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 community of researchers in the field to discuss the problems, the solutions, the victories, and the future of machine learning for differential equations.
If you are interested in joining this community and our mailing list, please feel free to email maths4dl@bath.ac.uk.
