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cleanup of PG code example

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NT committed 2022-04-20 08:58:04 +02:00
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physgrad-code.ipynb
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@@ -58,7 +58,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 143, "execution_count": 17,
"outputs": [], "outputs": [],
"source": [ "source": [
"!pip install --upgrade --quiet git+https://github.com/tum-pbs/PhiFlow\n", "!pip install --upgrade --quiet git+https://github.com/tum-pbs/PhiFlow\n",
@@ -87,7 +87,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 144, "execution_count": 18,
"outputs": [], "outputs": [],
"source": [ "source": [
"def generate_heat_example(*shape, bounds: Box = None):\n", "def generate_heat_example(*shape, bounds: Box = None):\n",
@@ -126,7 +126,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 145, "execution_count": 19,
"outputs": [ "outputs": [
{ {
"output_type": "display_data", "output_type": "display_data",
@@ -153,7 +153,7 @@
"height": 390 "height": 390
}, },
"id": "BHtnPdL3S2eO", "id": "BHtnPdL3S2eO",
"outputId": "819f73cc-1346-4243-94cc-8416e7c8c621" "outputId": "7937d111-1c65-44fb-e11a-1f219cc8ecb1"
} }
}, },
{ {
@@ -216,7 +216,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 146, "execution_count": 20,
"outputs": [], "outputs": [],
"source": [ "source": [
"def apply_damping(kernel, inv_kernel, amp, f_uncertainty, log_kernel):\n", "def apply_damping(kernel, inv_kernel, amp, f_uncertainty, log_kernel):\n",
@@ -272,7 +272,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 147, "execution_count": 21,
"outputs": [], "outputs": [],
"source": [ "source": [
"math.set_global_precision(64)\n", "math.set_global_precision(64)\n",
@@ -295,9 +295,10 @@
"source": [ "source": [
"Now we'll define loss function for phiflow.\n", "Now we'll define loss function for phiflow.\n",
"The gradients for the network weights are always computed as d(loss_function)/d$\\theta$.\n", "The gradients for the network weights are always computed as d(loss_function)/d$\\theta$.\n",
"For SIP, we invert the physics, and then define the proxy loss as $L^2$(prediction - correction), where correction is taken as constant. Below this is realized via `x = field.stop_gradient(prediction)`.\n",
"\n", "\n",
"The Adam / GD version for `sip=False` simply computes the L2 difference of two diffused $y$ fields for the gradient, as outlined above.\n", "For SIP, we invert the physics, and then define the proxy loss as $L^2$(prediction - correction), where correction is taken as constant. Below this is realized via `x = field.stop_gradient(prediction)`. This L2 loss triggers the backprop towards the neural network weights. For SIP, the `y_l2` is only computed for comparison, and is not crucial for training.\n",
"\n",
"The Adam / GD version for `sip=False` simply computes the L2 difference of the predicted, diffused $y$ field to the target, and backprops through the operations for the gradient.\n",
"\n", "\n",
"We also compute the reference $y = \\mathcal P(x^*)$ in the loss function on-the-fly.\n" "We also compute the reference $y = \\mathcal P(x^*)$ in the loss function on-the-fly.\n"
], ],
@@ -308,7 +309,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 148, "execution_count": 22,
"outputs": [], "outputs": [],
