Collaborative Research: CISE MSI: RDP: III: Physics-Guided Generative Artificial Intelligence for Inverting Chaotic Advection-Diffusion Dynamics

This project aims to understand complex physical processes like pollution transport, virus spread, and wildfire evolution by integrating physics and artificial intelligence. These movements of interest within each of these processes are influenced by uncertain background flow velocities; that is, how fast the pollution or virus moves, making identification of the source of the problem challenging. The proposed research combines equations from physics that govern physical movement with generative machine learning, specifically focusing on stable diffusion models. By incorporating uncertain flow velocity information, we aim to enable more accurate source identification from limited observations. This innovative approach promises to enhance our ability to manage environmental and societal disasters, leading to improved pollution control, risk assessment, and disaster response strategies. The project develops physics-constrained generative stable diffusion models to reverse advection-diffusion processes. It addresses uncertainties in background flow velocities by developing a stable-diffusion formulation to gradually remove the stochasticity in the backward process, and adopt appropriate diffusivity learned through the training data. This approach integrates physical governing equations as guidance, allowing for reliable modeling that can be conditioned on the limited information of background flow fields. The research aims to quantify how these uncertainties affect source identification accuracy, providing a transformative solution in environmental monitoring. By retrospectively interpreting observations, we aim to unravel causal relationships leading to current states. The project also aims to advance interdisciplinary education and support diverse student participation in engineering and environmental science research. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.