diff --git a/physicalloss-code.ipynb b/physicalloss-code.ipynb index daf9771..f7f9068 100644 --- a/physicalloss-code.ipynb +++ b/physicalloss-code.ipynb @@ -23,7 +23,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 1, "metadata": {}, "outputs": [ { @@ -71,7 +71,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ @@ -116,7 +116,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 3, "metadata": {}, "outputs": [], "source": [ @@ -139,9 +139,22 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 4, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "WARNING:tensorflow:From :7: dense (from tensorflow.python.layers.core) is deprecated and will be removed in a future version.\n", + "Instructions for updating:\n", + "Use keras.layers.Dense instead.\n", + "WARNING:tensorflow:From /usr/local/lib/python3.7/site-packages/tensorflow_core/python/layers/core.py:187: Layer.apply (from tensorflow.python.keras.engine.base_layer) is deprecated and will be removed in a future version.\n", + "Instructions for updating:\n", + "Please use `layer.__call__` method instead.\n" + ] + } + ], "source": [ "# generate array with positions: \n", "# -1 to 1 spatial with 128 cells\n", @@ -159,12 +172,14 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Let's give this a try: we can initialize a TF session, evaluate `grid_u` and show it in an image, just like the phiflow solution we computed previously." + "Let's give this a try: we can initialize a TF session, evaluate `grid_u` and show it in an image, just like the phiflow solution we computed previously. \n", + "\n", + "(Note, as before the x axis does not show actual simulation time, but is showing 32 steps \"blown\" up by a factor of 16 to make the changes over time easier to see in the image.)" ] }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 5, "metadata": { "scrolled": true }, @@ -174,13 +189,20 @@ "output_type": "stream", "text": [ "Size of grid_u: (1, 128, 33, 1)\n", - "-0.37623337\n", + "WARNING:tensorflow:From /Users/thuerey/Dropbox/mbaDevelSelected/phiflow-v1.5/phi/tf/session.py:17: The name tf.Session is deprecated. Please use tf.compat.v1.Session instead.\n", + "\n", + "WARNING:tensorflow:From /Users/thuerey/Dropbox/mbaDevelSelected/phiflow-v1.5/phi/tf/session.py:18: The name tf.get_default_graph is deprecated. Please use tf.compat.v1.get_default_graph instead.\n", + "\n", + "WARNING:tensorflow:From /Users/thuerey/Dropbox/mbaDevelSelected/phiflow-v1.5/phi/tf/session.py:28: The name tf.global_variables_initializer is deprecated. Please use tf.compat.v1.global_variables_initializer instead.\n", + "\n", + "WARNING:tensorflow:From /Users/thuerey/Dropbox/mbaDevelSelected/phiflow-v1.5/phi/tf/session.py:29: The name tf.train.Saver is deprecated. Please use tf.compat.v1.train.Saver instead.\n", + "\n", "Randomly initialized network state:\n" ] }, { "data": { - "image/png": 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\n", 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\n", "text/plain": [ "
" ] @@ -213,28 +235,12 @@ ] }, { - "cell_type": "code", - "execution_count": 10, + "cell_type": "markdown", "metadata": {}, - "outputs": [ - { - "ename": "SyntaxError", - "evalue": "invalid syntax (, line 1)", - "output_type": "error", - "traceback": [ - "\u001b[0;36m File \u001b[0;32m\"\"\u001b[0;36m, line \u001b[0;32m1\u001b[0m\n\u001b[0;31m random guess\u001b[0m\n\u001b[0m ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n" - ] - } - ], "source": [ - "explain results from random guess \n", + "This visualization already shows a smooth transition over space and time. So far, this is purely the random initialization of the NN that we're sampling here. So it has nothing to do with a solution of our PDE-based model up to now.\n", "\n", - "\n", - "TODO\n", - "\n", - "x\n", - "x\n", - "x\n" + "The next steps will actually evaluate the constraints in terms of data (from the `boundary` functions), and the model constraints from `f` to retrieve an actual solution to the PDE." ] }, { @@ -243,24 +249,25 @@ "source": [ "## The loss functions & training\n", "\n", - "set up losses...\n", + "As objective for the learning process we can now combine the _direct_ constraints, i.e., the solution at $t=0.5$ and the Dirchlet $u=0$ boundary conditions with the loss from the PDE residuals. For both boundary constraints we'll use 100 points below, and then sample the solution in the inner region with an additional 1000 points.\n", "\n", - "Note: very slow, needs _lots_ of iterations, only 10k for testing by default (`iters`), increase to get better results." + "The direct constraints are evaluated via `network(x, t)[:, 0] - u`, where `x` and `t` are the \"position\" where we'd like to sample out solution, and `u` provides the corresponding ground truth value.