"source": [ "source": [
"# @math.jit_compile\n", "# @math.jit_compile\n",
@@ -322,11 +323,11 @@
" y = diffuse.fourier(x, 8., 1)\n", " y = diffuse.fourier(x, 8., 1)\n",
" dx, _, amp, raw_kernel, kernel, sig_prob = inv_diffuse(y_target - y, 8., uncertainty=abs(y_target - y) * 1e-6)\n", " dx, _, amp, raw_kernel, kernel, sig_prob = inv_diffuse(y_target - y, 8., uncertainty=abs(y_target - y) * 1e-6)\n",
" correction = x + dx\n", " correction = x + dx\n",
" loss = field.l2_loss(prediction - correction)\n", " y_l2 = field.l2_loss(y - y_target) # not important, just for tracking \n",
" y_l2 = field.l2_loss(y - y_target)\n", " loss = field.l2_loss(prediction - correction) # proxy L2 loss for network\n",
" else:\n", " else:\n",
" y = diffuse.fourier(prediction, 8., 1)\n", " y = diffuse.fourier(prediction, 8., 1)\n",
" y_l2 = loss = field.l2_loss(y - y_target)\n", " loss = y_l2 = field.l2_loss(y - y_target) # for Adam we backprop through the loss and y\n",
" return loss, x, y, field.l2_loss(x_gt - x), y_l2\n" " return loss, x, y, field.l2_loss(x_gt - x), y_l2\n"
], ],
"metadata": { "metadata": {
@@ -364,9 +365,9 @@
"base_uri": "https://localhost:8080/" "base_uri": "https://localhost:8080/"
}, },
"id": "PK47PUNKaeA0", "id": "PK47PUNKaeA0",
"outputId": "2529bd34-0594-443e-8f71-9e1fe72d1435" "outputId": "f275a0bb-6fab-412a-fcc7-e2a786b8fa8b"
}, },
"execution_count": 149, "execution_count": 23,
"outputs": [ "outputs": [
{ {
"output_type": "stream", "output_type": "stream",
@@ -400,7 +401,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 150, "execution_count": 24,
"outputs": [ "outputs": [
{ {
"output_type": "stream", "output_type": "stream",
@@ -443,7 +444,7 @@
"colab": { "colab": {
"base_uri": "https://localhost:8080/" "base_uri": "https://localhost:8080/"
}, },
"outputId": "0b3f0a60-aa3a-4b5a-9e6d-dd4fef70f509" "outputId": "272f48e4-fadd-44d6-c8b3-3704c8135a9a"
} }
}, },
{ {
@@ -464,8 +465,8 @@
"source": [ "source": [
"import pylab as plt\n", "import pylab as plt\n",
"fig = plt.figure().gca()\n", "fig = plt.figure().gca()\n",
"pltx = range(len(loss_adam_x)) # np.linspace(-1,1,N)\n", "pltx = range(len(loss_gd_x)) \n",
"fig.plot(pltx, loss_adam_x , lw=2, color='blue', label=\"GD\") \n", "fig.plot(pltx, loss_gd_x , lw=2, color='blue', label=\"GD\") \n",
"fig.plot(pltx, loss_sip_x , lw=2, color='red', label=\"SIP\")\n", "fig.plot(pltx, loss_sip_x , lw=2, color='red', label=\"SIP\")\n",
"plt.xlabel('iterations'); plt.ylabel('x loss'); plt.legend(); plt.yscale(\"log\")\n" "plt.xlabel('iterations'); plt.ylabel('x loss'); plt.legend(); plt.yscale(\"log\")\n"
], ],
@@ -475,9 +476,9 @@
"base_uri": "https://localhost:8080/", "base_uri": "https://localhost:8080/",
"height": 300 "height": 300
}, },
"outputId": "3dd0ee6e-3592-4d03-d5ed-a886d7994b6e" "outputId": "aee621e7-d572-44fb-8100-43988e999ae1"
}, },
"execution_count": 151, "execution_count": 25,
"outputs": [ "outputs": [
{ {
"output_type": "display_data", "output_type": "display_data",
@@ -508,10 +509,10 @@
"cell_type": "code", "cell_type": "code",
"source": [ "source": [
"fig = plt.figure().gca()\n", "fig = plt.figure().gca()\n",
"pltx = range(len(loss_adam_y)) \n", "pltx = range(len(loss_gd_y)) \n",
"import scipy # for filtering\n", "import scipy # for filtering\n",
