Impact of Loss Weight and Model Complexity on Physics-Informed Neural Networks for Computational Fluid Dynamics
This addresses a critical bottleneck for researchers using PINNs in fluid dynamics, offering incremental improvements in training stability.
The paper tackles the sensitivity of Physics-Informed Neural Networks (PINNs) to loss weight selection in computational fluid dynamics by proposing two weighting schemes, with the second improving stability and accuracy over equal weighting, achieving stable predictions in high Peclet number convection diffusion where traditional solvers fail.
Physics Informed Neural Networks offer a mesh free framework for solving PDEs but are highly sensitive to loss weight selection. We propose two dimensional analysis based weighting schemes, one based on quantifiable terms, and another also incorporating unquantifiable terms for more balanced training. Benchmarks on heat conduction, convection diffusion, and lid driven cavity flows show that the second scheme consistently improves stability and accuracy over equal weighting. Notably, in high Peclet number convection diffusion, where traditional solvers fail, PINNs with our scheme achieve stable, accurate predictions, highlighting their robustness and generalizability in CFD problems.