This commit is contained in:
NT committed 2021-01-31 12:55:24 +08:00
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commit 3ac8cec965
8 files changed
+51 -35

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@@ -26,7 +26,7 @@
- file: diffphys-outlook.md
- file: jupyter-book-reference
sections:
- file: markdown
- file: notebooks
- file: jupyter-book-reference-markdown
- file: jupyter-book-reference-notebooks
- file: references
- file: notation
+16 -16
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@@ -151,15 +151,15 @@
"If using Keras pass *_constraint arguments to layers.\n",
"Train on 200 samples\n",
"Epoch 1/5\n",
"200/200 [==============================] - 1s 3ms/sample - loss: 0.5135\n",
"200/200 [==============================] - 1s 3ms/sample - loss: 0.4967\n",
"Epoch 2/5\n",
"200/200 [==============================] - 0s 355us/sample - loss: 0.5097\n",
"200/200 [==============================] - 0s 222us/sample - loss: 0.4958\n",
"Epoch 3/5\n",
"200/200 [==============================] - 0s 402us/sample - loss: 0.5077\n",
"200/200 [==============================] - 0s 453us/sample - loss: 0.4941\n",
"Epoch 4/5\n",
"200/200 [==============================] - 0s 399us/sample - loss: 0.5066\n",
"200/200 [==============================] - 0s 491us/sample - loss: 0.4933\n",
"Epoch 5/5\n",
"200/200 [==============================] - 0s 303us/sample - loss: 0.5054\n"
"200/200 [==============================] - 0s 493us/sample - loss: 0.4927\n"
]
}
],
@@ -184,7 +184,7 @@
"outputs": [
{
"data": {
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truncated
"image/png": 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truncated
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
@@ -254,7 +254,7 @@
"model_dp = tf.keras.models.Sequential([\n",
" tf.keras.layers.Dense(8, activation=act),\n",
" tf.keras.layers.Dense(8, activation=act),\n",
" tf.keras.layers.Dense(1,activation='linear')])"
" tf.keras.layers.Dense(1, activation='linear')])"
]
},
{
@@ -294,15 +294,15 @@
"Use tf.where in 2.0, which has the same broadcast rule as np.where\n",
"Train on 200 samples\n",
"Epoch 1/5\n",
"200/200 [==============================] - 0s 1ms/sample - loss: 0.2711\n",
"200/200 [==============================] - 0s 1ms/sample - loss: 0.2275\n",
"Epoch 2/5\n",
"200/200 [==============================] - 0s 282us/sample - loss: 0.0733\n",
"200/200 [==============================] - 0s 405us/sample - loss: 0.0520\n",
"Epoch 3/5\n",
"200/200 [==============================] - 0s 321us/sample - loss: 0.0028\n",
"200/200 [==============================] - 0s 338us/sample - loss: 0.0030\n",
"Epoch 4/5\n",
"200/200 [==============================] - 0s 322us/sample - loss: 0.0013\n",
"200/200 [==============================] - 0s 335us/sample - loss: 0.0025\n",
"Epoch 5/5\n",
"200/200 [==============================] - 0s 335us/sample - loss: 0.0012\n"
"200/200 [==============================] - 0s 340us/sample - loss: 0.0024\n"
]
}
],
@@ -325,7 +325,7 @@
"outputs": [
{
"data": {
"image/png": 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truncated
"image/png": "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 truncated
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
@@ -352,7 +352,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"This looks much better 😎, at least in the range of 0.2 to 1. \n",
"This looks much better 😎, at least in the range of 0.1 to 1. \n",
"\n",
"What has happened here?\n",
"\n",
@@ -360,7 +360,7 @@
"\n",
"- We're still only getting one side of the curve! This is to be expected, because we're representing the solutions with a deterministic function. Hence we can only represent a single mode. Interestingly, whether it's the top or bottom mode is determined by the random initialization of the weights in $f$ - run the example a couple of time to see this effect in action. To capture multiple modes we'd need to extend the model to capture the full distribution of the outputs and parametrize it with additional dimensions.\n",
"\n",
"- The region with $x$ near zero is typically still off in this example. The is caused by the larger curvature in this region, and the even sampling with points along $x$. This could be alleviated with more points, a larger network, and potentially longer training.\n"
"- The region with $x$ near zero is typically still off in this example. The model primarily learns a linear approximation of one half of the parabola here. This is primarily caused by the weak neural network: it is very small and shallow. (Give it a try - it's very easy to fix this in the `model_dp` defition.)\n"
]
},
{
@@ -381,7 +381,7 @@
"source": [
"## Next steps\n",
"\n",
"- The example above is itentionally using a fairly \"bad\" setup. Try to find out how to obtain a solution such as the green one shown in the very first image at the top.\n",
"- The example above is itentionally using a fairly \"bad\" setup. Change the code above to obtain a solution such as the green one shown in the very first image at the top.\n",
"\n",
"- Or you can try extending the setup to a 2D case, i.e. a paraboloid. Given the function $\\mathcal P:(y_1,y_2)\\to y_1^2+y_2^2$, find an inverse function $f$ such that $\\mathcal P(f(x)) = x$ for all $x$ in $[0,1]$."
]
-1
View File
@@ -151,5 +151,4 @@ time series, sequence prediction?] {cite}`wiewel2019lss,bkim2019deep,wiewel2020l
_Misc jupyter book TODOs_
- Fix latex PDF output
- How to include links to papers in the bibtex references?
File renamed without changes.
