Scientific machine learning for modeling and simulating complex fluids.

Area of Science:

• Rheology and Soft Matter Physics
• Computational Fluid Dynamics
• Materials Science

Background:

• Developing accurate rheological constitutive equations is crucial for engineering soft materials.
• Existing data-driven models struggle with diverse experimental data from complex fluid dynamics.
• Previous machine learning models lacked portability between different deformation protocols.

Purpose of the Study:

• To present a flexible, data-driven framework for constructing rheological constitutive equations.
• To enable the creation of models that incorporate physical constraints and are independent of experimental specifics.
• To overcome limitations of classical machine learning in complex fluid dynamics.

Main Methods:

• Developed a scientific machine learning framework using a universal approximator within a materially objective tensorial constitutive framework.
• Ensured models inherently respect physical constraints like frame-invariance and tensor symmetry.
• Trained models on limited data and validated their ability to describe complex flows.

Main Results:

• The framework facilitates rapid discovery of accurate constitutive equations from limited data.
• Learned models can describe kinematically complex flows, demonstrating high flexibility.
• Successfully deployed a trained model in a multidimensional computational fluid dynamics simulation.

Conclusions:

• The proposed framework offers a robust solution for data-driven rheological modeling of complex fluids.
• These 'digital fluid twins' are applicable to diverse material systems and engineering challenges.
• This approach advances the use of machine learning in rheology and fluid dynamics.