\n", + "\n", + "For the physical loss points, we have no ground truth solutions, but we'll only evaluate the PDE residual via the NN derivatives, to see whether the solution satisfies PDE model. If not, this directly gives us an error to be reduced via a update step in the optimization. The corresponding expression is of the form `f(network(x, t)[:, 0], x, t)` below. Note that for both data and physics terms the `network()[:, 0]` simply discard the last size-1 dimension of the $(n,1)$ tensor returned by the network." ] }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 6, "metadata": {}, "outputs": [ { - "name": "stderr", + "name": "stdout", "output_type": "stream", "text": [ - "/home/thuerey/anaconda3/envs/tf/lib/python3.8/site-packages/tensorflow/python/keras/legacy_tf_layers/core.py:171: UserWarning: `tf.layers.dense` is deprecated and will be removed in a future version. Please use `tf.keras.layers.Dense` instead.\n", - " warnings.warn('`tf.layers.dense` is deprecated and '\n", - "/home/thuerey/anaconda3/envs/tf/lib/python3.8/site-packages/tensorflow/python/keras/engine/base_layer_v1.py:1719: UserWarning: `layer.apply` is deprecated and will be removed in a future version. Please use `layer.__call__` method instead.\n", - " warnings.warn('`layer.apply` is deprecated and '\n" + "WARNING:tensorflow:From /usr/local/lib/python3.7/site-packages/tensorflow_core/python/ops/math_grad.py:1375: where (from tensorflow.python.ops.array_ops) is deprecated and will be removed in a future version.\n", + "Instructions for updating:\n", + "Use tf.where in 2.0, which has the same broadcast rule as np.where\n" ] } ], @@ -282,40 +289,49 @@ "loss = loss_u + ph_factor * loss_ph # allows us to control the relative influence of loss_ph \n", "\n", "optim = tf.train.GradientDescentOptimizer(learning_rate=0.05).minimize(loss)\n", - "#optim = tf.train.AdamOptimizer(learning_rate=0.001).minimize(loss) # not much benefit here\n" + "#optim = tf.train.AdamOptimizer(learning_rate=0.001).minimize(loss) # alternative, but not much benefit here\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The code above just initializes the evaluation of the loss, we still didn't do any optimization steps, but we're finally in a good position to get started with this.\n", + "\n", + "Note: despite the simple equation, the convergence is typicaly very slow. It needs a _lot_ of iterations. To keep the runtime in a reasonable range, we only do 10k iterations by default below (`iters`). You can increase this value to get better results." ] }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Step 0, loss: 0.238804\n", - "Step 500, loss: 0.051395\n", - "Step 1000, loss: 0.045798\n", - "Step 1500, loss: 0.043285\n", - "Step 2000, loss: 0.041360\n", - "Step 2500, loss: 0.039480\n", - "Step 3000, loss: 0.037504\n", - "Step 3500, loss: 0.035440\n", - "Step 4000, loss: 0.033171\n", - "Step 4500, loss: 0.031074\n", - "Step 5000, loss: 0.029556\n", - "Step 5500, loss: 0.028347\n", - "Step 6000, loss: 0.026291\n", - "Step 6500, loss: 0.024694\n", - "Step 7000, loss: 0.022832\n", - "Step 7500, loss: 0.020840\n", - "Step 8000, loss: 0.035597\n", - "Step 8500, loss: 0.021575\n", - "Step 9000, loss: 0.080320\n", - "Step 9500, loss: 0.036767\n", - "Step 10000, loss: 0.034146\n", - "Runtime 77.39s\n" + "Step 0, loss: 0.185030\n", + "Step 500, loss: 0.066632\n", + "Step 1000, loss: 0.050299\n", + "Step 1500, loss: 0.046025\n", + "Step 2000, loss: 0.042862\n", + "Step 2500, loss: 0.039872\n", + "Step 3000, loss: 0.037071\n", + "Step 3500, loss: 0.033701\n", + "Step 4000, loss: 0.026160\n", + "Step 4500, loss: 0.019593\n", + "Step 5000, loss: 0.064136\n", + "Step 5500, loss: 0.045300\n", + "Step 6000, loss: 0.040658\n", + "Step 6500, loss: 0.037709\n", + "Step 7000, loss: 0.033832\n", + "Step 7500, loss: 0.030921\n", + "Step 8000, loss: 0.027804\n", + "Step 8500, loss: 0.022738\n", + "Step 9000, loss: 0.075315\n", + "Step 9500, loss: 0.039424\n", + "Step 10000, loss: 0.033949\n", + "Runtime 83.99s\n" ] } ], @@ -340,21 +356,21 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "This training can take a significant amount of time, around 1 minute on a typical notebook, but at least the error goes down significantly, and the network seems to successfully converge to a solution.\n", + "This training can take a significant amount of time, around 1 minute on a typical notebook, but at least the error goes down significantly (roughly from around 0.2 to ca. 0.03), and the network seems to successfully converge to a solution.\n", "\n", "Let's show the reconstruction of the network, by evaluating the network at the centers of a regular grid, so that we can show the solution as an image. Note that this is actually fairly expensive, we have to run through the whole network with a few thousand weights for all of the $128 \\times 32$ points in the grid.