) for elem_ta in elems_ta])
481 packed_a = output_pack(a_flat)
--> 482 a_out = fn(packed_a, packed_elems)
483 nest.assert_same_structure(elems if initializer is None else initializer,
484 a_out)

~/anaconda3/envs/pde_TF/lib/python3.7/site-packages/tensorflow/python/eager/def_function.py in call(self, *args, **kwds)
412 # This is the first call of call, so we have to initialize.
413 initializer_map = {}
--> 414 self._initialize(args, kwds, add_initializers_to=initializer_map)
415 if self._created_variables:
416 try:

~/anaconda3/envs/pde_TF/lib/python3.7/site-packages/tensorflow/python/eager/def_function.py in _initialize(self, args, kwds, add_initializers_to)
355 self._concrete_stateful_fn = (
356 self._stateful_fn._get_concrete_function_internal_garbage_collected( # pylint: disable=protected-access
--> 357 *args, **kwds))
358
359 def invalid_creator_scope(*unused_args, **unused_kwds):

~/anaconda3/envs/pde_TF/lib/python3.7/site-packages/tensorflow/python/eager/function.py in _get_concrete_function_internal_garbage_collected(self, *args, **kwargs)
1347 if self.input_signature:
1348 args, kwargs = None, None
-> 1349 graph_function, _, _ = self._maybe_define_function(args, kwargs)
1350 return graph_function
1351

~/anaconda3/envs/pde_TF/lib/python3.7/site-packages/tensorflow/python/eager/function.py in _maybe_define_function(self, args, kwargs)
1650 graph_function = self._function_cache.primary.get(cache_key, None)
1651 if graph_function is None:
-> 1652 graph_function = self._create_graph_function(args, kwargs)
1653 self._function_cache.primary[cache_key] = graph_function
1654 return graph_function, args, kwargs

~/anaconda3/envs/pde_TF/lib/python3.7/site-packages/tensorflow/python/eager/function.py in _create_graph_function(self, args, kwargs, override_flat_arg_shapes)
1543 arg_names=arg_names,
1544 override_flat_arg_shapes=override_flat_arg_shapes,
-> 1545 capture_by_value=self._capture_by_value),
1546 self._function_attributes)
1547

~/anaconda3/envs/pde_TF/lib/python3.7/site-packages/tensorflow/python/framework/func_graph.py in func_graph_from_py_func(name, python_func, args, kwargs, signature, func_graph, autograph, autograph_options, add_control_dependencies, arg_names, op_return_value, collections, capture_by_value, override_flat_arg_shapes)
713 converted_func)
714
--> 715 func_outputs = python_func(*func_args, **func_kwargs)
716
717 # invariant: func_outputs contains only Tensors, CompositeTensors,

~/anaconda3/envs/pde_TF/lib/python3.7/site-packages/tensorflow/python/eager/def_function.py in wrapped_fn(*args, **kwds)
305 # wrapped allows AutoGraph to swap in a converted function. We give
306 # the function a weak reference to itself to avoid a reference cycle.
--> 307 return weak_wrapped_fn().wrapped(*args, **kwds)
308 weak_wrapped_fn = weakref.ref(wrapped_fn)
309

~/anaconda3/envs/pde_TF/lib/python3.7/site-packages/tensorflow/python/framework/func_graph.py in wrapper(*args, **kwargs)
703 except Exception as e: # pylint:disable=broad-except
704 if hasattr(e, "ag_error_metadata"):
--> 705 raise e.ag_error_metadata.to_exception(type(e))
706 else:
707 raise

TypeError: in converted code:
relative to /Users/yani:

Dropbox/MIT/projects/burgers_theta_updated/pde_superresolution_2d/datadrivenpdes/core/integrate.py:80 advance_until_saved_step
    while i < stop:
anaconda3/envs/pde_TF/lib/python3.7/site-packages/tensorflow/python/framework/ops.py:690 __bool__
    raise TypeError("Using a `tf.Tensor` as a Python `bool` is not allowed. "

TypeError: Using a `tf.Tensor` as a Python `bool` is not allowed. Use `if t is not None:` instead of `if t:` to test if a tensor is defined, and use TensorFlow ops such as tf.cond to execute subgraphs conditioned on the value of a tensor.

I use Python 3.7.3, and the packages versions that I use are:

absl-py==0.7.1
apache-beam==2.13.0
appnope==0.1.0
astor==0.8.0
attrs==19.1.0
avro-python3==1.9.0
backcall==0.1.0
bleach==3.1.0
certifi==2019.6.16
chardet==3.0.4
crcmod==1.7
cycler==0.10.0
decorator==4.4.0
defusedxml==0.6.0
dill==0.2.9
docopt==0.6.2
entrypoints==0.3
fastavro==0.21.24
future==0.17.1
gast==0.2.2
google-pasta==0.1.7
grpcio==1.22.0
h5py==2.9.0
hdfs==2.5.8
httplib2==0.12.0
idna==2.8
ipykernel==5.1.1
ipython==7.6.1
ipython-genutils==0.2.0
ipywidgets==7.5.0
jedi==0.13.3
Jinja2==2.10.1
jsonschema==3.0.1
jupyter==1.0.0
jupyter-client==5.3.1
jupyter-console==6.0.0
jupyter-core==4.5.0
Keras-Applications==1.0.8
Keras-Preprocessing==1.1.0
kiwisolver==1.1.0
Markdown==3.1.1
MarkupSafe==1.1.1
matplotlib==3.1.0
mistune==0.8.4
mkl-fft==1.0.12
mkl-random==1.0.2
mock==2.0.0
nbconvert==5.5.0
nbformat==4.4.0
notebook==5.7.8
numpy==1.16.4
oauth2client==3.0.0
pandas==0.24.2
pandocfilters==1.4.2
parso==0.5.0
pbr==5.4.0
pexpect==4.7.0
pickleshare==0.7.5
prometheus-client==0.7.1
prompt-toolkit==2.0.9
protobuf==3.9.0
ptyprocess==0.6.0
pyarrow==0.13.0
pyasn1==0.4.5
pyasn1-modules==0.2.5
pydot==1.2.4
Pygments==2.4.2
pyparsing==2.4.0
pyrsistent==0.14.11
python-dateutil==2.8.0
pytz==2019.1
PyYAML==3.13
pyzmq==18.0.0
qtconsole==4.5.1
requests==2.22.0
rsa==4.0
scipy==1.2.1
Send2Trash==1.5.0
six==1.12.0
tensorboard==1.14.0
tensorflow==1.14.0
tensorflow-estimator==1.14.0
termcolor==1.1.0
terminado==0.8.2
testpath==0.4.2
tornado==6.0.3
traitlets==4.3.2
urllib3==1.25.3
wcwidth==0.1.7
webencodings==0.5.1
Werkzeug==0.15.4
widgetsnbextension==3.5.0
wrapt==1.11.2
xarray==0.12.3
xgboost==0.90

I think you should tell us which version of TensorFlow is good for your work.
Maybe TensorFlow1.8 or older?
Excelent work by the way!