DE Seminar: Boris Muha (University of Zagreb)

Abstract: Partial differential equations (PDEs) are widely used to model physical phenomena and often depend on parameters, requiring multiple solutions to assess system behavior under varying conditions. Repeatedly solving PDEs is computationally expensive, so Reduced Order Models (ROMs) use snapshot datasets of parameter-solution pairs to accelerate computation. Recently, Deep Learning-based ROMs (DL-ROMs) have emerged as a novel way to construct ROMs. Many PDEs also depend on parameterized domains, which complicates ROM construction. We present a Deep-ROM method that captures domain parameterization without user-defined control points and handles domains with varying component counts. It also derives meaningful parameterizations without domain meshes—useful in biomedical settings—using deep neural networks to reduce the complexity of both PDEs and domains.

This joint work with M. Bukač, I. Manojlović and D. Vlah.

Preprint: https://arxiv.org/abs/2407.17171