Deep Particle Algorithms and Advection-Reaction-Diffusion Transport Problems

The project studies computational methods for learning and generating distributions of stochastic interacting particle representations of mathematical models in physics and biology. A new class of computational tools integrating particle simulation and machine learning will be developed for a wide range of applications in science and engineering such as modeling and prediction of large scale pattern formation of bacteria and insects, cancer cell invasion, wildfire spreading, and turbulent combustion in energy production. The light weight deep neural networks trained from data generated by particle simulations speed up prediction significantly, and potentially extend to field data in various domains with broader impacts. The planned education and out-reach activities help students, especially under-represented students, on multiple campuses to pursue advanced degrees and careers. The mathematical models under study are three space dimensional time dependent advection-reaction-diffusion partial differential equations challenging to compute by traditional mesh based methods especially when their solutions develop large gradients or concentrations at unknown locations. The project aims to address this challenge through an integrated framework of deep learning, optimal transport, and field-coupled stochastic interacting particle dynamics, the so called Deep Particle. The approach is mesh free, self-adaptive and does not require particle distributions to have invertible mappings between them. The project also investigates convergence and acceleration aspects of the resulting algorithms. 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.