🎓Neural Lattice-Boltzmann method for machine learning-based simulations: Data-driven collision operators and constraints

The research project combines physics and artificial intelligence by integrating neural networks directly into the Lattice Boltzmann Method (LBM) - an established method for simulating complex flows.

A key result is the "Lettuce" Python framework developed as part of the doctorate. This utilises PyTorch for GPU acceleration of simulations and enables the seamless integration of machine learning algorithms.

 The work presents two major innovations:
1. an invariant neural collision operator that removes numerical instabilities on coarse grids. This approach reproduces the finest turbulence structures that would normally only be achievable with extremely high resolution.
2. data-driven boundary conditions that enable a drastic reduction in memory requirements and outperform classical methods in terms of efficiency and scalability. The decisive advantage of neural networks lies in their ability to adapt the models to local flow conditions. These results open up new, fast and robust paths for flow simulations, which are of great benefit for both academic research and industrial applications.