This paper investigates a novel engineering problem

i.e.

security-constrained multi-period operation of micro energy-water nexuses. This problem is computationally challenging because of its high nonlinearity

nonconvexity

and large dimension. We propose a two-stage iterative algorithm employing a hybrid physics and data-driven contingency filtering (CF) method and convexification to solve it. The convexified master problem is solved in the first stage by considering the base case operation and binding contingencies set (BCS). The second stage updates BCS using physics-based data-driven methods

which include dynamic and filtered data sets. This method is faster than existing CF methods because it relies on offline optimization problems and contains a limited number of online optimization problems. We validate effectiveness of the proposed method using two different case studies: the IEEE 13-bus power system with the EPANET 8-node water system and the IEEE 33-bus power system with the Otsfeld 13-node water system.