Towards predictions of large dynamic systems' behavior using reduced-order modeling and interval computations

摘要

The ability to conduct fast and reliable simulations of dynamic systems is of special interest to many fields of operations. Such simulations can be very complex and, to be thorough, involve millions of variables, making it prohibitive in CPU time to run repeatedly for many different configurations. Reduced-Order Modeling (ROM) provides a concrete way to handle such complex simulations using a realistic amount of resources. However, uncertainty is hardly taken into account. Changes in the definition of a model, for instance, could have dramatic effects on the outcome of simulations. Therefore, neither reduced models nor initial conclusions could be 100% relied upon. In this research, Interval Constraint Solving Techniques (ICST) are employed to handle and quantify uncertainty. The goal is to identify key features of a given dynamical phenomenon in order to be able to propagate the characteristics of the model forward and predict its future behavior to obtain 100% guaranteed results. This is specifically important in applications, as a reliable understanding of a developing situation could allow for preventative or palliative measures before a situation aggravates.