This study proposes an inverse method for synthesizing shape-morphing structures in the lateral direction by integrating two-dimensional hexagonal unit cell with curved beams. Analytical expressions are derived to formulate the effective Young’s modulus and Poisson’s ratio for the base unit-cell as a function of its geometric parameters. The effective lateral Poisson’s ratio can be controlled by manipulating a set of geometric parameters, resulting in a dataset of over 6000 data points with Poisson’s ratio values ranging from −1.2 to 10.4. Furthermore, we utilize the established dataset to train an inverse design framework that utilizes a physics-guided neural network algorithm, and the framework can predict design parameters for a targeted shape-morphing structure. The proposed approach enables the generation of structures with tailored Poisson’s ratio ranging from −1.2 to 3.4 while ensuring flexibility and reduced stress concentration within the predicted structure. The generated shape-morphing structures’ performance is validated through numerical simulation and physical tensile testing. The finite element analysis (FEA) simulation results confirm agreement with the designed values for the shape-morphing structure, and the tensile testing results reveal the same trend in shape-morphing behavior. The proposed design automation framework demonstrates the feasibility of creating intricate and practical shape-morphing structures with high accuracy and computational efficiency.