Webrelaunch 2020

Data-driven approximation of transport-dominated PDEs

  • Speaker: Dr. Benjamin Unger
  • Place: 1.067
  • Time: 17.5.2024, 10:00
  • Invited by: Prof. Dr. Dorothee Frey


The standard task of projection-based model-order reduction (MOR) consists of finding a suitable low-dimensional subspace such that the solution of the dynamical system under investigation approximately evolves within this subspace. The best subspace of a given dimension and the corresponding worst-case approximation error are quantified by the Kolmogorov n-widths. If the n-widths have a slow decay, which is typical for transport phenomena, then a good approximation with a low-dimensional subspace cannot be expected. To overcome this issue, we present a novel model reduction method that allows the low-dimensional subspace to evolve along with the solution of the problem. Our MOR method is inspired by the moving finite element method, yielding a nonlinear projection approach. The resulting reduced model is designed to minimize the residual, which is also the basis for an a posteriori error bound. We discuss the solvability of the underlying infinite-dimensional optimization problem and present numerical evidence for a wildfire application. Moreover, to compare our method with other approaches in the literature, we introduce a novel framework for model reduction on manifolds.