Adding example on Physics-Informed Neural Networks for solving Eikonal equation #1345
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…g Eikonal equation
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examples/pinn/eikonal.py
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| two-point modification of the [eikonal | ||
| equation](https://en.wikipedia.org/wiki/Eikonal_equation): | ||
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| $$\Vert \nabla_r \tau(\textbf{x}_s, \textbf{x}_r) \Vert = \frac{1}{v(\textbf{x}_r)}$$ |
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Please don't use latex syntax. Either explain equations via python code snippets or pseudocode snippets, or include rendered images of equations. The former is better since it is more accessible to our audience.
examples/pinn/eikonal.py
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| @@ -0,0 +1,459 @@ | |||
| """ | |||
| Title: Neural Eikonal Solver | |||
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We should not create a new category specifically for this example. Is there an existing category that could be a good fit?
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best fit would be "quick keras recipes" perhaps; though PINNs probably don't fit in there.
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Thanks for your comments and reply!
I was also thinking about "quick keras recipes" but alternatively since eikonal is widely used in computer vision if I adapt the example to a computer vision context (e.g. to Shape-from-Shading problem), do you think that "computer vision" could be a good fit?
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I say we put it in quick keras recipes and focus on the concept of PINNs!
I think we should emphasize that in PINNs you simply add an L2 loss to enforce the implicit physics constraints of the system.
examples/pinn/eikonal.py
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| def build_model(input_scale, vmin, vmax, dim=2): | ||
| # Hyperparameters | ||
| n_layers = 5 # number of hidden layers |
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Naming nit: use num_ as number prefix.
examples/pinn/eikonal.py
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| inputs_list = xs_list + xr_list | ||
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| # Scaling of inputs, to avoid unit dependence | ||
| XsXr = Concatenate(name="x", axis=-1)([xs, xr]) |
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Naming nit: use snake case for all instances. Lowercase.
examples/pinn/eikonal.py
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| xr = Concatenate(name="xr", axis=-1)(xr_list) | ||
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| # Input 3: velocity model at Receiver coordinates | ||
| vr = Input(shape=(1,), name="vr") |
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Naming tips: strictly avoid non-obvious one-letter or two-letter names. Use fully-spelled out variable names everywhere.
examples/pinn/eikonal.py
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| import tensorflow as tf | ||
| from tensorflow.keras.layers.experimental.preprocessing import Rescaling | ||
| from tensorflow.keras.layers import Input, Concatenate, Dense |
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Just from tensorflow.keras import layers, then access elements of the module, e.g. layers.Dense
examples/pinn/eikonal.py
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| from tensorflow.keras.layers.experimental.preprocessing import Rescaling | ||
| from tensorflow.keras.layers import Input, Concatenate, Dense | ||
| from tensorflow.keras.layers import Multiply, Subtract, Lambda | ||
| from tensorflow.keras.models import Model |
examples/pinn/eikonal.py
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| ## Imports | ||
| """ | ||
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| import tensorflow as tf |
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Hello, |
sachinprasadhs
added
stat:awaiting keras-eng
and removed
keras-team-review-pending
labels
Hello,
According to my question, you might be interested in a new example of physics-informed neural networks (PINNs).
I created a new folder
pinnin the repo since it did not have any related to physics-informed neural networks (pinn)This
.pyfile contains the example with the neural eikonal solver.Serafim