Shape Memory Alloys (SMAs) are a multifunctional material used in a variety of industries due to their abilities to recover large deformations, even under load. The useful characteristics of SMAs are accompanied with complexities in its behavior, such as thermomechanical coupling, nonlinearity, and hysteresis. This work presents a hybrid constitutive modeling approach for capturing the complex behaviors of SMAs which combines data-driven models with traditional physics-based frameworks. Data-driven constitutive models can capture complex material behaviors from experimental data, reducing the need for predefined functional forms of the constitutive relations. However, heavy reliance on such approaches often requires extensive training data and exhibits poor extrapolation beyond the training domain. Additionally, core physical principles such as the second law of thermodynamics may not be inherently followed by such models. The hybrid modeling approach presented in this work addresses these limitations by integrating Artificial Neural Networks (ANNs) into an SMA model derived from continuum thermodynamics. This ensures adherence to physical principles while simultaneously enhancing model predictions of the SMA behavior. Varying degrees of the integration of ANNs into the underlying modeling framework will be considered. For example, the transformation hardening function can be directly represented using an ANN to improve the modeling accuracy of the first-order phase transformation behavior. Experimental data from the literature is used to train the hybrid constitutive models, and their performance is compared to that of traditional SMA modeling approaches. This hybrid approach demonstrates its value in accurately capturing the complex behaviors exhibited by SMAs while simultaneously avoiding manual calibration. Furthermore, the inherent variability in SMA behavior, which can be significant even with strict manufacturing controls, highlights the advantage of being able to directly train constitutive models using experimental data. Finally, the application of such models within finite element analysis for structural analysis is also explored.