Φ Flow is a Python-based simulation toolkit designed for machine learning applications, enabling end-to-end differentiable physics simulations. It targets researchers and engineers who need to integrate complex physical phenomena, particularly fluid dynamics, into deep learning models for tasks like optimization and control. The primary benefit is the seamless combination of physics-based simulations with ML frameworks, allowing for gradient-based optimization of simulation parameters or learning from simulation data.

How It Works

Φ Flow leverages automatic differentiation from popular ML frameworks (PyTorch, Jax, TensorFlow) to make its PDE solvers differentiable. This allows gradients to flow through the simulation, enabling gradient-based optimization of simulation parameters or the integration of simulations into larger neural network architectures. Its object-oriented, vectorized design and named/typed dimensions facilitate expressive, reusable, and backend-agnostic code for various dimensionalities and simulation types.

Quick Start & Requirements

• Install via pip: pip install phiflow
• Requires Python 3.6+.
• For ML capabilities and GPU execution, install PyTorch, TensorFlow, or Jax.
• For web UI: pip install dash
• Optional: Compile custom CUDA operators for optimal GPU performance.
• Verify installation: python3 -c "import phi; phi.verify()"
• Documentation: https://tum-pbs.github.io/PhiFlow/
• YouTube Tutorials: [https://www.youtube.com/playlist?list=PL_1_53_0_3f-9h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40j0h7j40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