Uniformly accurate machine learning-based hydrodynamic models for kinetic equations.

Area of Science:

• Multiscale modeling
• Computational physics
• Fluid dynamics

Background:

• Developing accurate reduced models for multiscale problems lacking scale separation is challenging.
• Existing methods often struggle with physical constraints and dataset representativeness.
• Hydrodynamic approximations to kinetic equations require robust closure strategies.

Purpose of the Study:

• Introduce a novel framework for constructing interpretable and reliable reduced models.
• Address the closure problem in kinetic theory for non-separable scales.
• Ensure physical consistency and data representativeness in reduced models.

Main Methods:

• Construct generalized moments to optimally represent velocity distributions.
• Solve the closure problem by optimally capturing kinetic equation dynamics.
• Employ an active-learning procedure to ensure dataset representativeness and address physical constraints like Galilean invariance.

Main Results:

• Developed a reduced system in the form of a conventional moment system.
• Demonstrated uniform accuracy across a wide range of Knudsen numbers (hydrodynamic to free molecular flow).
• Validated the framework using the Bhatnagar-Gross-Krook (BGK) model and binary collisions of Maxwell molecules.

Conclusions:

• The proposed framework provides interpretable and reliable reduced models for multiscale problems without scale separation.
• The method achieves high accuracy across diverse flow regimes, enhancing predictive capabilities.
• This approach offers a robust solution for kinetic theory closure problems in complex scenarios.