Machine-learning-based non-Newtonian fluid model with molecular fidelity.

Area of Science:

• Computational fluid dynamics
• Polymer physics
• Machine learning

Background:

• Traditional non-Newtonian fluid models often rely on empirical closures that may not fully capture complex molecular behaviors.
• Bridging the gap between microscale polymer dynamics and macroscale continuum models is challenging.

Purpose of the Study:

• To introduce a machine learning framework for constructing continuum non-Newtonian fluid dynamics models directly from microscale descriptions.
• To demonstrate the framework's ability to retain molecular fidelity and ensure model admissibility.

Main Methods:

• A micro-macro correspondence was established using encoders for microscale polymer configurations and macroscale conformation tensors.
• Machine learning was employed to parameterize the dynamics of these conformation tensors.
• The deep non-Newtonian model (DeePN²) was formulated to preserve rotational invariance.

Main Results:

• The DeePN² model successfully integrates microscale polymer dynamics into a continuum framework.
• The model demonstrated superior accuracy compared to empirical closure methods in numerical simulations.
• Rotational invariance was rigorously preserved in both the dynamic equation formulation and neural network representation.

Conclusions:

• The developed machine learning framework provides a robust method for creating accurate non-Newtonian fluid models.
• DeePN² offers a promising approach for simulating complex fluid behaviors with improved molecular fidelity.
• This work advances the integration of data-driven methods with classical fluid dynamics.