Add example page.

docs/examples/index.md

@@ -0,0 +1,28 @@
+---
+title: Examples
+---
+
+This is a collection of notebooks that showcase various applications of
+Continuity.
+
+::cards:: cols=2
+
+- title: The Basics
+  content: Learning function operators with Continuity
+  url: basics
+
+- title: Physics-informed
+  content: >
+    Training physics-informed neural operators
+  url: physicsinformed
+
+- title: Self-supervised
+  content: >
+    Self-supervised training of operators
+  url: selfsupervised
+
+- title: Super-resolution
+  content: Neural operators for super-resolution
+  url: superresolution
+
+::/cards::

docs/index.md

@@ -26,11 +26,16 @@ examples and benchmarks.
 
 - title: Learning Operators
   content: >
-    Basics of learning function operators with neural networks
+    Basics of learning function operators
   url: operators/index.md
 
+- title: Examples
+  content: >
+    Some notebooks using Continuity
+  url: examples/index.md
+
 - title: Browse the API
-  content: Full documentation of the API
+  content: Full class documentation
   url: api/continuity/index.md
 
 ::/cards::

docs/operators/index.md

@@ -86,4 +86,4 @@ Neural operators extend the concept of neural networks to function mappings, whi
 enables discretization-invariant and mesh-free mappings of data with
 applications to physics-informed training, super-resolution, and more.
 
-See our examples (e.g., <a href="../examples/basics">Basics</a>) for more details and further reading.
+See our <a href="../examples">Examples</a> for more details and further reading.

src/continuity/__init__.py

@@ -1,6 +1,8 @@
 """
 **Continuity** is a Python package for machine learning on function operators.
 
+The package is structured into the following modules:
+
 ::cards:: cols=2
 
 - title: Operators

src/continuity/data/__init__.py

@@ -1,6 +1,8 @@
 """
-This defines DataSets in Continuity.
-Every data set is a list of (x, u, y, v) tuples.
+`continuity.data`
+
+Data sets in Continuity.
+Every data set is a list of `(x, u, y, v)` tuples.
 """
 
 import math

src/continuity/operators/__init__.py

@@ -1,4 +1,15 @@
-"""Operators in Continuity."""
+"""
+`continuity.operators`
+
+Operators in Continuity.
+
+Every operator maps collocation points `x`, function values `u`,
+and evaluation points `y` to evaluations of `v`:
+
+```
+v = operator(x, u, y)
+```
+"""
 
 from .operator import Operator
 from .deeponet import DeepONet

src/continuity/pde/__init__.py

@@ -1,4 +1,10 @@
-"""Loss functions for physics-informed training."""
+"""
+`continuity.pde`
+
+PDEs in Continuity.
+
+Every PDE is implemented using a physics-informed loss function.
+"""
 
 from torch import Tensor
 from abc import abstractmethod

src/continuity/plotting/__init__.py

@@ -1,4 +1,8 @@
-"""Plotting utilities for Continuity."""
+"""
+`continuity.plotting`
+
+Plotting utilities for Continuity.
+"""
 
 import torch
 import numpy as np