Mathematical modeling plays a pivotal role in the study of continuum mechanics and material design, offering profound insights into material behaviors and microstructures, which in turn, support and guide material optimization and design. Typically, this modeling process involves formulating partial differential equations (PDEs) based on fundamental physical principles such as mass and energy conservation as well as force equilibrium. These PDEs, for given initial conditions and boundary values, are subsequently solved using numerical methods, with finite element and spectral methods being popular choices. Unfortunately, these traditional numerical techniques are computational very costly, a challenge that becomes particularly pronounced when dealing with design studies that require a multitude of simulations under varying configurations. To address this computational burden and streamline the design cycle, there is a pressing need to develop surrogate models that can replace the traditional simulations, often reliant on the methods mentioned above, like finite elements, spectral methods, or finite volume techniques. These surrogate models are particularly valuable during the design phase, offering a more computationally tractable solution.