<p>Porous functionally graded graphene origami enabled auxetic metamaterial (PFG-GOEAM) microbeam is the basic component of micro-electro-mechanical system (MEMS). However, classical elastic theory without strain gradient fails to describe the size-dependent mechanical response of PFG-GOEAM microbeam. In this paper, the general strain gradient theory (GSGT) and case-based reasoning (CBR) are combined to capture size effects. The variational principle is applied to derive governing equation, initial condition and boundary condition of the beam. The governing equation is then solved to construct the case base with strain gradient for case-based reasoning (CBR) modified by support vector regression (SVR). Subsequently, we apply the size-dependent CBR to conduct the forward and inverse design. For forward design, it is found that the bending deflection of size-dependent CBR decreases while natural frequency increases with the decrease of dimensionless thickness. Moreover, the effects of GOri content, GOri folding degree, GOri distribution pattern, pore distribution pattern, and porosity coefficient on the bending deflection and natural frequency are further studied. For inverse design, based on the customized mechanical behavior, the dimensionless length, dimensionless thickness, porosity coefficient, GOri content, GOri folding degree, and GOri distribution pattern of the beam are determined. Therefore, the combination of general strain gradient theory (GSGT) and case-based reasoning (CBR) can capture the size-dependent mechanical reponse of PFG-GOEAM microbeam appropriately.</p>