This is a one-week program gathering mathematicians, engineers, and scientists interested in reduced order models and methods (ROMs) for systems of partial differential equations. The general idea behind ROMs is to derive a low-dimensional model from a high-dimensional model, by integrating techniques from data science, modeling, and simulation, in order to obtain accurate and reliable results at greatly reduced computational costs. The high-dimensionality of the original model may be due to its intrinsic character, e.g. the problem may contain many parameters, or it may be due to the discretization, e.g. a fine discretization required by a complex geometry or a singularity in the solution that leads to a large number of degrees of freedom.
- Inverse problems arising in optimal control, parameter estimation, and data assimilation.
- Uncertainty quantification.
- Continuum Mechanics, including nonlinear problems and multiphysics.
- Scientific computing aspects of reduced order methods, with attention to the offline-online paradigm and High Performance Computing for the offline phase.
- Reduction and design of parameter spaces.