Physics informed neural networks for fluid flow analysis with repetitive parameter initialization.

Area of Science:

• Computational fluid dynamics
• Machine learning for scientific computing
• Partial differential equation solvers

Background:

• Physics-informed neural networks (PINNs) are effective for simulating fluid dynamics governed by PDEs.
• Existing PINNs face challenges with stiff fluid problems, leading to stagnation and convergence to local minima, yielding inaccurate solutions.
• High Reynolds number flows present significant computational challenges for standard neural network approaches.

Purpose of the Study:

• To develop a robust training strategy for PINNs that overcomes limitations in simulating stiff fluid dynamics.
• To enhance the ability of PINNs to escape local minima and achieve physically plausible solutions.
• To improve the accuracy and applicability of PINNs for complex fluid flow analysis.

Main Methods:

• A novel 're-initialization' training strategy was proposed, involving periodic modulation of PINN training parameters.
• The strategy was validated on 2D steady-state lid-driven cavity flow problems at high Reynolds numbers (700 and 1,000).
• Principal component analysis was employed to confirm the dynamic modulation of model parameters during training.

Main Results:

• The re-initialization strategy successfully simulated vortex and shear layers in high Reynolds number flows.
• The proposed method achieved the lowest mean square error compared to existing approaches.
• Validation confirmed the strategy's effectiveness in overcoming local minima and improving simulation accuracy.

Conclusions:

• The re-initialization strategy significantly enhances the performance of PINNs for stiff fluid dynamics problems.
• This approach provides a foundational method for addressing local minima issues in neural network training through direct parameter modulation.
• The findings expand the utility of PINNs for complex, high-fidelity fluid flow simulations.