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The lattice Boltzmann method (LBM) is an efficient simulation technique for computational fluid mechanics and beyond. It is based on a simple stream-and-collide algorithm on Cartesian grids, which is easily compatible with modern machine learning architectures. While it is becoming increasingly clear that deep learning can provide a decisive stimulus for classical simulation techniques, recent studies have not addressed possible connections between machine learning and LBM. Here, we introduce Lettuce, a PyTorch-based LBM code with a threefold aim. Lettuce enables GPU accelerated calculations with minimal source code, facilitates rapid prototyping of LBM models, and enables integrating LBM simulations with PyTorch's deep learning and automatic differentiation facility. As a proof of concept for combining machine learning with the LBM, a neural collision model is developed, trained on a doubly periodic shear layer and then transferred to a different flow, a decaying turbulence. We also exemplify the added benefit of PyTorch's automatic differentiation framework in flow control and optimization. To this end, the spectrum of a forced isotropic turbulence is maintained without further constraining the velocity field.
The lattice Boltzmann method (LBM) stands apart from conventional macroscopic approaches due to its low numerical dissipation and reduced computational cost, attributed to a simple streaming and local collision step. While this property makes the method particularly attractive for applications such as direct noise computation, it also renders the method highly susceptible to instabilities. A vast body of literature exists on stability-enhancing techniques, which can be categorized into selective filtering, regularized LBM, and multi-relaxation time (MRT) models. Although each technique bolsters stability by adding numerical dissipation, they act on different modes. Consequently, there is not a universal scheme optimally suited for a wide range of different flows. The reason for this lies in the static nature of these methods; they cannot adapt to local or global flow features. Still, adaptive filtering using a shear sensor constitutes an exception to this. For this reason, we developed a novel collision operator that uses space- and time-variant collision rates associated with the bulk viscosity. These rates are optimized by a physically informed neural net. In this study, the training data consists of a time series of different instances of a 2D barotropic vortex solution, obtained from a high-order Navier–Stokes solver that embodies desirable numerical features. For this specific text case our results demonstrate that the relaxation times adapt to the local flow and show a dependence on the velocity field. Furthermore, the novel collision operator demonstrates a better stability-to-precision ratio and outperforms conventional techniques that use an empirical constant for the bulk viscosity.