Physics Informed Neural Network for Ocean Pollutant Dispersal

Explore a comprehensive conference talk that demonstrates how to build Physics-Informed Neural Networks (PINNs) using Julia's SciML ecosystem to model oceanic pollutant transport and dispersal. Learn about the development of a PINN-based framework that serves as a powerful alternative to traditional numerical solvers for the advection-diffusion equation, which often face computational limitations when modeling ocean pollutant transport affecting marine ecosystems worldwide. Discover the methodology behind constructing a fully connected neural network using Lux.jl that approximates solutions to the 2D advection-diffusion equation, with particular emphasis on the innovative hybrid, weighted loss function developed using NeuralPDE.jl to enforce physical constraints and handle sharp initial conditions—a common challenge in PINN applications. Examine the systematic investigation into neural network architecture and hyperparameter optimization, including detailed experiments comparing networks with 9 hidden layers and varying neuron counts (64, 128, or 256 per layer), evaluating different optimizers (ADAM, ADAMW, and L-BFGS), and testing various learning rates for optimal convergence. Understand the comprehensive performance benchmarking that identifies the optimal configuration of a 9-layer, 128-neuron network trained with the ADAM optimizer, achieving approximately 8.25% relative error against high-resolution Finite Difference Method solutions while highlighting the "sweet spot" for model capacity. Gain insights into computational trade-offs through BenchmarkTools.jl analysis, showing how the resulting surrogate model achieves highly efficient full-field inference in just ~0.024 seconds despite significant training time requirements, establishing a robust methodology for tuning PINNs and providing a blueprint for future extensions incorporating real-world oceanographic data to address practical environmental challenges.