WG5 Meeting Announcement
Online meeting of the »Numerical methods and applications« working group (WG5) of the COST Action will take place on Friday, 22 October.
9:00–9:35: Matthias Ehrhardt (University of Wuppertal)
talk on "Deep Smoothness WENO Method with Applications in Finance"
9:45–10:35: panel discussion on the future of WG5
led by Csomós (Eötvös Loránd University, Budapest)
10:45–11:30: Luka Grubišić (University of Zagreb)
talk on "Rational function surrogate modeling for the optimal control of parabolic systems"
11:45–12:30: further discussion, questions, answers
Matthias Ehrhardt (University of Wuppertal)
"Deep Smoothness WENO Method with Applications in Finance"
We present the novel deep smoothness weighted essentially non-oscillatory (WENO-DS) method and its application in finance. To improve the existing WENO method, we apply a deep learning algorithm to modify the smoothness indicators of the method. This is done in a way that preserves the consistency and accuracy of the method. We present our results using a European digital option as an illustrating example. Here we avoid the undesirable oscillations, especially in the first time steps of the numerical solution.
Luka Grubišić (University of Zagreb)
"Rational function surrogate modeling for the optimal control of parabolic systems"
We consider an optimal control problem for a linear parabolic equation governed. We represent the solution operator for this problem as a function of a self-adjoint operator on an abstract Hilbert space. The task consists in identifying a control (entering the system through the initial condition) that minimizes the distance of the trajectory of the system from a given constraint while steering the final state at time T > 0 close to the given target. We present the closed form solution for several types of trajectory constraints and then develop a numerical scheme based on the award wining rkfit algorithm for approximating the trajectory of the system using spectral calculus and a rational function surrogate. Time permitting, we will also present considerations of the use of reduced order modelling in the space variable to speedup the computational time. This talk is based on joint work with Martin Lazar, Ivica Nakić and Martin Tautenhahn.
You are kindly invited to join us.