PARTIAL DIFFERENTIAL EQUATION (PDE) SOLVERS ENHANCED BY DEEP LEARNING FOR GENOMIC FLUID DYNAMICS

Abstract

The integration of deep learning with partial differential equation (PDE) solvers has emerged as a transformative paradigm in computational science, offering unprecedented capabilities for modeling complex biophysical systems. This paper presents a comprehensive framework for PDE solvers enhanced by deep learning, specifically tailored for genomic fluid dynamics applications. We propose a hybrid architecture combining Physics-Informed Neural Networks (PINNs) with operator learning techniques to efficiently solve nonlinear PDEs governing blood flow in viscoelastic arteries, with emphasis on the influence of external magnetic fields and genomic-scale parameter variations. Our methodology leverages the complementary strengths of neural networks and physics-based constraints, enabling accurate prediction of pressure and radius disturbances in arterial fluid flow while maintaining computational efficiency. The framework incorporates symbolic regression for model interpretability and demonstrates superior performance compared to conventional numerical solvers across multiple test cases. Experimental results indicate that our approach achieves up to 85% reduction in computational time while maintaining solution accuracy within 2% error margins. This research contributes to the growing field of scientific machine learning by providing a robust, interpretable, and efficient solution for genomic fluid dynamic simulations with potential applications in personalized medicine and biomedical device design.