University of Münster mathematician receives prestigious research grant
The European Research Council (ERC) has awarded a Consolidator Grant to Prof. Arnulf Jentzen. Jentzen, who carries out research at the Cluster of Excellence “Mathematics Münster” at the University of Münster, is working on the mathematical fundamentals of deep learning, which is a part of machine learning and forms the basis for the further development of applications involving artificial intelligence.
For the project entitled “Overcoming the curse of dimensionality through nonlinear stochastic algorithms” (short title: MONTECARLO), due to start in July 2023, Arnulf Jentzen will be receiving around 1.4 million euros for the next five years. “This is splendid news for Arnulf Jentzen personally,” says Rector Prof. Johannes Wessels, “and also for our core profile area of mathematics and for the University of Münster overall. I am delighted that the European Research Council has shown recognition for the important basic research being done in this pioneering area.”
Details of the project
“In many relevant real-world problems, it is of fundamental importance to be able to approximately compute evaluations of high-dimensional functions,” says Arnulf Jentzen. Such high-dimensional approximation problems occur, for example, in the approximative evaluation of complex financial products, in the approximative solution of stochastic optimal control problems, as well as in the approximative solution of filtering problems in which characteristic quantities of a physical system are only partially known. Such approximation problems are frequently described by means of appropriate high-dimensional partial differential equations (PDEs) and appropriate high-dimensional forward-backward stochastic differential equations (FBSDEs).
“Deterministic standard approximation methods for solving such equations suffer from the so-called ‘curse of dimensionality’ – which, roughly speaking, means that the number of computational operations involved in the method grows at least exponentially in the dimension of the equation,” Jentzen explains. “With such methods it would be impossible to approximately solve such equations in high dimensions in a reasonable computational time, even if we were to employ the most powerful computers in the world today simultaneously.”
The key objective of the ERC funded project MONTECARLO is to design and analyse random approximation algorithms which provably overcome the curse of dimensionality in the case of certain PDEs, FBSDEs, SOCPs, and data-driven learning problems.
Arnulf Jentzen
Born in 1983, Arnulf Jentzen studied at the Goethe University Frankfurt, where he also gained his PhD. After a period as an Assistant Professor (Akademischer Rat a.Z.) at the University of Bielefeld, he held a research fellowship from the German Research Foundation (DFG) to undertake research at Princeton University in the US. From 2012 to 2019 he was an Assistant Professor at ETH Zurich in Switzerland. Since 2019 he has been a Full Professor of Applied Mathematics at the Faculty of Mathematics at Münster University as well as a member of the Cluster of Excellence “Mathematics Münster”. Since 2021 he also holds a presidential chair professorship position at the School of Data Science at the Chinese University of Hong Kong, Shenzhen.
In 2020 Jentzen received the Felix Klein Prize, which is awarded every four years by the European Mathematical Society (EMS) and the Fraunhofer Institute of Industrial Mathematics (ITWM) to outstanding young mathematicians working in the field of applied mathematics. In 2022 he was awarded the Joseph F. Traub Prize for Achievement in Information-Based Complexity.
ERC Grants
The ERC grants are very prestigious funding programmes of the European Research Council directed at outstanding researchers. The ERC funding line “Consolidator Grants” is aimed at researchers in the period of between seven and twelve years after they have gained their PhD. It supports the setting-up or consolidation of an independent research group. Other ERC programmes include “Starting Grants” and “Advanced Grants”. Including the new “Consolidator Grant” awarded to Arnulf Jentzen, there are currently 13 researchers at Münster University who are receiving funding from the ERC, and five of them are members of the Cluster of Excellence “Mathematics Münster”.