An active learning framework for set inversion

Set inversion is a classical problem in control theory that has many important applications in various fields of science and engineering. The state-of-the-art method for solving this problem, Set Inverter Via Interval Analysis (SIVIA), usually does not work well in high dimensions and often fails to recover sets with complicated structures. In this work, we propose a new approach to the problem of set inversion, which employs techniques from machine learning to resolve these issues. Our algorithm can handle problems in high dimensions and achieve the same level of accuracy with fewer data points compared to SIVIA. We illustrate the performance of our method in various simulation studies and apply it to investigate the dynamics of the 17th-century plague in Eyam village, England.