Speaker
Description
Solving parameter-dependent Partial Differential Equations (PDE) for multiple parameters is often needed in physical, biomedical and engineering applications.Usually,PDEs are solved by transforming PDE to weak formulation. Usually, approximation of the solutions is found in finite-dimensional function space using Finite Element Method. This results in large number of equations and solving them form multiple parameters often becomes too prohibitive.
In order to mitigate these solutions, Reduced Order Models (ROM) is constructed. Classically, it is done by projecting solutions from Finite Element Method to lower-dimensional space. When PDE is linear, this results in smaller number of equations. However, classical ROM may be difficult to adapt to nonlinear methods.
To mitigate these difficulties, multiple techniques using Deep Learning for constructing ROMs are developed. This talk discusses our extension of encoder-decoder type Deep ROM for different domains. Our approach works when domains are given from measurements only, when we have it's exact parametrization and even when domain has varying number of components, or varying number of holes. We demonstrate proposed method on 2D problems. Furthermore, we will elaborate on possible extensions of our work.
