Monitoring the correctness of distributed cyber-physical systems is essential. We address the analysis of the log of a black-box cyber-physical system. Detecting possible safety violations can be hard when some samples are uncertain or missing. In this work, the log is made of values known with some uncertainty; in addition, we make use of an over-approximated yet expressive model, given by a non-linear extension of dynamical systems. Given an offline log, our approach is able to monitor the log against safety specifications with a limited number of false alarms. As a second contribution, we show that our approach can be used online to minimize the number of sample triggers, with the aim at energetic efficiency. We apply our approach to two benchmarks, an anesthesia model and an adaptive cruise controller.