In this paper we present a novel approach for the simulation of linear and nonlinear tissue response during real time surgical simulation. In this technique, physics-based computations using finite elements are used to generate a massive database to train neural networks during an offline pre-computation step. These neural networks are used during real time computations, resulting in massive computational efficiency. The significance of the method is that, for the first time, linear and nonlinear simulations may be performed with almost the same operational complexity. Additionally, the quality of the real time computations may be easily controlled by scaling the number of neurons used in the computations. This system provides a unique platform to leverage the computational speed and scalability of soft computation methods for real time interactive simulations.