Recent work has begun to explore the design of biologically inspired soft robots composed of soft, stretchable materials for applications including the handling of delicate materials and safe interaction with humans. However, the solid-state sensors traditionally used in robotics are unable to capture the high-dimensional deformations of soft systems. Embedded soft resistive sensors have the potential to address this challenge. However, both the soft sensors-and the encasing dynamical system-often exhibit nonlinear time-variant behavior, which makes them difficult to model. In addition, the problems of sensor design, placement, and fabrication require a great deal of human input and previous knowledge. Drawing inspiration from the human perceptive system, we created a synthetic analog. Our synthetic system builds models using a redundant and unstructured sensor topology embedded in a soft actuator, a vision-based motion capture system for ground truth, and a general machine learning approach. This allows us to model an unknown soft actuated system. We demonstrate that the proposed approach is able to model the kinematics of a soft continuum actuator in real time while being robust to sensor nonlinearities and drift. In addition, we show how the same system can estimate the applied forces while interacting with external objects. The role of action in perception is also presented. This approach enables the development of force and deformation models for soft robotic systems, which can be useful for a variety of applications, including human-robot interaction, soft orthotics, and wearable robotics.