Abstract Thermal–hydraulic coupling between power, flow rate and density, intensified by neutronics feedback are the main drivers determining the stability behavior of a boiling water reactor (BWR). High-power low-flow conditions in connection with unfavorable power distributions can lead the BWR system into unstable regions where power oscillations can be triggered. This important threat to operational safety requires careful analysis for proper understanding. Current design rules assure admissible operation conditions by exclusion regions determined by numerical calculations and analytical methods based on non-linear states for specific transients. Analyzing an exhaustive parameter space of the non-linear BWR system becomes feasible with methodologies based on reduced order models (ROMs), saving computational cost and improving the physical understanding. A new self-contained methodology is developed, based on the general general proper orthogonal decomposition (POD) reduction technique. It is mostly automated, applicable for generic partial differential equation (PDE) systems, and reduces them in a grid-free manner to a small ordinary differential equation (ODE) system able to capture even non-linear dynamics. This allows a much more extensive analysis of the represented physical system. Symbolic mathematical manipulations are performed automatically by Mathematica routines. A novel and general calibration roadmap is proposed which simplifies choices on specific POD variants when applying the ROMing to different fields of physics. Persecuting validation and verification, a wide and systematic spectrum of representative test examples has been treated. The desired goal of describing the non-linear stability behavior of the two-phase flow within a fuel assembly of a BWR will be achieved by the investigation of the time domain analysis of BWR instability (TOBI) model. This paper focuses on model-specific options and aspects of the POD-ROM methodology which are afterwards illustrated by means of a strongly non-linear dynamical system showing complex oscillating behavior.