2025-07-23 –, David Lawrence Hall Room 104
We present a Physics-Informed Neural Network (PINN) to model pollutant dispersion via the 2D advection-diffusion equation. Our approach focuses on a systematic hyperparameter and architecture investigation, training the network on noisy, synthetic FDM data. The resulting optimal model achieves high accuracy and serves as an efficient surrogate for near-instantaneous forecasting, providing a robust baseline for more complex environmental models.
Ocean pollutant transport is a critical issue affecting marine ecosystems worldwide. While traditional numerical solvers for the advection-diffusion equation face computational limits, Physics-Informed Neural Networks (PINNs) offer a powerful alternative. This talk presents a PINN-based framework developed entirely in Julia to model oceanic pollutant transport, with a specific focus on the methodology behind building and optimizing these complex models.
Our approach leverages Julia’s SciML ecosystem to create a robust and physically consistent model. The core of the framework is a fully connected neural network, built using Lux.jl, that approximates the solution to the 2D advection-diffusion equation. A key contribution of our work is the development of a hybrid, weighted loss function to enforce physical constraints and accurately fit the data. This loss function, constructed with NeuralPDE.jl, explicitly adds a heavily-weighted term to ensure the model precisely learns sharp initial conditions, a common challenge for PINNs. The network is trained on synthetic data generated from a Finite Difference Method (FDM) solver, with Gaussian noise added to simulate real-world measurement uncertainty.
The main focus of this talk is a systematic investigation into the role of neural network architecture and hyperparameters on solution accuracy and computational cost. We will detail our extensive experiments, which varied:
Network Architecture: Comparing networks with 9 hidden layers and 64, 128, or 256 neurons per layer.
Optimizers: Evaluating the performance of ADAM, ADAMW, and the quasi-Newton method L-BFGS.
Learning Rates: Testing a range of rates to find the optimal value for convergence.
We will present a comprehensive performance benchmark that identifies an optimal configuration—a 9-layer, 128-neuron network trained with the ADAM optimizer—capable of achieving a relative error of approximately 8.25% against the high-resolution FDM solution. This highlights a "sweet spot" for model capacity, as a larger 256-neuron network yielded worse accuracy and was far more expensive to train.
Finally, we will discuss the computational trade-offs, using benchmarks from BenchmarkTools.jl. While training our optimal PINN takes significant time, the resulting surrogate model is highly efficient, capable of a full-field inference in just ~0.024 seconds. This work establishes a robust methodology for tuning PINNs and provides a clear blueprint for future extensions that will incorporate real-world, non-constant oceanographic data to tackle practical environmental challenges.
I am a DevOps Engineer with 8 years of experience in IT, specializing in cloud infrastructure. My expertise includes automation, infrastructure as code, and building scalable system architectures, with a strong focus on optimizing cloud-native applications. I am keenly interested in AI/ML and enjoy working on projects integrating DevOps, AI, and large-scale simulations to drive innovation and efficiency.