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

TL;DR

This paper proves local well-posedness for a modified NSCH-Oldroyd system related to thrombus modeling and demonstrates PINN-based numerical solutions with energy-based sampling.

Contribution

It introduces a diffusion-enhanced system maintaining energy structure and provides the first PINN-based numerical illustrations for thrombus-related equations.

Findings

Proved local well-posedness of the modified system.

Presented PINN numerical results with residual losses and benchmark errors.

Used Metropolis-Hastings sampling based on energy decay.

Abstract

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.