XLB is a fully differentiable 2D/3D Lattice Boltzmann Method (LBM) library that leverages hardware acceleration. It's built on top of the JAX library and is specifically designed to solve fluid dynamics problems in a computationally efficient and differentiable manner. Its unique combination of features positions it as an exceptionally suitable tool for applications in physics-based machine learning.

Please refer to the accompanying paper for benchmarks, validation, and more details about the library.

If you use XLB in your research, please cite the following paper:

@article{ataei2023xlb,
      title={{XLB}: A Differentiable Massively Parallel Lattice Boltzmann Library in Python}, 
      author={Ataei, Mohammadmehdi and Salehipour, Hesam},
      journal={arXiv preprint arXiv:2311.16080},
      year={2023},
}

• Integration with JAX Ecosystem: The library can be easily integrated with JAX's robust ecosystem of machine learning libraries such as Flax, Haiku, Optax, and many more.
• Differentiable LBM Kernels: XLB provides differentiable LBM kernels that can be used in differentiable physics and deep learning applications.
• Scalability: XLB is capable of scaling on distributed multi-GPU systems, enabling the execution of large-scale simulations on hundreds of GPUs with billions of cells.
• Support for Various LBM Boundary Conditions and Kernels: XLB supports several LBM boundary conditions and collision kernels.
• User-Friendly Interface: Written entirely in Python, XLB emphasizes a highly accessible interface that allows users to extend the library with ease and quickly set up and run new simulations.
• Leverages JAX Array and Shardmap: The library incorporates the new JAX array unified array type and JAX shardmap, providing users with a numpy-like interface. This allows users to focus solely on the semantics, leaving performance optimizations to the compiler.
• Platform Versatility: The same XLB code can be executed on a variety of platforms including multi-core CPUs, single or multi-GPU systems, TPUs, and it also supports distributed runs on multi-GPU systems or TPU Pod slices.
• Visualization: XLB provides a variety of visualization options including in-situ on GPU rendering using PhantomGaze.

On GPU in-situ rendering using PhantomGaze library (no I/O). Flow over a NACA airfoil using KBC Lattice Boltzmann Simulation with ~10 million cells.

DrivAer model in a wind-tunnel using KBC Lattice Boltzmann Simulation with approx. 317 million cells

Airflow in to, out of, and within a building (~400 million cells)

The stages of a fluid density field from an initial state to the emergence of the "XLB" pattern through deep learning optimization at timestep 200 (see paper for details)

Lid-driven Cavity flow at Re=100,000 (~25 million cells)

• BGK collision model (Standard LBM collision model)
• KBC collision model (unconditionally stable for flows with high Reynolds number)

• Easy integration with JAX's ecosystem of machine learning libraries
• Differentiable LBM kernels
• Differentiable boundary conditions

• D2Q9
• D3Q19
• D3Q27 (Must be used for KBC simulation runs)

• Distributed Multi-GPU support
• Mixed-Precision support (store vs compute)
• Out-of-core support (coming soon)

• Binary and ASCII VTK output (based on PyVista library)
• In-situ rendering using PhantomGaze library
• Orbax-based distributed asynchronous checkpointing
• Image Output
• 3D mesh voxelizer using trimesh

• Equilibrium BC: In this boundary condition, the fluid populations are assumed to be in at equilibrium. Can be used to set prescribed velocity or pressure.

• Full-Way Bounceback BC: In this boundary condition, the velocity of the fluid populations is reflected back to the fluid side of the boundary, resulting in zero fluid velocity at the boundary.

• Half-Way Bounceback BC: Similar to the Full-Way Bounceback BC, in this boundary condition, the velocity of the fluid populations is partially reflected back to the fluid side of the boundary, resulting in a non-zero fluid velocity at the boundary.

• Do Nothing BC: In this boundary condition, the fluid populations are allowed to pass through the boundary without any reflection or modification.

• Zouhe BC: This boundary condition is used to impose a prescribed velocity or pressure profile at the boundary.

• Regularized BC: This boundary condition is used to impose a prescribed velocity or pressure profile at the boundary. This BC is more stable than Zouhe BC, but computationally more expensive.

• Extrapolation Outflow BC: A type of outflow boundary condition that uses extrapolation to avoid strong wave reflections.

• Interpolated Bounceback BC: Interpolated bounce-back boundary condition due to Bouzidi for a lattice Boltzmann method simulation.

To use XLB, you must first install JAX and other dependencies using the following commands:

Please refer to https://github.com/google/jax for the latest installation documentation. The following table is taken from JAX's Github page.

Note: We encountered challenges when executing XLB on Apple GPUs due to the lack of support for certain operations in the Metal backend. We advise using the CPU backend on Mac OS. We will be testing XLB on Apple's GPUs in the future and will update this section accordingly.

Install dependencies:

pip install pyvista numpy matplotlib Rtree trimesh jmp orbax-checkpoint termcolor

Run an example:

git clone https://github.com/Autodesk/XLB
cd XLB
export PYTHONPATH=.
python3 examples/CFD/cavity2d.py

Note: Some of the work-in-progress features can be found in the branches of the XLB repository. For contributions to these features, please reach out.

• 🚀 Warp Backend: Achieving state-of-the-art performance by leveraging the Warp framework in combination with JAX.

• 🌐 Grid Refinement: Implementing adaptive mesh refinement techniques for enhanced simulation accuracy.

• ⚡ Multi-GPU Acceleration using Neon + Warp: Using Neon's data structure for improved scaling.

• 💾 Out-of-Core Computations: Enabling simulations that exceed available GPU memory, suitable for CPU+GPU coherent memory models such as NVIDIA's Grace Superchips.

• 🗜️ GPU Accelerated Lossless Compression and Decompression: Implementing high-performance lossless compression and decompression techniques for larger-scale simulations and improved performance.

• 🌡️ Fluid-Thermal Simulation Capabilities: Incorporating heat transfer and thermal effects into fluid simulations.

• 🎯 Adjoint-based Shape and Topology Optimization: Implementing gradient-based optimization techniques for design optimization.

• 🧠 Machine Learning Accelerated Simulations: Leveraging machine learning to speed up simulations and improve accuracy.

• 📉 Reduced Order Modeling using Machine Learning: Developing data-driven reduced-order models for efficient and accurate simulations.

Contributions to these features are welcome. Please submit PRs for the Wishlist items.

• 🌊 Free Surface Flows: Simulating flows with free surfaces, such as water waves and droplets.

• 📡 Electromagnetic Wave Propagation: Simulating the propagation of electromagnetic waves.

• 🛩️ Supersonic Flows: Simulating supersonic flows.

• 🌊🧱 Fluid-Solid Interaction: Modeling the interaction between fluids and solid objects.

• 🧩 Multiphase Flow Simulation: Simulating flows with multiple immiscible fluids.

• 🔥 Combustion: Simulating combustion processes and reactive flows.

• 🪨 Particle Flows and Discrete Element Method: Incorporating particle-based methods for granular and particulate flows.

• 🔧 Better Geometry Processing Pipelines: Improving the handling and preprocessing of complex geometries for simulations.