\n", "\n", - "It looks pretty good on first sight, though:\n" + "It looks pretty good on first sight, though. There's been a very noticeable change compared to the random initialization shown above:\n" ] }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 8, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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sebEc8bxKnGxIcgAbJuzwCmw0T0hyW2LbW66R+3yhjXkRIFhVdiE+qRlvnRsEuc8cHtvqzpdlE6xKSpG2dULMlcsmxIjsTDw52aHrprgqd0OVEz1OgCfQdnbaEL3J8yoh0v3eA4BN0+S2XGt3a6GNA2C+EL3YhXYOVaJTCTb9dZ09IPR+5x0wCHKfu/HYVPDcRX3qyv6IF6vqlFMFIiHq3qmqL5BHVL3JheZNquSpepPpxNlohAiw6ZrsdCGSrEieM1FuPteIUyXiheuGz5NLQmR9IqyPchmRjNW2V4bc3TWvLtuLjZC7SoqqEVD1qXIqEUcmarLJWA3t5bDetLBeJeJNf1ySgwAZz1U57dxkk7GrcgGCHbxnrJadFqyZzGh7EOQ+d+fsZjc56eSe78WqnvamSJ4qyW6KD9+m+J5J1dsFON/kpgrUnKhKstOZRu6qt6sSMegphYUqJ3vGas52H7xrNd2LHT4Zq2NZGc994dqE0lycUZVTGWIuFmBL9EamYopCJePz4iz8plgBsCHmYiGftLNTFFsiuWfngAEWruaLcz3olNUtfaPUFr0iZK84MA6ZtNctLTN357Fp9829pXrFrhHsFnp5V3Y51lSUUwl2Kk6MTec6uWfngVXPON8rziXipbCaL5brp/S2JeQSrAUqy0p55I2454KJcqq+pU61j1rJd9MU3PI3Ewu0Sbmp+PBNRdLeDNSxTk3LiZ4X88BTxCqFQl4xRPLFyaRdyCt20SlYYh940AJk0u7Bi80mbXlSs4fUiEraa5eWmTPnrDDppaYeVK94UyRYiJCspnMmyk3naupBI8RQXlkkWdWD1lMP6iRfhIw1jeWgesZq+C9vVqOJhci9jAetpjxUr1gl7IhOvY+7X9Q5CHJfsJAqJDbVlAeinJjKgPx64FJVFCphw34g7WHv97PEapC2SsQRWTn/XIi0I6mRbNKOpIR2wiDIfc6Mx+zRTjmVYGci0YVSFIPPK6upB53c9TSFvEmC3HYZ5O++ZuobdZJJNp1gA2SjElMpMtZz8/p+V/KY5VTUqnjuvsUTs4u+avVpmInEpBOsnnMf+iRfPhHD8MlYhbhneeTVZuke77AnDSNebCkyzs57jwIEK3vu6rlZlZy7s5C8aJVgeyl9WxnSXhXChnTS7iGvvCqk3Uf+eeikHaqWEe8xte2VWcS08DmbW+c65fS9KDTiVIk4olMvkVvHvLKqrUwqI1I+uCpknE3EkbZHQyd3AgZNvGflPgba3gmDIHfcJeLOJu1+6pqzKzhKotRk4LBTHpG2S5H2SHy/nzrBF/Eks0k7O5WhknYvaRnVCKyK5+4smAulgfKeFXJVRsQrHnraI5eIlxrLkHGpUro+vNP0FEVytUUfKQo99SCmMkQy1ic1c9uFCLnnGoFLYRDkDiJxp5N2yYUo2ZUZyd4zFCunK0XaRfPKAyftiBeb7RmrxCkbAZncA8Y+2SNvxNcfXgoDIXfHpb2Y98OqQPUiZ68M7KNeOVenTCRqSmEN88p6u6Jcslcc0plMstkEO/b8CVXdc9+Dd6ia2fuBNwFn3P3322NXAx8FbgAeAm5397NmZsB7gFuBJ4G/cPevdXfDySXu/I2LViVfvB/qlbPzxb14p9kedLK3qxKsLpfvxY5E8lQJUTcqYpVVwHvWSXtA5A58APhX4EPbjp0A7nP3u83sRPv5HcAbgRvbn1cA721/d8DIJOTYJkeq0kIpimSPPOSBNQc1nYVSFGNL9vAD5F7KM84m7bEoF5ngUz1e1dsdqx65SMbZRLyUVctyB0Tu7v5FM7vhGYdvA25u//4g8AWW5H4b8CF3d+D/zOyImR1z90e62pEIeQ1TFHoqI5eII22rpDhW+1jIKx6b1j/IJ9ls71Ql2GxvF/I9crXtkZwa0fRFxqw6lH20vROebc796DbC/hlwtP37+cBPt8k93B77NXI3s+PA8faTRNy19G33+lQjsGw7l2RHInkO3SuOyKqesUqIeru53u44lJYZNhlnE3GobRs+uT8Fd3czC9f/uftJ4CSA2dib5lDn/6xS6Vv2pGG2Vww6yY7pvnaRtkulHlSCjbWdm3+WSVudNOwhTTBK1plNiHLRsNhuqG1RZUlyf/RCusXMjgEXNoY5DVy/Te669lgHTCLuUtUWkJ9XVj3oUl4xBAhMbTt58q5UigJg5Gq+WG0714tVSTubiCGfjEfZ5N4DwQbsQHrbO+HZkvs9wJ3A3e3vT2w7/jYz+wjLidRzSr69sYYDoys6Gy3lFUO5fHG2VzwR9UE+yU5cO4elvF2VYCGSesj1oFXiHKmpB1XfPvBiG7WgTTYWOtLJPUGfUgr5YZaTp881s4eBv2dJ6h8zs7uAnwC3t+KfYlkGeYplKeRfSr2whtGom5BLecVL2Vyd2d7uGJU49TFPXDOSskdeyNvN9mIjOodOxtlEDDAWhbNJVjYWfRTTJRugDCjVMnfs8NXrLiLrwFujnWgYcWh8pFtOJPexad5pH9UR2SRbimABDshplDIkO5I3YcolzmXbZUh2JLJDSULMJjo9R67K5ebmI9Cji923NYgVqo2NuKx5Tqdctrc7EYkY8kl24skTcqLcJJB6kMlY3o0vlxBLEeeybU1OVamOZT8QXTaB5RuqPl7Kkos9ScvsBYyGiV3WKaeScXYOeCmrkrGa+1bzxWW83aVO7Q6bNMn1yiq5i09ANhEvdeaS4lhsPJvcswk2pLOQQVNRMueegUGQe8OYK/yaTrlSBLuUTU49iCQ7KeQVQz556n3U9GV7xTFy1+RKEd04vX9iwwGkG6pn3ZPdtdsHVsZzbzAOCl70RPTID8ipDN02T8T3KWaTrEzuyUS8lB02GY/Ey6de5UhaJpuYss/h0Ikz0nY2yZYcy15iEOQ+YsQRDnfLFfJ2ASYyeeYSUzbBxjx3VWdu26UIMWL48nPfZdotlfIo2XZJIt7LpgdB7gYcaLo94/QUReAqTwZOxtlEHGk7OwVQirRjFSG5Ooeuryy5l3kBzgCd8RAGQe4jM66cdHclmzhVbxzKebEqcfZB7vpkYG7bQ095QD4xDX3SsI8Jw+yNuUtOajYDfNfxIMh96bl3Xxm1oiCbbJaywybjfipCcuXKkXYuwS51inKivlJlgSr6IK/9kEvfzxgEuY8a44oD3bftpKAXm010pUg7MmaVFOU+iu1mE91IHMd+yCurJJtP7uUwxMnKZ8Kq535xjAyuFAphShEnRKKBXC+xVD4bdCLJNkDZBCa/BSCUlsl9mMuV+w3fI8/GEIm4DwyC3JdpmW45lUSyiRjyyTi7TnrcQ+pB1lmIZNWHtA/izCbF7DFnt9sHSkYD64BBkHtjzhWT7ptWD8NVOf1ByU+PiMSkqesl9ZA9aViKtPV0kH4/ZBNTtrEo6TyXqm6peDpsuddX4U6YPQ48WLofBfFc4OelO1EI6zx2WO/x17HvHr/t7tde7ItBeO7Ag+7+8tKdKAUz+8q6jn+dxw7rPf469n7HXtNeFRUVFSuISu4VFRUVK4ihkPvJ0h0ojHUe/zqPHdZ7/HXsPWIQE6oVFRUVFbkYiudeUVFRUZGI4uRuZreY2YNmdsrMTpTuTzbM7P1mdsbMHth27Gozu9fMftj+fk573MzsX9pz8S0ze2m5nufAzK43s8+b2XfN7Dtm9vb2+MqfAzM7ZGZfNrNvtmP/h/b4C8zsS+0YP2pmB9rjB9vPp9rvbyjZ/wyY2cjMvm5mn2w/r9PYHzKzb5vZN8zsK+2xPbvvi5K7mY2AfwPeCLwIuMPMXlSyTz3gA8Atzzh2ArjP3W8E7ms/w/I83Nj+HAfeu0d97BMz4K/d/UXAK4G3ttd4Hc7BJvBad38x8BLgFjN7JfBPwLvd/XeAs8BdrfxdwNn2+Ltbuf2OtwPf2/Z5ncYO8Bp3f8m2sse9u+/dvdgP8Crg09s+vxN4Z8k+9TTOG4AHtn1+EDjW/n2MZZ0/wPuAOy4mtyo/wCeA16/bOQAuB74GvILl4pVxe/ypZwD4NPCq9u9xK2el+76LMV/XEthrgU+yXDi7FmNvx/EQ8NxnHNuz+750Wub5wE+3fX64PbbqOOruj7R//ww42v690uejDbX/EPgSa3IO2rTEN4AzwL3Aj4DH3H3Wimwf31Njb78/B3S/XHi4+Gfgb4BF+/ka1mfsAA58xsy+ambH22N7dt8PZYXq2sLd3SKbmuxTmNlvAP8N/JW7/9K27Ta2yufA3efAS8zsCPBx4PcKd2lPYGZvAs64+1fN7ObS/SmEV7v7aTN7HnCvmX1/+5d93/elPffTwPXbPl/XHlt1PGpmxwDa32fa4yt5PsxswpLY/8Pd/6c9vFbnwN0fAz7PMhVxxMwuOFbbx/fU2NvvrwJ+scddzcIfAX9sZg8BH2GZmnkP6zF2ANz9dPv7DEvDfhN7eN+XJvf7gRvbGfQDwFuAewr3aS9wD3Bn+/edLPPQF47/eTtz/krg3LYQbl/Cli76vwPfc/d3bftq5c+BmV3beuyY2WUs5xq+x5Lk39yKPXPsF87Jm4HPeZuA3W9w93e6+3XufgPL5/pz7v5nrMHYAczssJldceFv4A3AA+zlfT+ASYdbgR+wzEX+ben+9DC+DwOPAFss82h3scwl3gf8EPgscHUrayyrh34EfBt4een+J4z/1Sxzj98CvtH+3LoO5wD4A+Dr7dgfAP6uPf5C4MvAKeC/gIPt8UPt51Pt9y8sPYak83Az8Ml1Gns7zm+2P9+5wG17ed/XFaoVFRUVK4jSaZmKioqKih5Qyb2ioqJiBVHJvaKiomIFUcm9oqKiYgVRyb2ioqJiBVHJvaKiomIFUcm9oqKiYgVRyb2ioqJiBfH/nkMdMjPeUNQAAAAASUVORK5CYII=\n", 