Invariant Guided PINN for Fluid Flow Computation

Abstract

Physics-informed neural networks (PINNs) often become difficult to optimize for incompressible flow problems with large spatial domains, multiscale stresses, or long-time invariant dynamics. We propose an invariant-guided PINN (IG-PINN) framework that uses partitioned training as a conservative preconditioning stage rather than as the final piecewise representation. A globally defined architecture is trained successively on spatial subdomains or temporal slabs; selected field traces, structural information, and conservative diagnostics are then transferred to a final global correction, yielding a single neural field on the full spatial or space-time domain. The framework is tested on two incompressible flow problems: steady Oldroyd--B flow past a confined cylinder and a rotational Newtonian flow with helicity diagnostics. In the Oldroyd--B case, IG-PINN transfers velocity, polymeric stress, and mass-flux information while avoiding pressure traces at artificial interfaces. In the helicity case, endpoint velocity is transferred through a hard temporal constraint and kinetic energy is controlled during slab training and residual global correction. The experiments demonstrate improved optimization robustness, reduced conservation errors for the cylinder wake, and controlled energy and helicity diagnostics for the transient rotational flow.