Nonlinear reduced modeling for state and parameter estimation (B01)

• Subject Area: Mathematics
• Term: since 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 442047500

The goal of this project is to develop nonlinear reduced models for parameter dependent families of PDEs. We combine machine learning concepts, involving Deep Neural Networks (DNNs), with stable variational formulations to warrant a rigorous accuracy quantification fora wide range of problem types. Primary research topics include state or parameter estimation as well as the identification and analysis of appropriate notions of compositional sparsity to understand when the use of DNNs allows one to avoid the curse of dimensionality.

• DFG Programme: Collaborative Research Centres
• Subproject of: SFB 1481: Sparsity and Singular Structures
• Applicant Institution: Rheinisch-Westfälische Technische Hochschule Aachen
• Project Heads: Professor Dr. Markus Bachmayr; Professor Dr. Wolfgang Dahmen