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" ] @@ -366,7 +382,7 @@ } ], "source": [ - "show_state(session.run(grid_u)) # note, this helper internally does a `sess.run()`" + "show_state(session.run(grid_u)) " ] }, { @@ -382,22 +398,22 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "" + "" ] }, - "execution_count": 8, + "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -410,7 +426,7 @@ ], "source": [ "u = session.run(grid_u)\n", - "#[u,gx,gt] = session.run([grid_u,grid_x,grid_t]) # print(gt[0:5,17]) # check time...\n", + "\n", "# solution is imposed at t=1/2 , which is 16 in the array\n", "bc_tx = 16 \n", "uT = u[0,:,bc_tx,0]\n", @@ -424,33 +440,31 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Not too bad at the sides of the domain (the Dirichlet boundary conditions $u=0$ are fulfilled), but the shock at $x=0$ is not well represented.\n", + "Not too bad at the sides of the domain (the Dirichlet boundary conditions $u=0$ are fulfilled), but the shock in the center (at $x=0$) is not well represented.\n", "\n", "Let's check how well the initial state at $t=0$ was reconstructed. That's the most interesting, and toughest part of the problem (the rest basically follows from the model equation and boundary conditions, given the first state).\n", "\n", - "And turns out, it's actually not that great, blue curve from PINN quite far away from constraits (in gray)... Solution get's better with larger number of iterations, but requires a surprisingly large number of them for a fairly simple case. The shock in the middle is not well recovered (the maximum is still much too low).\n", - "\n", - "... shown in blue, compared ot the (known) ground truth solution in gray ..." + "It turns out, the accuracy of the initial state is actually not that great: the blue curve from the PINN is quite far away from the constraits (shown in gray)... The solution will get better with larger number of iterations, but it requires a surprisingly large number of them for a fairly simple case. \n" ] }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "[]" + "[]" ] }, - "execution_count": 9, + "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -476,16 +490,17 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "That's not very close...\n", - "especially the maximum / minimum at $x=\\pm 1/2$ are far off, and the boudaries at $x=\\pm 1$ are not fulfilled.\n", + "Especially the maximum / minimum at $x=\\pm 1/2$ are far off, and the boudaries at $x=\\pm 1$ are not fulfilled: the solution is not at zero.\n", "\n", "We have the forward simulator for this simulation, so we can use the $t=0$ solution of the network to \n", - "evaluate how well the temporal evoluation was reconstructed by the PINN. This measures how well the temporal evolution of the model equation was captured via the soft constraints of the PINN loss." + "evaluate how well the temporal evoluation was reconstructed by the PINN. This measures how well the temporal evolution of the model equation was captured via the soft constraints of the PINN loss.\n", + "\n", + "The graph below shows the initial state in blue, and two evolved states at $t=8/32$ and $t=15/32$. Note that this is the simulated version, we'll show the PINN version next." ] }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 19, "metadata": {}, "outputs": [ { @@ -498,16 +513,16 @@ { "data": { "text/plain": [ - "[]" + "[]" ] }, - "execution_count": 10, + "execution_count": 19, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -519,7 +534,7 @@ } ], "source": [ - "# re-run with phiflow from solution at t=0\n", + "# re-simulate with phiflow from solution at t=0\n", "dt = 1./32.\n", "steps = 32-bc_tx # depends on where BCs were imposed\n", "initial = u[...,bc_tx:(bc_tx+1),0] # np.reshape(u0, [1,len(u0),1]) \n", @@ -533,14 +548,14 @@ " state.append( physics.step(state[-1],dt=dt) )\n", "\n", "# we only need \"velocity.data\" from each phiflow state\n", - "vels = [x.velocity.data for x in state]\n", + "vel_resim = [x.velocity.data for x in state]\n", "\n", "fig = plt.figure().gca()\n", "pltx = np.linspace(-1,1,len(vels[0].flatten()))\n", - "fig.plot(pltx, vels[ 0].flatten(), lw=2, color='blue')\n", - "#fig.plot(pltx, vels[steps//4].flatten(), lw=2, color='green')\n", - "fig.plot(pltx, vels[steps//2].flatten(), lw=2, color='cyan')\n", - "fig.plot(pltx, vels[steps-1].flatten(), lw=2, color='purple')\n", + "fig.plot(pltx, vel_resim[ 