Numerical Methods for Partial Differential Equations Seminar

Building 2, 449

Speaker: Mohammed Alhashim (Harvard University)Title: Towards designing the flow behavior of complex fluids using automatic differentiationAbstract:Automatic differentiation is a key driver of the recent innovations in machine learning; allowing for deep learning of complex neural network architectures with billions of parameters. While open-source libraries like JAX, Tensorflow or PyTorch have greatly simplified the implementation of this technique to compute gradients of computer programs, its adaptation to PDE-constrained optimal control problems, a mathematical structure prevalent in science, remains relatively less known within the scientific community. This presentation aims to shed light on automatic differentiation—what it entails and its recent applications in expediting direct numerical solvers, formulating innovative models, and targeting intricate flows. A special focus will be directed towards the utilization of automatic differentiation in the design of complex flows. While breakthroughs in direct numerical simulation over the last century have substantially deepened our understanding of the fundamental physics governing the motion of particles or objects within fluids, the task of designing or optimizing flows for specific applications remains a formidable challenge. This challenge stems from the necessity to solve high-dimensional optimization problems, making it an intriguing application for the automatic differentiation technique.