Local bi-fidelity field approximation with Knowledge Based Neural Networks for Computational Fluid Dynamics

Area of Science:

• Computational Science
• Machine Learning
• Fluid Dynamics

Background:

• Bi-fidelity modeling balances accuracy and computational cost.
• Existing methods may struggle with scalability for complex systems.
• Accurate simulations are crucial for design and analysis.

Purpose of the Study:

• Introduce a novel machine learning method for bi-fidelity modeling.
• Demonstrate the efficacy of Knowledge Based Neural Networks (KBaNNs) in improving coarse model outputs.
• Explore the application of KBaNNs in Computational Fluid Dynamics (CFD).

Main Methods:

• Developed a Knowledge Based Neural Network (KBaNN) for additive corrections.
• Trained KBaNNs on a limited dataset of simple 2D flows.
• Applied KBaNNs to correct velocity fields in CFD simulations, accounting for mesh effects.

Main Results:

• KBaNNs successfully provided local corrections to velocity fields, enhancing accuracy.
• The method demonstrated generalization capabilities to new geometries (NACA 2412 airfoil).
• The approach showed scalability with input and output features.

Conclusions:

• KBaNNs offer an effective bi-fidelity modeling strategy.
• This machine learning approach can improve accuracy in CFD and other fields.
• KBaNNs pave the way for data-informed, computer-based design systems.