remove duplicate text in design section of doc (#14)

* remove duplicate text in design section of doc

* fix links in readme

* more readme links

README.md

@@ -5,7 +5,7 @@
 `weather-model-graphs` is a package for creating, visualising and storing message-passing graphs for data-driven weather models.
 
 The package is designed to use `networkx.DiGraph` objects as the primary data structure for the graph representation right until the graph is to be stored on disk into a specific format.
-This makes the graph generation process modular (every step outputs a `networkx.DiGraph`), easy to debug (visualise the graph at any step) and allows output to different file-formats and file-structures to be easily implemented. More details are given in the [background and design](#background-and-design) section below.
+This makes the graph generation process modular (every step outputs a `networkx.DiGraph`), easy to debug (visualise the graph at any step) and allows output to different file-formats and file-structures to be easily implemented. More details are given in the [background](https://mllam.github.io/weather-model-graphs/background.html) and [design](https://mllam.github.io/weather-model-graphs/design.html) section of the online [documentation](https://mllam.github.io/weather-model-graphs/).
 
 
 ## Installation
@@ -31,8 +31,7 @@ pdm install --group pytorch
 
 # Usage
 
-The best way to understand how to use `weather-model-graphs` is to look at the [notebooks/constructing_the_graph.ipynb](notebooks/constructing_the_graph.ipynb) notebook, to have look at the tests in [tests/](tests/) or simply to read through the source code.
-In addition you can read the [background and design](#background-and-design) section below to understand the design principles of `weather-model-graphs`.
+The best way to understand how to use `weather-model-graphs` is to look at the [documentation](https://mllam.github.io/weather-model-graphs) (which are executable Jupyter notebooks!), to have look at the tests in [tests/](tests/) or simply to read through the source code.
 
 ## Example, Keisler 2021 flat graph architecture
 

docs/design.ipynb

@@ -4,36 +4,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# Design\n",
-    "\n",
-    "The only input the graph generation in `weather-model-graphs` requires is the static `(x,y)` *grid* coordinates of the atmospheric state as the state changes over time. These coordinates are used to create the **grid nodes** nodes of the graph, with a node for each `(x,y)` coordinate.\n",
-    "In addition to grid nodes the graph also contains **mesh nodes** that represent the latent space of the model at a set of `(x,y)` coordinates (this is in general a different set of coordinates to the **grid nodes** coordinates).\n",
-    "\n",
-    "In summary, there are two sets of nodes in the graph:\n",
-    "\n",
-    "- **grid nodes**: representing the physical variables of the atmospheric state at a specific `(x,y)` coordinate\n",
-    "\n",
-    "- **mesh nodes**: representing the latent space of the model at specific `(x,y)` coordinate\n",
-    "\n",
-    "With these two sets of nodes, the graph is constructed by connecting the **grid nodes** to the **mesh nodes** and the **mesh nodes** to each other.\n",
-    "The edges between the **grid nodes** and the **mesh nodes** represent the encoding of the physical variables into the latent space of the model, while the edges between the **mesh nodes** represent the processing of the latent space through the time evolution of the atmospheric state.\n",
-    "\n",
-    "In summary, the complete message-passing graph consists of three components:\n",
-    "\n",
-    "- **grid-to-mesh** (`g2m`): the encoding compenent, where edges represent the encoding of physical variables into the latent space of the model\n",
-    "\n",
-    "- **mesh-to-mesh** (`m2m`): the processing component, where edges represent information flow between nodes updating the latent presentation at mesh nodes through the time evolution of the atmospheric state\n",
-    "\n",
-    "- **mesh-to-grid** (`m2g`): the decoding component, where edges represent the decoding of the latent space back into physical variables\n",
-    "\n",
-    "Practically, the **mesh-to-grid** and **grid-to-mesh** updates can probably also encode some of the time evolution processing, in addition to the latent space encoding/decoding, unless the GNN is trained specifically as an auto-encoder using the same graph as input and output.\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Design principles\n",
+    "# Design principles\n",
     "\n",
     "The key design principle of `weather-model-graphs` is to work with `networkx.DiGraph` objects as the primary data structure for the graph representation right until the graph is to be stored on disk into a specific format.\n",
     "Using only `networkx.DiGraph` objects as the intermediate representations makes it possible to\n",
@@ -69,7 +40,7 @@
     }
    },
    "source": [
-    "### Diagram of the graph generation process:\n",
+    "## Diagram of the graph generation process:\n",
     "\n",
     "Below, the graph generation process is visualised in `weather-model-graphs` for the example given above:\n",
     "\n",