5 papers
Equidistribution-based training of Free Knot Splines and ReLU Neural Networks
Simone Appella, Simon Arridge, Chris Budd +2
We consider the problem of univariate nonlinear function approximation using shallow neural networks (NN) with a rectified linear unit (ReLU) activation function. We show that the…
Models for information propagation on graphs
Oliver R. A. Dunbar, Charles M. Elliott, Lisa Maria Kreusser
We propose and unify classes of different models for information propagation over graphs. In a first class, propagation is modelled as a wave which emanates from a set of \emph{kno…
Learning efficient and provably convergent splitting methods
L. M. Kreusser, H. E. Lockyer, E. H. Müller +1
Splitting methods are widely used for solving initial value problems (IVPs) due to their ability to simplify complicated evolutions into more manageable subproblems which can be so…
Parallel-in-Time Solutions with Random Projection Neural Networks
Marta M. Betcke, Lisa Maria Kreusser, Davide Murari
This paper considers one of the fundamental parallel-in-time methods for the solution of ordinary differential equations, Parareal, and extends it by adopting a neural network as a…
A Rule-Based Epidemiological Modelling Framework
David Alonso, Steffen Bauer, Markus Kirkilionis +2
Motivated by chemical reaction rules, we introduce a rule-based epidemiological framework for the systematic mathematical modelling of future pandemics. Here we stress that we do n…