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FEniCS finite element function (spaces) as PyTorch neural networks

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# Finite Element Neural Networks

Representation of some finite element function spaces (as defined in
FEniCS) in terms of neural networks. That is, we construct neural networks
whose weights are the coefficient vectors (as ordered in FEniCS)

## Dependencies
- `FEniCS` (2019.1.0 and higher) stack
- `pytorch`
- [`gmshnics`](https://github.com/MiroK/gmshnics) for some tests

## Usage
Basic idea (taken from [`examples/compare_plot.py`](https://github.com/MiroK/fem-nets/blob/master/examples/compare_plot.py))

```python
import torch
import fem_nets
import dolfin as df
import numpy as np
import gmshnics

mesh, _ = gmshnics.gDisk(center=(0, 0), inradius=0.2, outradius=1.0, size=0.8)

V = df.VectorFunctionSpace(mesh, 'CG', 1)
f = df.Expression(('x[0]-2*x[1]', '2*x[0]+3*x[1]'), degree=1)
fh = df.interpolate(f, V)

nn = fem_nets.to_torch(V)
nn.double()
nn.set_from_coefficients(fh.vector().get_local())

# We will do the visual comparison in piecewise constants
Q = df.VectorFunctionSpace(mesh, 'DG', 0)
fh_true = df.interpolate(f, Q)

Qi = Q.sub(0).collapse()
# NOTE: eval on subspace
x = torch.tensor(Qi.tabulate_dof_coordinates()).unsqueeze(0)
y = nn(x)  # first colum is x, second is y

# Want to build back a function
fh_x, fh_y = df.Function(Qi), df.Function(Qi)
fh_x.vector().set_local(y[..., 0].detach().numpy().flatten())
fh_y.vector().set_local(y[..., 1].detach().numpy().flatten())

fh_mine = df.Function(Q)
df.assign(fh_mine, [fh_x, fh_y])

error = df.sqrt(df.assemble(df.inner(fh_true - fh_mine, fh_true - fh_mine)*df.dx))
assert error < 1E-14
# Now you can just plot the two for example
df.File('nn.pvd') << fh_mine
```

And voila

We can combine FE spaces with other neural networks as follows (snippet based on 
taken from [`examples/compate_plot.py`](https://github.com/MiroK/fem-nets/blob/master/examples/function_fit.py))

```python
import fem_nets
import dolfin as df
import torch
import torch.optim as optim
import torch.nn as nn
import numpy as np

class Network(nn.Module):
    def __init__(self):
        super().__init__()
        self.lin1 = nn.Linear(1, 10)
        self.lin2 = nn.Linear(10, 1)
 
    def forward(self, x):
        y = self.lin1(x)
        y = torch.relu(y)
        y = self.lin2(y)
        return y

mesh = df.UnitIntervalMesh(7)
V = df.FunctionSpace(mesh, 'CG', 1)

model_fe = fem_nets.to_torch(V)
model_fe.double()

model_nn = Network()
model_nn.double()

params = list(model_fe.parameters()) + list(model_nn.parameters())

model = lambda x: model_fe(x).unsqueeze(2) + model_nn(x)
```

The complete code then produces something like
  <p align="center">
    <img src="https://github.com/MiroK/fem-nets/blob/master/docs/function_fit.png">
  </p>

For more functionality, such as computation of derivatives see [tests](https://github.com/MiroK/fem-nets/blob/master/test/test_lagrange1.py#L36).

## TODO
- [x] Suport for 1, 2, 3 d
- [x] Support for Discontinuous Lagrange
- [x] Convenience functions `to_torch(V)` where `V` is a function space
----------------------------------------------------------------------
- [x] Example with training a hybrid model
----------------------------------------------------------------------
- [x] Support for higher order `CG|DG_2`
- [ ] Support for `CR_1`
- [ ] Support for `RT_1`
----------------------------------------------------------------------
- [ ] Isolate FEniCS bits `F(G(Omega_hat; theta_G); theta_F): R2 -> R1`

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