Toward learning Lattice Boltzmann collision operators.

Area of Science:

• Computational fluid dynamics
• Machine learning
• Scientific computing

Background:

• The Lattice Boltzmann Method (LBM) is a powerful numerical technique for simulating fluid dynamics.
• Developing accurate and efficient collision operators is crucial for LBM performance.
• Deep learning offers a novel approach to learn complex physical phenomena.

Purpose of the Study:

• To investigate the use of deep learning to learn collision operators for the Lattice Boltzmann Method.
• To evaluate the performance of neural network-based LBM in simulating canonical fluid flows.
• To determine the impact of incorporating physical constraints on the accuracy of learned operators.

Main Methods:

• A hierarchy of neural network (NN) designs for the collision operator was developed and compared.
• The LBM method with NN collision operators was used to reproduce time dynamics of several fluid flows.
• Data for training was generated using a single relaxation time BGK operator.
• Physical properties, including conservation laws and symmetries, were embedded into the NN architecture.

Main Results:

• A standard neural network (NN) architecture showed limited accuracy in reproducing fluid flow dynamics.
• Embedding physical properties like conservation laws and symmetries into the NN dramatically improved accuracy by several orders of magnitude.
• The enhanced NN-LBM approach correctly reproduced both short and long-time dynamics of canonical fluid flows.

Conclusions:

• Deep learning can be effectively used to learn collision operators for the Lattice Boltzmann Method.
• Incorporating physical constraints into neural networks is essential for achieving high accuracy in LBM simulations.
• This approach holds significant potential for advancing computational fluid dynamics simulations.