Abstract

We investigate the application of Physics-Informed Neural Networks (PINNs) to a coupled bio-physical modeling problem involving turbulent fluid dynamics and nutrient transport-processes that are central to oceanographic and environmental systems. Our approach leverages recent advances in deep learning to solve partial differential equations (PDEs) by embedding physical constraints directly into the network architecture. Specifically, we model two-dimensional decaying turbulence using the incompressible Navier-Stokes equations and couple it with a passive scalar advection equation for nutrient transport. We evaluate three PINN variants: vanilla PINN, causal PINN (cPINN), and Causal R3 PINN, comparing their performance using a high-resolution numerical solver as reference. Results show that cPINN achieves the lowest mean spatial L-2 error (approximately 50% lower than vanilla PINN), while Causal R3 PINN fails to converge effectively. Computational throughput analysis reveals vanilla PINN processes 24.05 iterations per second compared to cPINN's 12.57, representing a 2x speed difference. This work contributes to the growing field of scientific machine learning by providing quantitative benchmarks and revealing method-specific limitations in realistic, coupled environmental scenarios.