# Machine Learning methods for Parallel-in-time algorithms

### Working Groups: Chair Computational Mathematics

### Collaborators (MAT): Abdul Qadir Ibrahim, M. Sc., Prof.Â Dr.Â Daniel Ruprecht, Dr.Â Sebastian GÃ¶tschel

## Description

We explore the use of machine learning based coarse propagators in the Parareal parallel-in-time algorithm. The aim is to solve nonlinear time-dependent partial differential equations faster. We consider, as an example, the time-dependent nonlinear Black-Scholes equation, which may be used to value financial options and to calculate implied volatilities. We will show that that an ML-based coarse propagator can lead to faster Parareal convergence. Faster convergence would mean better speedup which, in turn, could help to build financial analysis tools that enable traders to make a rapid and systematic evaluation of buy/sell contracts.