0].flatten(), lw=2, color='blue')\n", + "#fig.plot(pltx, vel_resim[steps//4].flatten(), lw=2, color='green')\n", + "fig.plot(pltx, vel_resim[steps//2].flatten(), lw=2, color='cyan')\n", + "fig.plot(pltx, vel_resim[steps-1].flatten(), lw=2, color='purple')\n", "#fig.plot(pltx, t0gt, lw=2, color='gray') # optionally show GT, compare to blue\n" ] }, @@ -548,12 +563,12 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Versus the PINN output:\n" + "And here is the PINN output from `u` at the same time steps:\n" ] }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 18, "metadata": {}, "outputs": [ { @@ -566,16 +581,16 @@ { "data": { "text/plain": [ - "[]" + "[]" ] }, - "execution_count": 11, + "execution_count": 18, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -606,30 +621,29 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "[(2048,), (2048,)]\n", - "Mean absolute error across 16 steps: 0.01397\n" + "Mean absolute error for re-simulation across 16 steps: 0.01142\n" ] }, { "data": { "text/plain": [ - "[]" + "[]" ] }, - "execution_count": 20, + "execution_count": 13, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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ec8D+WtWV1bHxuY1seHoD1YXVrdtbojyUzBlG6dR0qselUDMskcZBUXhjIomsbyaqrpGEI7VkHTxGVkE1SVtLaSyto3BlIYUr7Zw6ETERjJg7gpzrcph4w0RSJ6ZqjqGH/BenOo49A+Qeb+DX978FwGX/dhmJwxJdfT9fBr2xH+UIju4/ykc//4iNz21sDWzxafGM//x4xl87nqzZWSSPSyYiKqL1HNNig0HZtjKObD5C6eZSjmw6QsWuCip22kdH3vnOCuK+kIP3P66gbEo6ccAY7JSF5wGx3fLX9g7eRi/5b+ez5aUt7PrzLozX3oxOunESV/38KpLHp3Af8DTwBPCPLr//gAsElfmVfPT4R2x5aQveRvshN1kJbPy7yWxdMImiC0bSHB/FSOwQAhOwNerNQCVQhh2q4KTfayaU1DDqw4Nkv3+AiWsPkLS1jANrD3Bg7QFW/WAVKeNTmHDDBCbNn8Soi0YhHg0KbjPAfwD/4qz/Gvgy8NbDqzhedJxhucOY++3QWwoF8rUcqu8HgaD2SC3v/fg9Nj670f4QCeR8IYfZX5tNznU5p/3wBxKPkDgskcRhiYy7ehwGqAOq6pup2FFOxeYjnCyro+lkM03NLZxMiKYmIZqiFsPhk03IR4cYtzyfE2/spnFlIe/++jo2L5rZ+vqxwMXAlc5jJn27pUvTiSbKtpVR/Gkx+1bvY997+2g41gCARAjTb5/OhQ9eyNCZQwH4ATYIxALndkN6BkwgqCur4+1vvc2O13ZgWgziERK+OIGXv57L5qvHYSI8XAE8AlwPZLbzWi3YSshdzmN7ViJ5N09lxc1TWQ7EVZ1kzLv7mPCXPUx4aw8UVLHuv9ax7r/WkTAskWm3TmXabdMYljtMcwouOAHch52DWLA5gbuBvSv3kvfrPDyRHm549gY8ke7/dPgCwcmYCGLpm62Gmhua+dsv/saHj31IU10TEiHM+PIMLnr4ItInd25+8J3AUiAP2Iydy9kLEBsJs7PsowNTSmu56sGVJL+0hRvveoMFHxxk36+/wOboCDYDK50HwGBsMJjl9zwFCGdthGkxnKw6yYmKE5yoPMHJytOX68rrOH7wONX7qjm67+gZRdAZ0zOY8eUZTL9tOoNHDG7d/jPg59gf6yXYgOg2VwKBiFyLLZqNAJ4xxjwWsD8GeBEbzCqBW40x+519DwP3YD833zLGrHAjTYFikmI48P4BJEKYds8sln//czw7PgWAS4GfAhd28rU8wGjncY3f9pPARmB9Shyf3jSFT2+awrLmFkZ8fIiJy3YzZclO2H+UdU+sY90T64gZn8I5C6eSe9t00qd07gunTrcHuAX74zMI+B12UuzqfdW8vtBOfjfvh/PInNFeaD97vkBQFxtpA0EfyxEUrirkrQfeoirfzhA7cf5ErnzsStImpXV47gngOWAxsDXI/njsD3Y09ochAvvdiQGGOo8p2B+Fc4GUzATMCwvYdFk2y7+xnOZnN3Lpnkp+86dbqU2L511gFTYYHATedx4+0cA0bFCY7vdw85tVV15H+fZyyraVUb6znJqiGmpKaqgtqaX2SC0tzS2deh2JEDKmZTB05lCyL8tmzBVjzmjE4MXO6/vf2BucF4EvuPi3nJaeUEdLdCaf3wNche1bsx64zRizw++YB4AZxpj7RWQhcKMx5lYRmQK8gi0CHIb9P08wxrRb45abm2vy8vK6nNb9a/ZTPz6FW0cMZgsQB/wncD/2QneHSuAjnA+tMZR+UsyUV7Yy9Y87SDxyqnNI84xMRi46h+vumMEIrTDrUDO2PuDHQD0wHntHOg2b7X72wmcp3VxKznU5LFy2sMszkHXWx9gbiK888Bajf5PHdb+6jjkPnN2Ipj2psbaRFd9dwYanNwCQNjmN6351HWMu63huhjrsj9MTQLmzbQhwI3A59g49B/uDf7ZKNpTwyhdfoeZwDcljk7n5tZvJ8stVHMHedG0ENjnPBW281lBODwzjsXUPWbRfvORt8nJ4/WH2vbePA2sPcGTTEU6Un2g33bFDYolPjyc+NZ74tHjiUuOIS41rXfe1Nkwek9xug5KjwJ3AX7C5nOeAO9p9584Rkc+MMWcMsuVGILgA+Ikx5hpn/WEAY8zP/I5Z4RzzsYhEYv+P6TiT2PuO9T+uvfc820Ags4E3sSFnF/aTu6vLLxOaBOBCkItayE7cz/TN25j8553EHa0HwBvpIf9zOWwcM5P80hxaPoqwDdXVKVcAv8De+gG8AHwbOAYeWriZ15jMLipJ4Wm+Rn13VjOOBA7CNV97hwue+YQVXM3HXNB97+eCERziSywlhWqaiWAtl/A3LsRL23UAgL2lvwt4FPsdAvgUO+XbXwCXp2NIpIbbeIVhlODFw2qu4GMuwLR125YIzMBGIv9f/rbaB9QD+4D92F6BxZCys4qJW3YxrqiQUbUHiTan/1ENRFNGBmWkU046xxhCDQnUkkgtCTS7UchyGzbKZmLvJG8EPji1O5Sf7LYCgRtFQ8OxReY+RcD5bR1jjGkWkWPYgSCHA+sCzh1OECJyL3AvwKhRo7qcyL1gb8sTgDXAl4Dqdk7oLrXAX8H81cM+xrIvdixv5X6BnGF7mFW0iZxP8pm0djeT1u6mNmMQW+6ezqbzZlF2IAPeAz7E5skHoguAHwKfd9YPYisH3rGrQgs3spTJ7KKeGF5lYfcGAYASoAWaU+xXKZLeWzTkwcslrOViPsSD4QiZ/IkvUUZGxyffiC0/neysrwcexo7h0U1qSOQ5vsJVrOR81nM1K5nMTlZwNUWtIz2ddoLNfn/kt02wZbjTsUFiKjY7MBbIAJloGFZzmIkf7mLSn3eTsaP8tJcsn5jG/jnZ7JuUTXHKCI41DIYSaQ0cFAOHsdmkUCRge0DeB/h+pj/AVna1ldVxUZ+pLDbGLMYWR5Kbm9vlmDgWuDfB3gQ8fSlEV7mbvtBEYL9hkyk/Usvylzaz7/lNJOys4MIn13Eh6yjOHcamr8xk56vTmJEcx+XAZdjfxriwpr17NWFvNp/AxkCwN3gPA98eBfFv220tzS0s++oyNr+wjeiEaO5ZeQc/m9sz9S5DgeZ4+1X61x81c9m/9sjbdkn1vmqW3LKEw3mHQeDCBy/kskcv4zcdzM62Bptt/8RZH4uNB7fMAc+qbk2yIwq4jj1vjmfZV5cxsrSIr/Ick780mfO+dR6j543ucoOLhpoGClcVsv3NPRQsL6DBr4i2JSmGqutyKLx+Alsuy6Yoq3PNjROwRRwZzrP/ciq2/sr3PfViY1YpNjPyKbZoy5f3SMVWDt91MXjyu/SnnTU3AkExnBaeRzjbgh1T5BQNJWEzPZ051xWCbVLoofvqA9yQPjSBRQ9+DvO9Cyn+tJj1z29i+yvbGJ53mOF5h7nmuyvY+aXJ/P7uWfz08jFEe4S50BoYzsdWmvVlBvvFeA1b+XvE2T4E+Aa2FMj/J76hpoHXF75O/vJ8ouKjuH357a53wW/PCMDbi0cfLVhRwOu3vU59dT1Jo5JY8OKCdnunGuBdbOmbr+VGBna8pq8Rns/XhOsn8A/5/8BHj3/Ex//5MTv/tJOdf9pJ2uQ0Js6fyLirxjFszjBiEk+vmTDGcKL8BKVbSilaV8SB922zbl/TcYDBIwczcf5EJs2fxOh5o4mIPlVEVo+94S8O8uy/XOs89p3l3yfY1kBfwzZ26OmbOzfqCCKxlcVXYK/JeuB2Y8x2v2O+AUz3qyz+kjHmFhGZCvyeU5XFq4Gc7qos7quaTjSxc+lONj2/iX2rT33UToxKYv1d57DxrpkcHZMM2A/Q57AVmOdjL2zH7T/CrwV7Z7QE+BOnf6EmY3PMd3Nmce+xg8d4df6rHNl0hLjUOBb+eSGjLup60WEo5gNlT67j2u+s4Lxvncfnf/n5Ds/pCcYY/vaLv7HqoVVgbJ+AG1+6kbjk4D8z+4HXgecB35c3EXgQO2RHQg+kuTNqDteQ99s8Njy9gdqS00fjjEuNI2FoAhhb2VtzuIamuoDKC4GRF4wk5/ocJlw/gYxpGSE14zbYarxybD+j8oDlKmxprq9ENwKbQ8jE/uidix0PazDdr9sqi50Xvw54Evs3PmeM+amIPArkGWOWiUgsdrrYWdjrstAYU+ic+wj2O94M/KMx5u2O3m+gBQJ/R/cfZdMLm9j0/KbTxntpunwMG+6eycovTaY5YGyXsdig4AsMM7AfxHBqAbZgq23WOs/+fU+HYoulbwMuIngubufSnSy7Zxn11fWk5KRw+1u3uzKqaFc9AKx/Ko/rv/4W5953Ltc/dX2PpwFskUMB9gt2tMnLvm8sp9xpFTTuJ5cw6YeXEOMRooEGbPXGQeyd2zpObwKahf277qf33kh4m7zsW72PwlWFFK4qpGJXRdAhPmKHxJI6IZXhc4cz8oKRjL1yLPFp8WFIcfh1ayDoaQM5EPiYFsP+NfvZ+NxGdr6+s7VIIjophkG3TaP47lmsyx1GnsgZdcuCrS+bhq07m4ptUpeNLQJwu+isFnuHuQ37Y7MV2IBtIudvJLYO/yZs3UdbbVjqj9Wz8vsr2bDY/sjlXJfDghcXEJ8ani/3T4Elz29kwd3LOGfROSz43YIee+9jwLPYqTjzsHWWUXWN3Pp3f2T8ir00xUay9KUb2XHTlA5faxC2M+XNwBfpe0WMpsVQV1ZHXVkd4hEkQkjMSiR2SH8enKJrurPVkAoD8QhjLh/DmMvHUP+/9Wx7dRubnt9E8afFND71GfFPfcatU9P56V0zibh1KttGJvEJtvhlJ3agtELsD4i/OGxAGIW9E0z1ewzGVt1FOo8ooBH741PHqXLSEmwZYZHzaGuUmdHAJcA853kc7QchYww7luzgnW+9Q+2RWjxRHq76+VWc/+3zw9pDewTQ3MNDTNRi+1AsdpZ9xh1v4AvX/56UDw7SlB7P9mW3kTp3BOdjKyMbnUcEtlhiGLa15fnAbPp2wwPxCAlDE2zRkOoSDQT9QOyQWHLvzyX3/lzKtpWx8fmNbHlpC+Xby1n94Ep4cCWjLhrFvQun8uRNU4jOTCCfU3fp27Hlw/uxxQo7nYdbooBJnN60+xxODdjWGQc/OsiqH6zi0Ee2pfKIC0Zw/W+vJ3N69/QY7orhnAoEPTH66EZsS8M9zvrlwNeB84/Ws+Kalyn+tJjE4YncufpO0ib21oId1ZtoIOhnMqZlcM1/XsOVP7uS/OX5bHtlG7v/srt1eOB3vvUOYy4fw9SFU/nijZO5JeX0e8Bj2HFiDmGbdfkeFdgmb17snWWz8xyNLVJI8HvOxP7I+x7pnN0AYcbY4q+PHv+IvSv2AnYUzMv+/TLO/dq5vWbwvuH0XKuh32NnXWvEFu39DlvZ2HSyiZdveIXiT4sZkj2EO9+9k2SnAYFSHdFA0E9FREcwacEkJi2YRENNA3v+sodtr26j4J2C1sq1N+97k1EXjSLnC7b1RNqkNJJEmIGtUA6XhpoGtr2yjc9++xklG0oAiBoUxQX/dAEX/tOFxAwOZfAC951WNNSNg869gR12wIttRfUEtiinxdvCn/7+Txz84CCJwxO5a+1dJI1K6rZ0qP5HA8EAEJMYw/TbpzP99umcrD7JrqW72PbKttYxVA6sPcCq769iyJghjL92vJ1gZ95o18fub0/TiSYK3ilgx2s72P2X3a1N/uLT4jnvW+cx54E5YasM7kgiEO0EgvpuyhG8ix1cz4sdavvf/Pat+M4Kdi3dReyQWO5YcYcGAdVlGggGmLjkOGbdPYtZd8+i/mg9e/+6lz1v7iF/eT5H9x0l7zd55P3GtshKHpfM6HmjGTZnGJnTM8mYnkFskjstMBrrGin5rIRDHx9i36p9HPjgwGnl66PnjWb212Yz+e8m94mpDjOcOYtPdEMgOIBtStsIfBM71I/P1le28un/fEpEdAQLly0kY2onhotQKoAGggEsdkgsU2+ZytRbptLibaH402L2v7efA+8f4NBHh6jeW0313mo2Pb+p9ZzBIweTOT2TwSMHkzgskYSsBBKzEolPj8cT6cET4UEiBE+Eh5bmFuqP1nOy+iTHi45z/NBxqvKrKN9RTmV+ZessTAAIDD9vOJNvmsyUm6b0ufLtoU6OoMHlyuIW7Dhvx7Ed137JqZZVFbsrePPeNwG49pfXMvri0a6+txo4NBAoADwRHkZeMJKRF4zk4n++mJbmFo5sOsKBDw5QurmUsq1llO8o5/gh+4MeKvEIQ2cOZfj5w8m+1I7HPig93N3czt4wp7K40eUcwS+x4/1kYGeo8lW6N9c3s+SWJTTWNjJt4TTOva875q1SA4UGAhWUJ9LDsNxhDMsd1rqtpbmFqgJ7R19z+NSEHDWHazhZeZIWbwvGa1qfPZEeYpJiiB0SS+LwRAaPGEzy2GTSp6STNjGNqPjeX+TTWcNjIzkBeF0MBLuwg+uBnXXNf3ylDx/7kNItpaTkpHD94ut1pjsVEg0EqtM8kR7SJqV1avaqgWZUbCS7gBYXWw19DzsUxFewPX19qgqq+PAxOxbrDc/ecMZAa0p1VV+e/1mpXiPbqSzGpRzBWuAtbL8M/3lfjTEs/+ZyvA1ezll0jtYLKFdoIFDKBdlOZbHHhUBggO87y9+H06aN2bV0F3tX7CV2SCxX/fyqkN9LKdBAoJQr0iM9tHgEj9dQ1ckJzNuyBDsm1FDs5OU+psXw7r+8C8Bl/34Zg3Rua+USDQRKucAjQotTPFQYQj1BC3YCGICfcPpw4bve2EXFzgoGjxzMuV/TVkLKPRoIlHKLUzx0IITioeXY1kKjsJN0+Bhj+PA/bAXxhQ9eeNosWkqFSgOBUi4RJxAcDKFT2f9znv8RO2qrT+GqQg7nHSY+PZ7Z98w+69dXKpiQAoGIpIjIShHJd56DdgcVkUXOMfkisshv+xoR2S0im5yH9o9XfVak06ms6CxzBOuxrYUGA/cE7PPlBuZ+Z26/6n+heodQcwQPAauNMTnY+YYfCjxARFKwc2j4Zkr8cUDA+HtjzEznURZiepQKmygnR3D4LOsI/tN5vo/T56+t2FXB/jX7iU6MZs4Dc0JKo1LBhBoI5gMvOMsvAAuCHHMNsNIYU2WMqQZWAteG+L5K9ToxTiA4chY5ggPAa9gent8K2Lf5pc0ATL1lqmuD/inlL9RAkGmMKXGWj2DnJAk0HDvPiU+Rs83neadY6IfSTj95EblXRPJEJK+8vDzEZCvlvjin1VDpWQSCp7Ethm7m9JnbTIthy0tbADjnznNCTqNSwXQ4xISIrMI2aQ70iP+KMcaIiAlyXHv+3hhTLCKJwOvAl4EXgx1ojFmMnaKV3Nzcrr6PUt0uzskRnGzwcpzTi3fa04SdgB7g/oB9+9fu5/ih4wzJHsKoi0a5k1ClAnQYCIwxV7a1T0RKRSTLGFMiIllAsDL+YuBSv/UR2AEVMcYUO881IvJ7bB1C0ECgVG8X6QSCyPpmDmDnZu6MN7HZ6cnAxQH7trxocwMzvjyj10zNqfqfUIuGlgG+VkCLsLPpBVoBXC0iyU4l8dXAChGJFJE0ABGJAq7HzqWuVJ/kazUUWd/M/i6c91vn+V5OzTUAdvKeHUt2ADYQKNVdQg0EjwFXiUg+cKWzjojkisgzAMaYKuzMeuudx6POthhsQNgCbMLmHJ4OMT1KhY0vRxDR0Ex+J8/ZB/wV+2W4M2Dfnr/sobG2kREXjCA1J9W9hCoVIKRhqI0xlcAVQbbnAV/1W38OeC7gmDpA+8mrfiPCqSyOrG9mfSfPeRo7yNzNQErAvvy3bDiZcvMUl1KoVHDas1gpl/jXEXzSieObOHV3dF/APtNiKFhRAEDO53PcSqJSQWkgUMolvkAQ3+BlH8FbTvh7AygFpgCfC9hXsrGEE+UnSBqdROpELRZS3UsDgVIu8RUNZTv9CDrKFSx2nu/j9EpigIJ3bG5g/LXjdRpK1e00ECjlEl+OYGRDx4FgL7aLfSy288wZ+9/ZC9hAoFR300CglEt8gWBEJ3IEvuZxtwCBIzXWH63n0MeH8ER6GHP5GLeTqdQZNBAo5RJfP4JMJxB8ih02ItBJ2q4kBihcXYjxGkZ+biQxg3VietX9NBAo5RJfjiC2wcsI4Dh2kplAzwHlwCzggiD7/esHlOoJGgiUcokvEDTXN3O+sy2weKgReNxZ/hfOrCQG2P/ufgDGXT3O9TQqFYwGAqVc4ms11FzfzFxnW2AgeBk7FO8Ugo/ZXldWR3VhNVGDosicEWwwX6Xcp4FAKZf4cgTeBm9rIFgGVDnLzcDPnOV/JviXr+iTIgCGzxmOJ1K/nqpn6CdNKZf4Fw1dgB1KtwQ71koL8H2gABgH3NrGaxStcwLB3OFtHKGU+0Iaa0gpdYqv1VBzfTMRwCvYCuGlwGxgM/YL9wRtf/GKPykGYMTcEW0coZT7NEeglEtacwROh7KxnOo9vBlIBJYDX2zj/BZvC8WfOoHgfA0EqudojkApl/gXDfncCuwA3sZ2ImtvssmKnRU01jSSNDqJhKEJ3ZhSpU6nOQKlXOJrNeRt8J62/V+xncs6mnHYVz+gxUKqp