The full characterization of three-dimensional (3D) mechanical behaviour of myocardium is essential in understanding their function in health and disease. The hierarchical structure of myocardium results in their highly anisotropic mechanical behaviors, with the spatial variations in fiber structure giving rise to heterogeneity. The optimal set of loading paths has been used to estimate the constitutive parameters of myocardium using a novel numerical-experimental approach with full 3D kinematically controlled (triaxial) experiments [1, 2]. Due to the natural variations in soft tissue structures, the mechanical behaviors of myocardium can vary dramatically within the same organ. To alleviate the associated computational costs for obtaining responses of myocardium under a range of loading conditions with a given realization of structure, we developed a neural network-based method integrated with finite elements. The boundary conditions were parameterized. The neural network generated a corresponding trial solution of the underling hyperelasticity problem for each boundary condition. Thus, the neural network approximated the parameter-to-state map. A physics-informed approach was used to train the neural network. Due to their learnability characteristics, the neural network was able to predict solutions for a range of boundary conditions with given individual specimen fiber structures. The neural network was validated with finite element solutions. This method will provide efficient and robust computational models for clinical evaluation to improve patient outcomes.