Impact of Loss Weight and Model Complexity on Physics-Informed Neural Networks for Computational Fluid Dynamics

TL;DR

This work tackles the sensitivity of physics-informed neural networks (PINNs) to loss weighting in CFD problems. It proposes two dimensional analysis–based weighting schemes, the second including unquantifiable terms, and validates them on conduction, convection–diffusion, and lid-driven cavity benchmarks. The results show that incorporating unquantifiable terms improves stability and accuracy in conduction and lid-driven cavity, while convection–diffusion is well-captured by both schemes, with high Peclet number cases highlighting PINN robustness. The study also discusses practical aspects of integrating Python-based learning with C++ solvers, underscoring the potential of informed loss weighting to broaden PINN applicability in CFD.

Abstract

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.

Figures (24)

• Figure 1: Relationship between AI, ML, and DL.
• Figure 2: Schematic of training a physic-informed neural network (PINN).
• Figure 3: PINN
• Figure 4: Problem domain and boundary conditions of conduction problem
• Figure 5: PINN’s prediction of temperature distribution at y = 0.5 at (a) $\frac{1}{10}$ (b) $\frac{1}{30}$ (c) $\frac{1}{50}$