Abstract.

This paper proposes a framework that integrates the Level Set Method (LSM) with neural networks to reconstruct image via Navier-Stokes-driven modelling. By combining physics-constrained learning with geometric deep learning, the approach preserves physical consistency in the recovered structures while capturing complex flow dynamics. The approach uses a Denoising Convolutional Neural Network (DnCNN) denoiser to improve reconstruction quality, trained with a composite objective that combines perceptual, adversarial Generative Adversarial Network (GAN), and PDE-based losses. Experimental results show that our method reliably reconstructs high-quality images from corrupted data, indicating the potential for robust image recovery applications.

Keywords:

physics-constrained learning, geometric deep learning, Level Set Method, neural networks.