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+32 -15
View File
@@ -18,21 +18,24 @@
title={Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers},
author={Um, Kiwon and Brand, Robert and Holl, Philipp and Fei, Raymond Thuerey, Nils},
journal=NeurIPS,
year={2020}
year={2020},
url={https://ge.in.tum.de/publications/2020-um-solver-in-the-loop/},
}
@article{kohl2020lsim,
title={Learning Similarity Metrics for Numerical Simulations},
author={Kohl, Georg and Um, Kiwon and Thuerey, Nils},
journal=ICML,
year={2020}
year={2020},
url={https://ge.in.tum.de/publications/2020-lsim-kohl/},
}
@article{wiewel2020lsssubdiv,
title={Latent Space Subdivision: Stable and Controllable Time Predictions for Fluid Flow},
author={Wiewel, Steffen and Kim, Byungsoo and Azevedo, Vinicius C and Solenthaler, Barbara and Thuerey, Nils},
journal=SCA,
year={2020}
year={2020},
url={https://ge.in.tum.de/publications/2020-lssubdiv-wiewel/},
}
@article{chu2020tecogan,
@@ -43,7 +46,8 @@
number={4},
pages={75--1},
year={2020},
publisher={ACM New York, NY, USA}
publisher={ACM},
url={https://ge.in.tum.de/publications/2019-tecogan-chu/},
}
@@ -52,28 +56,32 @@
author={Weiss, Sebastian and Maier, Robert and Cremers, Daniel and Westermann, Rudiger and Thuerey, Nils},
booktitle=CVPR,
pages={4686--4695},
year={2020}
year={2020},
url={https://ge.in.tum.de/publications/2020-cvpr-weiss/},
}
@inproceedings{holl2019pdecontrol,
title={Learning to Control PDEs with Differentiable Physics},
author={Holl, Philipp and Thuerey, Nils and Koltun, Vladlen},
booktitle=ICLR,
year={2019}
year={2019},
url={https://ge.in.tum.de/publications/2020-iclr-holl/},
}
@article{prantl2019tranquil,
title={Tranquil clouds: Neural networks for learning temporally coherent features in point clouds},
author={Prantl, Lukas and Chentanez, Nuttapong and Jeschke, Stefan and Thuerey, Nils},
journal=ICLR,
year={2019}
year={2019},
url={https://ge.in.tum.de/publications/2020-iclr-prantl/},
}
@inproceedings{ummenhofer2019contconv,
title={Lagrangian fluid simulation with continuous convolutions},
author={Ummenhofer, Benjamin and Prantl, Lukas and Thuerey, Nils and Koltun, Vladlen},
booktitle=ICLR,
year={2019}
year={2019},
url={https://ge.in.tum.de/publications/2020-ummenhofer-iclr/},
}
@article{eckert2019scalarflow,
@@ -84,7 +92,8 @@
number={6},
pages={1--16},
year={2019},
publisher={ACM New York, NY, USA}
publisher={ACM},
url={https://ge.in.tum.de/publications/2019-tog-eckert/},
}
@@ -93,7 +102,8 @@
author={Thuerey, Nils and Weissenow, Konstantin and Prantl, Lukas and Hu, Xiangyu},
journal={AIAA Journal}, year={2020},
volume={58}, number={1}, pages={25--36},
publisher={American Institute of Aeronautics and Astronautics}
publisher={American Institute of Aeronautics and Astronautics},
url={https://ge.in.tum.de/publications/2018-deep-flow-pred/},
}
@article{prantl2019rtliq,
@@ -101,7 +111,8 @@
author={Lukas Prantl and Boris Bonev and Nils Thuerey},
journal=ICLR,
year={2019},
pages={20}
pages={20},
url={https://ge.in.tum.de/publications/2017-prantl-defonn/},
}
@@ -113,6 +124,7 @@
volume={38},
number={2},
pages={12},
url={https://ge.in.tum.de/publications/latent-space-physics/},
}
@article{bkim2019deep,
@@ -123,6 +135,7 @@
volume={38},
number={2},
pages={12},
url={http://www.byungsoo.me/project/deep-fluids/},
}
@article{xie2018tempoGan,
@@ -131,7 +144,8 @@
journal = ACM_TOG,
volume = {37(4)},
year = {2018},
publisher = {ACM}
publisher = {ACM},
url={https://ge.in.tum.de/publications/tempogan/},
}
@article{hikaru2018simulating,
@@ -159,7 +173,8 @@
author={Kiwon Um and Xiangyu Hu and Nils Thuerey},
journal=EG_CGF,
volume={37(8)},
year={2018}
year={2018},
url={https://ge.in.tum.de/publications/2018-mlflip-um/},
}
@article{eckert2018oiof,
@@ -230,7 +245,8 @@
number={4},
pages={69},
year={2017},
publisher={ACM}
publisher={ACM},
url={http://ge.in.tum.de/publications/2017-sig-chu/},
}
@article{thuerey2017interpolations,
@@ -835,7 +851,7 @@
@article{alquraishi2019alphafold,
title={AlphaFold at CASP13},
author={AlQuraishi, Mohammed},
author={Quraishi, Mohammed Al},
journal={Bioinformatics},
volume={35},
number={22},
@@ -844,3 +860,4 @@
publisher={Oxford University Press}
}
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+1 -1
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@@ -25,7 +25,7 @@
"\n",
"## Code coming up...\n",
"\n",
"Let's get started with the implementation. Note that we'll skip the data generation process here. This example is adapted from [this codebase](https://github.com/thunil/Deep-Flow-Prediction), which you can check out for details. Here, we'll simply download a small set of training data generated with a Spalart-Almaras RANS simulation in [OpenFOAM](openfoam)."
"Let's get started with the implementation. Note that we'll skip the data generation process here. This example is adapted from [this codebase](https://github.com/thunil/Deep-Flow-Prediction), which you can check out for details. Here, we'll simply download a small set of training data generated with a Spalart-Almaras RANS simulation in [OpenFOAM](https://openfoam.org/)."
]
},
{