Project Overview#

From modeling population dynamics to understanding the formation of stars, PDE permeate the world of science and engineering. For most real-world problems, the lack of closed-form solutions requires computationally expensive numerical solvers, sometimes consuming millions of core hours and terabytes of storage.

This project aims to identify the conceptual and mathematical relationship among a few different types of neural representation for PDEs, on regular grids or irregular geometries, and design machine learning models that could solve Naivier Stokes equations efficiently and accurately.

  1. https://en.wikipedia.org/wiki/Physics-informed_neural_networks
  2. Tran, Alasdair, A. Mathews, Lexing Xie and Cheng Soon Ong. “Factorized Fourier Neural Operators.” (2021)

Requirements#

  • Solid knowledge of machine learning or time series models, e.g. COMP4670/8600 or equivalent.
  • Comfortable prototyping machine learning algorithms or simulation, python or R.
  • Strong ability to critically examine mathematical or empirical results.
  • Able to communicate technical ideas clearly, and work effectively in a research team.

Info#

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