2kgUMolwXIEXaGBQIVLSIFARFJEZKWI5DvPgcOm+I57R0SOisibAdvHiMgnIlIgIn8QkehQ0qNUOGkgUH1VqDmCh4DVxpgcYLWzHswvCD7I4uPAE8aY8UA1cE+I6VEqbFpbDTV0PRDUH6unfEc5EdERDJ011O2kKdWuUAPBfOAFZ/kFgneWxBizGqjx3yZ2kPXLgSUdna9UXxBKjuDIxiNgIPOczNaAolRPCTUQZBpjSpzlI0BX+sSnAkeNMb5vTRHQZi8aEblXRPJEJK+8vPzsUqtUN/IfYqKryrbZ+cx0WAkVDh3eeojIKiBYXvUR/xVjjBER41bCAhljFuM0y87Nze2291HqbPnu5L0NXowxXZpZrHRrKQAZ0zK6JW1KtafDQGCMubKtfSJSKiJZxpgSEcmi42la/VUCQ0Qk0skVjACKu3C+Ur2KeISI6Ai8jV68jd4uFfGUb7O53IzpGghUzwu1aGgZsMhZXoSdj7tTjDEGeA+46WzOV6o3OpviIWNMa9GQ5ghUOIQaCB4DrhKRfOBKZx0RyRWRZ3wHicgHwGvAFSJSJCLXOLt+AHxXRAqwdQbPhpgepcLKfwTSzjp+6DgNxxuIT48nIVN7FKueF1LzBGNMJXBFkO152EEXfesXt3F+IXaQRqX6hbNpOaT1AyrctGexUi46m74ErcVCWj+gwkQDgVIuOpscQdlWrR9Q4aWBQCkXnVUg8PUhmK59CFR4aCBQykVtjUDaFm+Tl4qdFQCkT03vtnQp1R4NBEq5qKs5gqqCKryNXoZkDyEmMaY7k6ZUmzQQKOWirgYCrR9QvYEGAqVc1NVWQ9piSPUGGgiUclFXcwSt9QNTtH5AhY8GAqVcFBHbtSEmKvMrAUidkNptaVKqIxoIlHJRa9FQJwKBMYaq/CoAUnJSujVdSrVHA4FSLopOtLOtNtY0dnhszeEamk40EZcaR1xyXHcnTak2aSBQykUxg20T0IbjDR0e68sNpOZosZAKLw0ESrkoNikWsHMQd0TrB1RvoYFAKRfFJDk5gmOdzxFo/YAKNw0ESrmoK0VDlXtsjkADgQo3DQRKuchXNNSVHIEWDalwCykQiEiKiKwUkXznObmN494RkaMi8mbA9t+JyD4R2eQ8ZoaSHqXCzVc01FEdgWkxVO11iobGa45AhVeoOYKHgNXGmBxgtbMezC+AL7ex70FjzEznsSnE9CgVVp0tGjp26BjeBi8JQxN0sDkVdqEGgvnAC87yC8CCYAcZY1YDNSG+l1K9XmeLhrR+QPUmoQaCTGNMibN8BDibmTV+KiJbROQJEWnz1khE7hWRPBHJKy8vP6vEKtXdfDmC+mP1GGPaPE7rB1Rv0mEgEJFVIrItyGO+/3HGfurb/uQH9zAwCZgDpAA/aOtAY8xiY0yuMSY3PV0H6FK9U0R0BJGxkRivoflk28NM+PoQaI5A9QaRHR1gjLmyrX0iUioiWcaYEhHJAsq68uZ+uYkGEXke+F5XzleqN4pJiqG5vpn6Y/VExUcFPUZ7FaveJNSioWXAImd5EfBGV052ggciItj6hW0hpkepsOtMhbGvjkCLhlRvEGogeAy4SkTygSuddUQkV0Se8R0kIh8ArwFXiEiRiFzj7Po/EdkKbAXSgH8PMT1KhV1HFcYtzS0c3XcUgORxQVtcK9WjOiwaao8xphK4Isj2POCrfusXt3H+5aG8v1K9UUd9CY4dPEZLcwuJwxOJigtedKRUT9KexUq5rKOioerCagBSxmlFseodNBAo5bKOioZ8PYq1WEj1FhoIlHJZR0VD1XttjiB5rAYC1TtoIFDKZR0WDfkCgeYIVC+hgUApl3U0J4HWEajeRgOBUi5rb5YyY4zWEaheRwOBUi7zFQ01Hj9zAvsTFSdorGkkJimGuBSdsF71DhoIlHJZe5XF/hXFtkO9UuGngUApl7VWFgepI2idjEbrB1QvooFAKZe19iMI0mrIV1Gs9QOqN9FAoJTLOlU0pIFA9SIaCJRyWXtFQ9qZTPVGGgiUcll0QjTiEZpONNHS3HLaPq0jUL2RBgKlXCYiQXsXN51oorakFk+Uh8EjB4creUqdQQOBUt3Af+5in+p9tlhoSPYQPBH61VO9h34aleoGrcNM+OUIfPUDWiykepuQAoGIpIjIShHJd57PqAETkZki8rGIbBeRLSJyq9++MSLyiYgUiMgfRCQ6lPQo1VsEG4q6YncFAMnjtaJY9S6h5ggeAlYbY3KA1c56oBPAncaYqcC1wJMiMsTZ9zjwhDFmPFAN3BNiepTqFYIVDZVtLQMgc3pmWNKkVFtCDQTzgRec5RewE9CfxhizxxiT7ywfBsqAdGfC+suBJe2dr1RfFKxoyBcIMqZlhCVNSrUl1ECQaYwpcZaPAO3e6ojIeUA0sBdIBY4aY5qd3UXA8HbOvVdE8kQkr7y8PMRkK9W9AvsStDS3UL7Tfm41EKjepsPJ60VkFTA0yK5H/FeMMUZETDuvkwW8BCwyxrR0dcAtY8xiYDFAbm5um++jVG8Q2Lu4qqAKb4OXpNFJrUFCqd6iw0BgjLmyrX0iUioiWcaYEueHvqyN4wYDbwGPGGPWOZsrgSEiEunkCkYAxV3+C5TqhQLHGyrdWgpobkD1TqEWDS0DFjnLi4A3Ag9wWgItBV40xvjqAzDGGOA94Kb2zleqLwosGirb5tQPTNdAoHqfUAPBY8BVIpIPXOmsIyK5IvKMc8wtwDzgLhHZ5DxmOvt+AHxXRAqwdQbPhpgepXqFwOkqtcWQ6s06LBpqjzGmErgiyPY84KvO8svAy22cXwicF0oalOqNAouGtMWQ6s20Z7FS3cC/H0FjXSNVe6vwRHpIm5QW5pQpdSYNBEp1g/i0eADKd5Rz4P0DYCB1YioR0RFhTplSZ9JAoFQ3SJ+Szuh5ozlZeZKldywFtFhI9V4aCJTqBuIRbnz5RmKTYzlZdRLQFkOq99JAoFQ3SRqZxA3P3NC6ri2GVG+lgUCpbjT5S5O55MeXMPLCkWRfmh3u5CgVlNh+XX1Lbm6uycvLC3cylFKqTxGRz4wxuYHbNUeglFIDnAYCpZQa4DQQKKXUAKeBQCmlBjgNBEopNcBpIFBKqQFOA4FSSg1wGgiUUmqA65MdykSkHDhwlqenARUuJsctmq6u0XR1jaara/prukYbY9IDN/bJQBAKEckL1rMu3DRdXaPp6hpNV9cMtHRp0ZBSSg1wGgiUUmqAG4iBYHG4E9AGTVfXaLq6RtPVNQMqXQOujkAppdTpBmKOQCmllB8NBEopNcD1y0AgIjeLyHYRaRGRNptaici1IrJbRApE5CG/7WNE5BNn+x9EJNqldKWIyEoRyXeek4Mcc5mIbPJ71IvIAmff70Rkn9++mT2VLuc4r997L/PbHs7rNVNEPnb+31tE5Fa/fa5er7Y+L377Y5y/v8C5Htl++x52tu8WkWtCScdZpOu7IrLDuT6rRWS0376g/9MeStddIlLu9/5f9du3yPm/54vIoh5O1xN+adojIkf99nXL9RKR50SkTES2tbFfROS/nTRvEZHZfvtCv1bGmH73ACYDE4E1QG4bx0QAe4GxQDSwGZji7PsjsNBZfgr4ukvp+jnwkLP8EPB4B8enAFVAvLP+O+CmbrhenUoXUNvG9rBdL2ACkOMsDwNKgCFuX6/2Pi9+xzwAPOUsLwT+4CxPcY6PAcY4rxPRg+m6zO8z9HVfutr7n/ZQuu4C/jfIuSlAofOc7Cwn91S6Ao7/B+C5Hrhe84DZwLY29l8HvA0IMBf4xM1r1S9zBMaYncaY3R0cdh5QYIwpNMY0Aq8C80VEgMuBJc5xLwALXErafOf1Ovu6NwFvG2NOuPT+belqulqF+3oZY/YYY/Kd5cNAGXBGz0kXBP28tJPeJcAVzvWZD7xqjGkwxuwDCpzX65F0GWPe8/sMrQNGuPTeIaWrHdcAK40xVcaYamAlcG2Y0nUb8IpL790mY8z72Ju+tswHXjTWOmCIiGTh0rXql4Ggk4YDh/zWi5xtqcBRY0xzwHY3ZBpjSpzlI0BmB8cv5MwP4U+drOETIhLTw+mKFZE8EVnnK66iF10vETkPe5e312+zW9errc9L0GOc63EMe306c253psvfPdg7S59g/9OeTNffOf+fJSIysovndme6cIrQxgDv+m3uruvVkbbS7cq1igwpaWEkIquAoUF2PWKMeaOn0+PTXrr8V4wxRkTabLvrRPvpwAq/zQ9jfxCjse2JfwA82oPpGm2MKRaRscC7IrIV+2N31ly+Xi8Bi4wxLc7ms75e/ZGI3AHkApf4bT7jf2qM2Rv8FVz3F+AVY0yDiNyHzU1d3kPv3RkLgSXGGK/ftnBer27TZwOBMebKEF+iGBjptz7C2VaJzXZFOnd1vu0hp0tESkUkyxhT4vxwlbXzUrcAS40xTX6v7bs7bhCR54Hv9WS6jDHFznOhiKwBZgGvE+brJSKDgbewNwHr/F77rK9XEG19XoIdUyQikUAS9vPUmXO7M12IyJXY4HqJMabBt72N/6kbP2wdpssYU+m3+gy2Tsh37qUB565xIU2dSpefhcA3/Dd04/XqSFvpduVaDeSiofVAjtgWL9HYf/oyY2tg3sOWzwMsAtzKYSxzXq8zr3tG2aTzY+grl18ABG1h0B3pEpFkX9GKiKQBnwN2hPt6Of+7pdjy0yUB+9y8XkE/L+2k9ybgXef6LAMWim1VNAbIAT4NIS1dSpeIzAJ+C9xgjCnz2x70f9qD6cryW70B2OksrwCudtKXDFzN6Tnjbk2Xk7ZJ2MrXj/22def16sgy4E6n9dBc4Jhzo+POteqOGvBwP4AbsWVlDUApsMLZPgxY7nfcdcAebER/xG/7WOwXtQB4DYhxKV2pwGogH1gFpDjbc4Fn/I7LxkZ6T8D57wJbsT9oLwMJPZUu4ELnvTc7z/f0husF3AE0AZv8HjO743oF+7xgi5pucJZjnb+/wLkeY/3OfcQ5bzfweZc/7x2la5XzPfBdn2Ud/U97KF0/A7Y77/8eMMnv3Lud61gAfKUn0+Ws/wR4LOC8brte2Ju+EuezXISty7kfuN/ZL8CvnDRvxa81pBvXSoeYUEqpAW4gFw0ppZRCA4FSSg14GgiUUmqA00CglFIDnAYCpZQa4DQQKKXUAKeBQCmlBrj/D/24iEkUwMnNAAAAAElFTkSuQmCC\n", + "image/png": 