Post-doctor position in numerical analysis within the research group for Numerical Analysis at the Centre for Mathematical Sciences, Lund University.
The Division of Mathematics LTH and Numerical analysis is seeking candidates for three postdoctoral projects. Project 3 is funded by WASP.
- Project 1: Locally Adaptive Methods for Free Discontinuity Problem
- Project 2: Randomized time stepping schemes
- Project 3: Convergence analysis of neural/universal differential equations
Description of WASP funded project (project 3)
Here, we will study and develop numerical methods for so-called neural differential equations and more generally, universal differential equations. These are differential equations with embedded universal approximators such as neural networks. Such equations have recently proven to be very useful e.g. for data-driven model discovery and for solving high-dimensional partial differential equations. To use them effectively, they require accurate, stable and fast methods for both forward- and backward-integration of the underlying differential equation, corresponding to evaluation and training of the neural network. Most of the focus in the literature so far has been on implementation issues and on maximising speed, while less effort has been made on quantifying errors. You will help us remedy this situation by performing rigorous convergence analyses in appropriate functional analytic frameworks for both existing methods and for novel methods to be developed within the project.