Wire braided tubular architectures exhibit mode dependent deformation that is governed by coupled bending and twist. Such deformation is constrained by braided helical wires [1]. Because equilibrium is typically obtained through repeated nonlinear solves, design exploration and inverse identification of braid parameters have remained computationally expensive. A physics informed neural operator framework is proposed to approximate the solution operator that maps wire design parameters and actuation conditions to equilibrium responses. The forward problem is defined as identifying equilibrium structural parameters for a given wire combination and temperature, where the equilibrium is determined by minimizing the total energy of the braided wires. The inverse problem is defined as identifying wire combination conditions that reproduce prescribed equilibrium structural parameters or target deformation metrics, without requiring repeated nonlinear equilibrium iterations. The mapping is learned to enable rapid evaluation of equilibrium structures and responses across diverse wire combinations and temperatures, so that target deformation metrics can be matched without repeated equilibrium iterations while remaining consistent with mechanics based energy minimization. The proposed approach is expected to provide a scalable pathway for rapid design of braided architectures by integrating mechanics with operator based surrogates. Further, it can accelerate the development of soft robotics applications, including compact mobile robots and wearable assistive devices.