Directional deformation prediction of strut-based lattices via Gauss map embedding

This paper aims to develop an efficient and topology-agnostic framework for predicting direction-dependent mechanical responses of strut-based lattice materials. A Gaussian sphere (GS)-based representation is introduced, in which strut orientations and node positions are mapped onto discretized Gauss maps to jointly encode load-bearing directions, strut weighting, and nodal topology. A dataset of 28 cubic lattice architectures sampled over 380 loading orientations was generated using finite element analysis (FEA), where directional deformation served as the learning target. The originality of the work lies in replacing topology-specific graph or homogenization-based descriptions with a compact orientation-space embedding that explicitly preserves anisotropic geometric features. The proposed Gauss-map model achieved accurate directional deformation prediction with an overall MAE of 0.0220 mm and a 2232 × inference speedup over a tuned Message Passing Neural Networks baseline, while maintaining comparable held-out test performance. Experimental validation using rotated Octet-truss specimens further showed that FEA agrees more closely with measured directional modulus responses than homogenization, with MAEs of 0.56 MPa and 6.26 MPa, respectively. These findings demonstrate that GS-based embeddings provide a physically meaningful and computationally efficient descriptor for learning anisotropic lattice behavior, with practical implications for rapid lattice screening, inverse design, and optimization of directionally tailored architected materials.