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\n", 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" ] @@ -641,35 +655,35 @@ } ], "source": [ - "error = np.sum( np.abs( np.asarray(vels[0:16]).flatten() - np.asarray(velP[bc_tx:bc_tx+steps]).flatten() )) / (steps*n)\n", + "error = np.sum( np.abs( np.asarray(vel_resim[0:16]).flatten() - np.asarray(velP[bc_tx:bc_tx+steps]).flatten() )) / (steps*n)\n", "print(\"Mean absolute error for re-simulation across {} steps: {:7.5f}\".format(steps,error))\n", "\n", "fig = plt.figure().gca()\n", - "fig.plot(pltx, (vels[0 ].flatten()-velP[bc_tx ].flatten()), lw=2, color='blue')\n", - "#fig.plot(pltx, (vels[steps//4].flatten()-velP[bc_tx+steps//4].flatten()), lw=2, color='green')\n", - "fig.plot(pltx, (vels[steps//2].flatten()-velP[bc_tx+steps//2].flatten()), lw=2, color='cyan')\n", - "fig.plot(pltx, (vels[steps-1 ].flatten()-velP[bc_tx+steps-1 ].flatten()), lw=2, color='purple')" + "fig.plot(pltx, (vel_resim[0 ].flatten()-velP[bc_tx ].flatten()), lw=2, color='blue')\n", + "#fig.plot(pltx, (vel_resim[steps//4].flatten()-velP[bc_tx+steps//4].flatten()), lw=2, color='green')\n", + "fig.plot(pltx, (vel_resim[steps//2].flatten()-velP[bc_tx+steps//2].flatten()), lw=2, color='cyan')\n", + "fig.plot(pltx, (vel_resim[steps-1 ].flatten()-velP[bc_tx+steps-1 ].flatten()), lw=2, color='purple')\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "This should show a mean absolute error of ca. $1.4 \\cdot 10^{-2}$, which is significant for the value range of the simulation.\n", + "This should show a mean absolute error of ca. $1.5 \\cdot 10^{-2}$ between ground truth re-simulation and the PINN evolution, which is significant for the value range of the simulation.\n", "\n", - "And for comparison with the forward simulation and following cases, here are also all steps over time with a color map... (note x axis does not show actual simulation time)" + "And for comparison with the forward simulation and following cases, here are also all steps over time with a color map." ] }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 14, "metadata": { "scrolled": false }, "outputs": [ { "data": { - "image/png": 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\n", 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" ] @@ -681,10 +695,9 @@ } ], "source": [ - "# show solution again as full image over time\n", - "sn = np.concatenate(vels, axis=-1)\n", + "# show re-simulated solution again as full image over time\n", + "sn = np.concatenate(vel_resim, axis=-1)\n", "sn = np.reshape(sn, list(sn.shape)+[1] ) # print(sn.shape)\n", - "\n", "show_state(sn)" ] }, @@ -692,29 +705,14 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "More important, though, the mean absolute error (MAE) for the whole solution, i.e., from start to end:\n" + "Next, we'll store the full solution over the course of the $t=0 \\dots 1$ time interval, so that we can compare it later on to the full solution from a regular forward solve and compare it to the differential physics solution.\n", + "\n", + "Thus, stay tuned for the full evaluation and the comparison. It will follow in the file `diffphys-code-tf.ipynb`, after we've discussed the details of how to run the differential physics optimization." ] }, { "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "error_full = np.sum( np.abs( np.asarray(vels[0:16]).flatten() - np.asarray(velP[bc_tx:bc_tx+steps]).flatten() )) / (steps*n)\n", - "print(\"Overall MAE: {:7.5f}\".format(error_full))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "... store solution , just for comparison ..." - ] - }, - { - "cell_type": "code", - "execution_count": 29, + "execution_count": 20, "metadata": {}, "outputs": [ { @@ -741,7 +739,7 @@ "\n", "## Next steps\n", "\n", - "This setup is just a starting point, of course. The parameters of the setup were chosen to compare to run relatively quickly. As we'll show in the next sections, the behavior of such an inverse solve can be improved substantially by a tighter integration of solver and learning. \n", + "This setup is just a starting point for PINNs and physical soft-constraints, of course. The parameters of the setup were chosen to compare to run relatively quickly. As we'll show in the next sections, the behavior of such an inverse solve can be improved substantially by a tighter integration of solver and learning. \n", "\n", "The solution of the PINN setup above can also directly be improved, however. E.g., try to:\n", "\n",