Ionic polymer-metal composites (IPMCs) are functional smart materials that exhibit both electromechanical and mechanoelectrical transduction properties, and the physical phenomenon underlying the transduction mechanisms have been studied across the literature extensively. Here we use a new modeling framework to conduct the most comprehensive dimensional analysis of IPMC transduction phenomena, characterizing the IPMC actuator displacement, actuator blocking force, short-circuit sensing current, and open-circuit sensing voltage under static and dynamic loading. The information obtained in this analysis is used to construct nonlinear regression models for the transduction response as univariant and multivariant functions. Automatic differentiation techniques are leveraged to linearize the nonlinear regression models in the vicinity of a typical IPMC description and derive the sensitivity of the transduction response with respect to the driving independent variables. Further, the multiphysics model is validated using experimental data collected for the dynamic IPMC actuator and voltage sensor. With data collected from physical samples of IPMC materials in-lab, the regression models developed under the new computational framework are verified.