The aim of this seminar is to provide insights into uncertainty quantification and the approximation theory of neuronal networks, both hot topics in classical and numerical analysis.
In many applications the input data of a given model have some uncertainty, possibly due to inaccurate measurements. The aim of uncertainty quantification (UQ) is to determine how the uncertainty propagates through the model. Here, possible models are differential equations, which depend on uncertain parameters.Some problems in UQ can be efficiently approximated by neuronal networks (NN), which together with machine learning and artificial intelligence produce quite a hype in recent times. In this seminar, we are especially interested in neural networks as universal function approximators.Possible topics are: random fields, Multi-Level and Quasi Monte Carlo methods, numerical methods for stochastic ODEs, parameter uncertainty in option pricing, linear and non-linear approximation-theory of NN, topological properties of NN, solving high-dimensional problems with NN, ...
90-minute talk
Not necessary
Differential equations 1, functional analysis 1, numerical mathematics
