MDS Seminar

With the MDS Seminar, we would like to launch a lecture series in which both researchers from the University of Twente and external researchers present their current work in the field of mathematics of data science. The aim is to get to know and understand the research of other groups and disciplines better. It offers the opportunity for regular exchange as well as a basis for possible collaborations. 

Format
Seminars are held on campus and via Teams. All seminars occur every fortnight on Mondays at 4 p.m. unless otherwise stated (see the program below for the dates and the rooms).

Upcoming seminars

• Speaker: Michael R.A. Abdelmalik (TU/e)
  Title: Neural Green’s Operators for Parametric Partial Differential Equations.
  Abstract:
  In this talk, we consider operator networks as promising machine learning tools for reduced order modeling of a wide range of physical systems described by partial differential equations (PDEs). This work introduces neural Green's operators (NGOs)  [1], a neural operator network architecture that learns the solution operator for a parametric family of linear partial differential equations (PDEs). Our construction of NGOs is derived directly from the Green's formulation of such a solution operator. Such a NGO acts as a surrogate for the PDE solution operator: it maps the PDE’s input functions (e.g. forcing, boundary conditions, PDE coefficients) to the solution. We apply NGOs to relevant canonical PDEs to demonstrate their efficacy and robustness as compared to a standard Deep Operator Networks [2], Variationally Mimetic Operator Networks [3] and Fourier Neural Operators [4]. Furthermore, we show that the explicit representation of the Green's function that is returned by NGOs enables the construction of effective matrix preconditioners for numerical solvers for PDEs. Finally, we show that we can leverage the parametric nature of NGOs to embed them within iterative algorithms to approximate solutions of time dependent and nonlinear PDEs.
  References
  [1] Melchers, et al. "Neural Green's Operators for Parametric Partial Differential Equations." arXiv preprint arXiv:2406.01857 (accepted in CMAME)
  [2] Lu, Lu, et al. "Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators.” In: Nat. Mach. Intell. 3.3 (2021). 
  [3] Dhruv Patel et al. “Variationally mimetic operator networks”. In: Comput. Methods Appl. Mech. Eng. 419 (2024). 
  [4] Zongyi Li et al. “Fourier neural operator for parametric partial differential equations”. In: arXiv preprint

• Speaker: Alex Massucco (University of Cambridge)
  Title: T.b.a

• Speaker: Tom Jacobs (CISPA)
  Title: T.b.a.

• Speaker: Serte Donderwinkel (RUG)
  Title: T.b.a.

• Speaker: Yongdai Kim (Seoul National University)
  Title: T.b.a.

• Speaker: Alexis Derumigny (TU Delft)
  Title: T.b.a.

Read more about the past seminars >>