fixed and clarified input structure for supervised code example

supervised-airfoils.ipynb

@@ -47,8 +47,9 @@
         "$u_x,u_y$ and $p$ each have a dimension of $128^2$.\n",
         "As inputs we have the Reynolds number $\\text{Re} \\in \\mathbb{R}$, the angle of attack\n",
         "$\\alpha \\in \\mathbb{R}$, and the airfoil shape $\\mathbf{s}$ encoded as a rasterized grid with $128^2$.\n",
-        "Both constant, scalar inputs $\\text{Re}$ and $\\alpha$ are likewise extended to a size of $128^2$.\n",
-        "Thus, put together, both input and output have the same dimensions: $x,y^* \\in \\mathbb{R}^{3\\times128\\times128}$.\n",
+        " $\\text{Re}$ and $\\alpha$ are encoded in terms of the freestream flow velocity $\\mathbf{f}$, the x and y components of which are encoded as constant fields of size $128^2$, and contain zeros in the airfoil region.\n",
+        "Thus, put together, both input and output have the same dimensions: $x,y^* \\in \\mathbb{R}^{3\\times128\\times128}$. The inputs contain \n",
+        "$[f_x,f_y,\\text{mask}]$, while the outputs store the channels $[p,u_x,u_y]$.\n",
         "This is exactly what we'll specify as input and output dimensions for the NN below.\n",
         "\n",
         "A point to keep in mind here is that our quantities of interest in $y^*$ contain three different physical fields. While the two velocity components are quite similar in spirit, the pressure field typically has a different behavior with an approximately squared scaling with respect to the velocity (cf. [Bernoulli](https://en.wikipedia.org/wiki/Bernoulli%27s_principle)). This implies that we need to be careful with simple summations (as in the minimization problem above), and that we should take care to normalize the data.\n"
@@ -73,7 +74,7 @@
           "base_uri": "https://localhost:8080/"
         },
         "id": "JwZudtWauiGa",
-        "outputId": "44bb304e-5839-41a1-9cb0-2f52a41f0d90"
+        "outputId": "ac464e27-1aad-4a64-d748-6bb1b6b566a5"
       },
       "outputs": [
         {
@@ -162,7 +163,7 @@
           "height": 353
         },
         "id": "6y6YGxMeNECD",
-        "outputId": "20e4ed46-2ec0-4144-d9da-e49a9f6aa6a2"
+        "outputId": "ac8e0746-a975-4dc9-de80-cc8202b36f6e"
       },
       "outputs": [
         {
@@ -171,7 +172,7 @@
             "text/plain": [
               "<Figure size 1152x360 with 2 Axes>"
             ],
-            "image/png": 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truncated
+            "image/png": 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truncated
           },
           "metadata": {
             "needs_background": "light"
@@ -198,7 +199,7 @@
         "  if title is not None: pylab.title(title)\n",
         "\n",
         "NUM=72\n",
-        "showSbs(npfile[\"inputs\"][NUM],npfile[\"targets\"][NUM], stats=False, bottom=\"Target Output\", top=\"Inputs\", title=\"3 inputs are shown at the top (in-ux, in-uy, mask), with the 3 output channels (p,ux,uy) at the bottom\")\n"
+        "showSbs(npfile[\"inputs\"][NUM],npfile[\"targets\"][NUM], stats=False, bottom=\"Target Output\", top=\"Inputs\", title=\"3 inputs are shown at the top (free-ux, free-uy, mask), with the 3 output channels (p,ux,uy) at the bottom\")\n"
       ]
     },
     {
@@ -216,7 +217,7 @@
     },
     {
       "cell_type": "code",
-      "execution_count": 3,
+      "execution_count": null,
       "metadata": {
         "colab": {
           "base_uri": "https://localhost:8080/"
@@ -282,7 +283,7 @@
     },
     {
       "cell_type": "code",
-      "execution_count": 4,
+      "execution_count": null,
       "metadata": {
         "id": "PVNjz4FjGhdY"
       },
@@ -389,7 +390,7 @@
     },
     {
       "cell_type": "code",
-      "execution_count": 5,
+      "execution_count": null,
       "metadata": {
         "colab": {
           "base_uri": "https://localhost:8080/"
@@ -451,7 +452,7 @@
     },
     {
       "cell_type": "code",
-      "execution_count": 6,
+      "execution_count": null,
       "metadata": {
         "colab": {
           "base_uri": "https://localhost:8080/"
@@ -540,7 +541,7 @@
     },
     {
       "cell_type": "code",
-      "execution_count": 7,
+      "execution_count": null,
       "metadata": {
         "colab": {
           "base_uri": "https://localhost:8080/",
@@ -597,7 +598,7 @@
     },
     {
       "cell_type": "code",
-      "execution_count": 8,
+      "execution_count": null,
       "metadata": {
         "colab": {
           "base_uri": "https://localhost:8080/",
@@ -659,7 +660,7 @@
     },
     {
       "cell_type": "code",
-      "execution_count": 9,
+      "execution_count": null,
       "metadata": {
         "colab": {
           "base_uri": "https://localhost:8080/",
@@ -808,4 +809,4 @@
   },
   "nbformat": 4,
   "nbformat_minor": 0
-}
+}