In essence, machine learning provides us with powerful methods to approximate very complicated non-linear functions of many variables. Because this is such a general concept, it has seen applications in many different areas, for instance computer vision, language processing and all sorts of classification problems. But function approximation is of course something we do all the time in physics, where we are typically interested in finding numerical approximations to solutions of differential equations.
In recent years, there has been a flurry of activity around the idea of using neural networks as 'black boxes' to provide solutions to differential equations, complementing existing numerical methods. Once the networks have been trained using solutions found using standard techniques, they can then be utilised to provide large sets of new solutions, for different initial conditions or different parameters, in a fraction of the time required by standard methods.
In this project, you will investigate how machine learning techniques can be used to 'solve' systems from physics, and compare how they differ from and complement established numerical integration methods.
You need to have good Python skills or experience with another programming language, e.g. C++ or Julia.