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Top AI Repos tracks AI repositories on GitHub and answers two different questions about each one: is it moving right now, and would you bet a product on it.
A differentiable PDE solving framework for machine learning
| Date | Stars |
|---|---|
| 2026-07-31 | 1916 |
| 2026-08-04 | 1920 |
| 2026-08-06 | 1920 |
Today
— stars today
This week
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Momentum
0.0
growth rate 0.00%/day
# 

[](https://pypi.org/project/phiflow/)
[](https://pypi.org/project/phiflow/)
[](https://codecov.io/gh/tum-pbs/PhiFlow/branch/develop/)
[](https://colab.research.google.com/github/tum-pbs/PhiFlow/blob/develop/docs/Fluids_Tutorial.ipynb)
Φ<sub>Flow</sub> is an open-source simulation toolkit built for optimization and machine learning applications.
It is written mostly in Python and can be used with
[NumPy](https://numpy.org/),
[PyTorch](https://pytorch.org/),
[Jax](https://github.com/google/jax)
or [TensorFlow](https://www.tensorflow.org/).
The close integration with these machine learning frameworks allows it to leverage their automatic differentiation functionality,
making it easy to build end-to-end differentiable functions involving both learning models and physics simulations.
## Examples
### Grids
<table>
<tbody>
<tr>
<td style="width: 25%;"><a href="https://tum-pbs.github.io/PhiFlow/examples/grids/Fluid_Logo.html"><img src="docs/figures/examples/grids/Fluid_Logo.gif"></a></td>
<td style="width: 25%;"><a href="https://tum-pbs.github.io/PhiFlow/examples/grids/Wake_Flow.html"><img src="docs/figures/examples/grids/Wake_Flow.png"></a></td>
<td style="width: 25%;"><a href="https://tum-pbs.github.io/PhiFlow/examples/grids/Lid_Driven_Cavity.html"><img src="docs/figures/examples/grids/Lid_Driven_Cavity.png"></a></td>
<td style="width: 25%;"><a href="https://tum-pbs.github.io/PhiFlow/examples/grids/Taylor_Green.html"><img src="docs/figures/examples/grids/Taylor_Green.jpg"></a></td>
</tr>
<tr>
<td align="center">Fluid logo</td>
<td align="center">Wake flow</td>
<td align="center">Lid-driven cavity</td>
<td align="center">Taylor-Green</td>
</tr>
<tr>
<td style="width: 25%;"><a href="https://tum-pbs.github.io/PhiFlow/examples/grids/Smoke_Plume.html"><img src="docs/figures/examples/grids/Smoke_Plume.png"></a></td>
<td style="width: 25%;"><a href="https://tum-pbs.github.io/PhiFlow/examples/grids/Variable_Boundaries.html"><img src="docs/figures/examples/grids/Variable_Boundaries.jpg"></a></td>
<td style="width: 25%;"><a href="https://tum-pbs.github.io/PhiFlow/examples/grids/Batched_Smoke.html"><img src="docs/figures/examples/grids/Batched_Smoke.png"></a></td>
<td style="width: 25%;"><a href="https://tum-pbs.github.io/PhiFlow/examples/grids/Moving_Obstacles.html"><img src="docs/figures/examples/grids/Moving_Obstacles.png"></a></td>
</tr>
<tr>
<td align="center">Smoke plume</td>
<td align="center">Variable boundaries</td>
<td align="center">Parallel simulations</td>
<td align="center">Moving obstacles</td>
</tr>
<tr>
<td style="width: 25%;"><a href="https://tum-pbs.github.io/PhiFlow/examples/grids/Rotating_Bar.html"><img src="docs/figures/examples/grids/Rotating_Bar.jpg"></a></td>
<td style="width: 25%;"><a href="https://tum-pbs.github.io/PhiFlow/examples/grids/Multi_Grid_Fluid.html"><img src="docs/figures/examples/grids/Multi_Grid_Fluid.jpg"></a></td>
<td style="width: 25%;"><a href="https://tum-pbs.github.io/PhiFlow/examples/grids/Higher_order_Kolmogorov.html"><img src="docs/figures/examples/grids/Higher_Order_Kolmogorov.jpg"></a></td>
<td style="width: 25%;"><a href="https://tum-pbs.github.io/PhiFlow/examples/grids/Heat_Flow.html"><img src="docs/figures/examples/grids/Heat_Flow.png"></a></Excerpt of 16,957 characters
Read on GitHub3.2k
Nils Thuerey · TUM
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Marcel Rød · Stanford · United States
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Vincent Gao · France
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Would you bet a product on this? Bounded 0–100 and slow moving.
matched fp:85fa1964f2614c6b, topic:deep-learning, readme:automatic differentiation