AI is having a profound impact on science by accelerating discoveries across physics, chemistry, biology, and engineering. This course aims to present a highly topical selection of state of the art AI applications across these fields. Emphasis will be placed on using AI, particularly deep learning, to understand physical and engineering systems, mathematically modelled by PDEs.

AI is having a profound impact on science by accelerating discoveries across physics, chemistry, biology, and engineering. This course aims to present a highly topical selection of AI applications across these fields. Emphasis will be placed on using AI, particularly deep learning, to understand systems modelled by PDEs, and key scientific machine learning concepts and themes will be discussed.

This course will focus on teaching different advanced topics in numerical methods for science and engineering. The main aim would be introduce novel algorithms and discuss their implementation.

The course gives an introduction to the numerical methods for the solution of ordinary and partial differential equations that play a central role in engineering applications. Both basic theoretical concepts and implementation techniques necessary to understand and master the methods will be addressed.

This course treats numerical methods for hyperbolic initial-boundary value problems, ranging from wave equations to the equations of gas dynamics. The principal methods discussed in the course are finite volume methods, including TVD, ENO and WENO schemes. Exercises involve implementation of numerical methods in MATLAB.