"fig.plot(pltx, scipy.ndimage.filters.gaussian_filter1d(loss_adam_y,sigma=2) , lw=2, color='blue', label=\"GD\") \n", "fig.plot(pltx, scipy.ndimage.filters.gaussian_filter1d(loss_gd_y,sigma=2) , lw=2, color='blue', label=\"GD\") \n",
"fig.plot(pltx, scipy.ndimage.filters.gaussian_filter1d(loss_sip_y ,sigma=2) , lw=2, color='red', label=\"SIP\")\n", "fig.plot(pltx, scipy.ndimage.filters.gaussian_filter1d(loss_sip_y ,sigma=2), lw=2, color='red', label=\"SIP\")\n",
"plt.xlabel('iterations'); plt.ylabel('y loss'); plt.legend(); plt.yscale(\"log\")\n" "plt.xlabel('iterations'); plt.ylabel('y loss'); plt.legend(); plt.yscale(\"log\")\n"
], ],
"metadata": { "metadata": {
@@ -520,9 +521,9 @@
"height": 300 "height": 300
}, },
"id": "KcJemrzNu6dm", "id": "KcJemrzNu6dm",
"outputId": "284fe910-faf9-4452-aa1b-b533e77a1818" "outputId": "d3f1bf55-4673-44a8-8793-a58c99442753"
}, },
"execution_count": 152, "execution_count": 26,
"outputs": [ "outputs": [
{ {
"output_type": "display_data", "output_type": "display_data",
@@ -552,57 +553,25 @@
{ {
"cell_type": "code", "cell_type": "code",
"source": [ "source": [
"#todo plot outputs\n", "vis.plot(x_gd.values.batch[0], x_sip.values.batch[0], data.values.batch[0]);"
"\n",
"#vis.plot(generate_heat_example(batch(view_examples=2), spatial(x=64, y=64)));\n",
"#vis.plot(x_gd);\n",
"#print(format( tensor(x_gd.values,convert=True) ))\n",
"\n",
"#t1=tensor(x_gd.values,convert=True)\n",
"t2a=math.Tensor.numpy(x_gd.values ,\"batch,y,x\")\n",
"t2b=math.Tensor.numpy(x_sip.values,\"batch,y,x\")\n",
"t2c=math.Tensor.numpy(data.values,\"batch,y,x\")\n",
"t3=math.tensor( np.concatenate([ t2a[0],t2b[0],t2c[0] ],axis=0) , spatial(x=3*64, y=64))\n",
"print(format( t2a.shape ))\n",
"vis.plot(t3)\n",
"\n",
"#vis.plot( [math.tensor( t2a[0] , spatial(x=64, y=64)) , math.tensor( t2b[0] , spatial(x=64, y=64))] , row_dims=\"2\", col_dims=\"1\" )\n"
], ],
"metadata": { "metadata": {
"id": "gNvf0FuxwfdF", "id": "gNvf0FuxwfdF",
"colab": { "colab": {
"base_uri": "https://localhost:8080/", "base_uri": "https://localhost:8080/",
"height": 759 "height": 390
}, },
"outputId": "775f10d9-a956-40d5-926e-63a9098c7c3e" "outputId": "dbea2b17-baf0-43a7-bceb-43921beb4b97"
}, },
"execution_count": 154, "execution_count": 27,
"outputs": [ "outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"(128, 64, 64)\n"
]
},
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<Figure size 864x360 with 2 Axes>"
],
"image/png": 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truncated
},
"metadata": {},
"execution_count": 154
},
{ {
"output_type": "display_data", "output_type": "display_data",
"data": { "data": {
"text/plain": [ "text/plain": [
"<Figure size 864x360 with 2 Axes>" "<Figure size 864x360 with 6 Axes>"
], ],
"image/png": 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}, },
"metadata": { "metadata": {
"needs_background": "light" "needs_background": "light"
@@ -615,7 +584,7 @@
"source": [ "source": [
"## Next steps\n", "## Next steps\n",
"\n", "\n",
"* For this example, it's worth experimenting with various training parameters: run it longer, with varying learning rates, and different network sizes (or even different architectures)." "* For this example, it's worth experimenting with various training parameters: run the training longer, with varying learning rates, and different network sizes (or even different architectures).\n"
], ],
"metadata": { "metadata": {
"id": "pC5xFvjv7wGz" "id": "pC5xFvjv7wGz"