Adaptively balanced Poisson-constrained physics-informed neural networks for robust displacement integration in...

Area of Science:

• Fluid Dynamics
• Computational Physics
• Machine Learning

Background:

• Displacement integration is crucial for reconstructing physical fields in background-oriented Schlieren (BOS) imaging.
• Conventional methods like high-order fitting and discrete Poisson solvers have limitations in accuracy and robustness.

Purpose of the Study:

• To introduce a novel physics-informed neural network (PINN) framework, the adaptively balanced Poisson-constrained PINN (AB-PoissonPINN), for improved displacement integration in BOS.
• To evaluate the performance of AB-PoissonPINN against established numerical integration techniques.

Main Methods:

• Developed the AB-PoissonPINN framework, incorporating a Poisson equation constraint and a novel relative loss balancing with random backtracking (ReLoBRaLo) strategy.
• Benchmarked AB-PoissonPINN against weighted cubic spline least squares integration (WCSLI), discrete Poisson solvers, and standard PINNs using simulated and experimental BOS data.

Main Results:

• AB-PoissonPINN demonstrated superior accuracy compared to WCSLI, discrete Poisson solvers, and standard PINNs.
• The proposed method maintained high accuracy under both noise-free conditions and various levels of experimental noise.

Conclusions:

• The AB-PoissonPINN framework offers a significant advancement in displacement integration for BOS applications.
• This physics-informed machine learning approach provides a more accurate and robust solution for reconstructing physical fields from experimental data.