Abstract: For lightweight cellular structures with classical rod/beam-based configurations as the fundamental topology, cumulative errors in the rod/beam system model increase drastically when the unit cell geometry is complex and the static indeterminacy among components is high, due to the superposition of multiple error sources. This poses significant challenges to theoretical characterization methods based on ideal rod/beam system assumptions. The problem of predicting the mechanical performance of complex two-dimensional unit cells, after preprocessing via dimensional analysis, aligns closely with the architecture of multilayer perceptron (MLP) networks. This study selects a two-dimensional pinwheel-shaped unit cell as the research subject and develops an MLP network based on its geometric features. First, the optimizing effect of heuristic search algorithms on size-constrained networks is examined, analyzing the performance improvement guided by hidden layer depth and the degradation caused by excessive depth. Subsequently, the influence of gradient distribution among neurons in networks with equal parameter counts but multiple hidden layers is discussed, exploring the adaptive performance of "deep-narrow" versus "shallow-wide" networks. Finally, based on the mechanical performance predictions from the MLP network, theoretical corrections are proposed for potential errors that may be overlooked during the characterization by ideal rod/beam system models. Through dimensional analysis and gradient design in hidden layers, this research reduces structural parameter dimensionality, simplifies multi-level logical relationships, and optimizes network parameter allocation, offering a compact network design approach based on the MLP architecture for characterizing the mechanical performance of complex 2D unit cells that are difficult to model explicitly.