It is a major challenge to turn raw data into models that are not just predictive (data assimilation), but also provide insight into the nature of the underlying dynamical system that generated the data. Model order reduction via reduced basis methods will be of great interest in this context. Also, quantifying uncertainty, both in model-based data
assimilation as well as in partial differential equations, is important for many of our research areas (inverse problems, model order reduction). Deep recurrent artificial neural networks share a lot of structural and numerical similarities with nonlinear dynamical systems and are able to represent complex nonlinear, multiscale maps in a compressible linearizable fashion. Whereas, nearly all past approximation algorithms for PDEs suffered from the well-known curse of dimensionality, deep learning networks are able to tackle this dimensionality reduction efficiently via automatically learned emerging multiscale patterns (wavelet scattering, low-rank methods).
People working on this subject within SACS are:
Post Doc / PhD