Shape-programmable matter comprises a class of stimuli-responsive materials whose geometry can be controlled by external inputs such as thermal, optical, chemical, electrical, or magnetic stimuli, enabling the realization of prescribed time-varying shapes. Within this broad category, Electro-Active Polymers (EAPs) and Magneto-Active Polymers (MAPs) represent two of the most prominent material families. EAPs constitute a class of smart materials capable of undergoing substantial deformations in response to electrical excitation. Among them, dielectric elastomers have attracted particular attention owing to their remarkable actuation performance, including low density, rapid response, high flexibility, and low elastic stiffness. MAPs consist of a highly compliant polymeric matrix embedding magnetically hard particles, such as neodymium–iron–boron (NdFeB) inclusions. Their defining characteristic lies in the high magnetic coercivity of the embedded particles, which allows the material to retain a significant remanent magnetization once magnetically saturated. The application of an external magnetic field to a premagnetized MAP can then induce complex shape-morphing responses over a wide range of magnetic field intensities, a behavior directly associated with the high coercivity and remanence of the magnetic inclusions. This work addresses two representative problems: dielectric elastomers subjected to multiple voltage levels applied through distinct electrodes, and magneto-active polymers featuring spatially varying premagnetization regions. In both cases, the space of electrically or magnetically induced deformation configurations is exceedingly large. To address this challenge, we propose the construction of neural-network-based surrogate models that parametrize the deformation response of the active materials. These surrogates enable the solution of the inverse problem, namely, the determination of suitable voltage distributions or premagnetization directions required to achieve a prescribed target shape. Representative examples demonstrate that the proposed neural networks accurately reproduce finite-element solutions while providing a substantial reduction in computational cost. In addition, reduced-order modelling techniques based on Proper Orthogonal Decomposition (POD) are employed to identify low-dimensional solution manifolds.