B01 Nonlinear reduced modeling for state and parameter estimation

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 for a 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.