Working groups

We have two active working groups. These working groups meet regularly and bring together researchers within the team and beyond to identify and work on key challenges in the field.

Working group on machine learning for differential equations (ML4DE)

The use of differential equations is central to scientific modelling and exploration. Consequently, a significant amount of modern scientific computing revolves around the approximation of solutions to differential equations. In recent years, machine learning techniques have gained traction as a promising tool for addressing this approximation problem. One notable example is the development of physics-informed neural networks (PINNs), which have shown early success in providing efficient methods for simulating physical phenomena. However, these approaches are still in the early stages of development and ongoing investigation. 

The relationship between machine learning and differential equations is, in fact, reciprocal: ideas from numerical methods for differential equations have significantly influenced the design of neural networks, particularly in the context of Neural ODEs.

In this working group we explore topics and research projects in this general field connecting machine learning with differential equations. Since March 2022 we have held regular meetings bringing together a researchers in the field to discuss the problems, the solutions, the victories, and the future of machine learning for differential equations.

Most recently we held a hackathon which brought together students and researchers from across the UK to compete in two exciting challenges focused on solving differential equations using machine learning tools.

Working group on machine learning for inverse problems (ML4IP)

Deep learning has emerged as a powerful tool in solving inverse problems with impressive empirical results across a number of applications.

However, many approaches still lack theoretical foundations and often struggle with generalisation to different problem settings. In particular, there is no consensus which theoretical guarantees are actually desired. Additionally, much of the existing theory neglects the role of the training data, despite its central importance in data-driven approaches.

This working group is formed discuss open problems and research directions of data-driven methods in inverse problems.

The primary goal of the working group is to produce a perspective, position, or roadmap paper that highlights challenges and outlines research directions. The working group will explore topics such as: non-linear inverse problems, multi-resolution and multi-scale learning, learning in function spaces and data-driven regularisation.

If you are interested in finding out more about our working groups, please feel free to email maths4dl@bath.ac.uk