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Precise and timely fault diagnosis is crucial in many practical systems and control processes. Particularly due to the increasing amount of available data collected by sensors, data-driven fault diagnosis has been a hot research topic in the prognosis and health management of industrial systems. In this paper, a reliable, accurate, and interpretable data-driven fault detection and isolation method is proposed for the general class of nonlinear systems. The proposed approach is based on the integration of the bilinear Koopman model realization, deep learning, and a bilinear parity-space framework. This work leverages the potential of neural networks to investigate lifting functions and bilinear Koopman realization simultaneously. Furthermore, to enhance the stability of the realized model, the input-to-state stability constraint is enforced on the training algorithm, ensuring the realized model is integral input-to-state …