Merge pull request #18 from aai-institute/feature/improve-notebooks

Feature/improve notebooks

mkdocs.yml

@@ -176,9 +176,9 @@ nav:
   - Learning Operators:
       - Introduction: operators/index.md
       - Examples:
-          - Intro: examples/intro.ipynb
-          - Sine: examples/sine.ipynb
+          - Basics: examples/basics.ipynb
           - Physics-informed: examples/physicsinformed.ipynb
+          - Self-supervised: examples/selfsupervised.ipynb
   - Code:
       - API: api/continuity/
       - Changelog: CHANGELOG.md

src/continuity/data/datasets.py

@@ -140,6 +140,18 @@ class Sine(SelfSupervisedDataSet):
     sine waves is evenly distributed between $\pi$ for the first observation
     and $2\pi$ for the last observation, respectively.
 
+    The `Sine` dataset generates $N$ sine waves
+    $$
+    f(x) = \sin(w_k x), \quad w_k = 1 + \frac{k}{N-1}, \quad k = 0, \dots, N-1.
+    $$
+    As a `SelfSupervisedDataset` it exports batches of samples for self-supervised
+    training, namely
+    $$
+    \left(\mathbf{x}, f(\mathbf{x}), x_j, f(x_j)\right), \quad \text{for } j = 1, \dots, M,
+    $$
+    where $\mathbf{x} = (x_i)_{i=1 \dots M}$ are the $M$ equidistantly
+    distributed sensor positions.
+
     - coordinate_dim: 1
     - num_channels: 1
 
@@ -172,7 +184,7 @@ def generate_observation(self, i: float):
         if self.size == 1:
             w = 1
         else:
-            w = i / self.size + 1
+            w = 1 + i / (self.size - 1)
 
         u = np.sin(w * np.pi * x)
 

src/continuity/operators/neuraloperator.py

@@ -21,22 +21,22 @@ class ContinuousConvolution(Operator):
     where $(x_i, u_i)$ are the $N$ sensors of the mapped observation.
 
     Args:
+        kernel: Kernel function $\kappa$ or network (if $d$ is the coordinate dimension, $\kappa: \R^d \times \R^d \to \R$)
         coordinate_dim: Dimension of coordinate space
         num_channels: Number of channels
-        kernel: Kernel function $\kappa$ or network (if $d$ is the coordinate dimension, $\kappa: \R^d \times \R^d \to \R$)
     """
 
     def __init__(
         self,
-        coordinate_dim: int,
-        num_channels: int,
         kernel: Union[Callable[[Tensor], Tensor], torch.nn.Module],
+        coordinate_dim: int = 1,
+        num_channels: int = 1,
     ):
         super().__init__()
 
+        self.kernel = kernel
         self.coordinate_dim = coordinate_dim
         self.num_channels = num_channels
-        self.kernel = kernel
 
     def forward(self, x: Tensor, u: Tensor, y: Tensor) -> Tensor:
         """Forward pass through the operator.
@@ -123,26 +123,26 @@ def __init__(
         self.num_channels = num_channels
 
         self.lifting = ContinuousConvolution(
+            NeuralNetworkKernel(kernel_width, kernel_depth),
             coordinate_dim,
             num_channels,
-            NeuralNetworkKernel(kernel_width, kernel_depth),
         )
 
         self.hidden_layers = torch.nn.ModuleList(
             [
                 ContinuousConvolution(
+                    NeuralNetworkKernel(kernel_width, kernel_depth),
                     coordinate_dim,
                     num_channels,
-                    NeuralNetworkKernel(kernel_width, kernel_depth),
                 )
                 for _ in range(depth)
             ]
         )
 
         self.projection = ContinuousConvolution(
+            NeuralNetworkKernel(kernel_width, kernel_depth),
             coordinate_dim,
             num_channels,
-            NeuralNetworkKernel(kernel_width, kernel_depth),
         )
 
     def forward(self, x: Tensor, u: Tensor, y: Tensor) -> Tensor:

tests/test_convolution.py

@@ -24,9 +24,9 @@ def dirac(x, y):
 
     # Operator
     operator = ContinuousConvolution(
+        kernel=dirac,
         coordinate_dim=dataset.coordinate_dim,
         num_channels=dataset.num_channels,
-        kernel=dirac,
     )
 
     # Create tensors