In many areas of physics, we have a reasonable idea about the types of differential equations that govern their behaviour. Examples are fluid dynamics, which is described by Navier-Stokes equations, or gravity, which is described by the Einstein equations. Very few analytic solutions to these equations exists, so most practical applications use numerical techniques.
A particular problem with numerical techniques is that for every change in boundary conditions and for every change in the parameters of the differential equations, one needs to construct a completely new numerical solution from scratch. This is computationally costly.
In recent years, machine learning techniques have been used successfully to address this problem, and complement existing numerical techniques. Instead of treating each solution independently, they detect patterns in sets of solutions, guided by built-in knowledge of the differential equations that underly them. These "physics informed neural networks" thus combine modern machine learning techniques (which often produce answers but no real insight into what governs a system) with old-school knowledge (which provides insight, but is too complex in many cases to provide answers).
In this project, you will investigate how machine learning techniques can be used to "solve" dynamical 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.