The main objective of this article is to develop scalable anomaly detectors for high-fidelity simulators of power systems. On the one hand, high-fidelity models are typically too complex to apply existing model-based approaches in the fault/anomaly detection literature. On the other hand, pure data-driven approaches developed primarily in the machine learning literature neglect our knowledge about the underlying dynamics of power systems. To address these shortcomings, we develop a data-assisted model-based diagnosis filter that utilizes both the model-based knowledge and also the simulation data from the simulator. The diagnosis filter aims to achieve two desired features: (i) performance robustness with respect to output mismatches; (ii) high scalability. To this end, we propose a tractable optimization-based reformulation in which decisions are the filter parameters, the model-based information introduces feasible sets, and the data from the simulator forms the objective function to-be-minimized regarding the effects of output mismatches on the filter performance. To validate the theoretical results and its effectiveness, we implement the developed diagnosis filter in DIgSILENT PowerFactory to detect false data injection attacks on the Automatic Generation Control measurements in the three-area IEEE 39-bus system.