Local Well-Posedness of a Modified NSCH-Oldroyd System: PINN-Based Numerical Computation

Motivated by thrombus modeling, we study a modified Navier-Stokes-Cahn-Hilliard system and consider PINN-based numerical illustrations for the modified system. To enable the analysis, we introduce a diffusion-enhanced system for the deformation variable while preserving the associated dissipative energy structure. We prove local well-posedness for this new system. We also present PINN-based numerical illustrations for representative thrombus cases and report residual losses and benchmark errors obtained with Metropolis-Hastings sampling based on the energy decay.