Computational efficiency is still an open challenge in solving optimization and inverse uncertainty quantification problems in engineering and clinical settings. The techniques adopted for these problems usually rely on iterative or sampling procedures, which require, at each iteration, the numerical approximation of a differential problem describing the underlying physical process. The computational complexity of this approximation, especially in the case of nonlinear and multiphysics problems, can compromise the efficiency of the estimation procedure.
In this talk, we present some strategies combining dimensionality reduction techniques with artificial neural networks for solving inverse and parameter estimation problems. Specifically, we show how to construct neural network architectures that exploit reduced-order solvers or low-fidelity surrogates in a multi-fidelity framework.
We show some numerical results related to benchmark test cases and some applications in the field of cardiac electrophysiology. In this context, the developed strategies combining dimensionality reduction techniques with artificial neural networks provide an efficient and accurate estimation of electrophysiological quantities of interest.
This work is in collaboration with R. Tenderini (EPFL), F. Regazzoni (Politecnico di Milano), A. Manzoni (Politecnico di Milano), S. Deparis (EPFL) and A. Quarteroni (Politecnico di Milano-EPFL).
This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 740132, iHEART).
