This study addresses the persistent multifidelity gap between numerical simulations and experimental observations in the design of elastic metamaterials, specifically focusing on wave transmission spectra of the triply periodic minimal surface lattices. We propose the Dual Elastic Alignment Network (DEAN), a learning framework that uses elastic functional data analysis (EFDA) to separate transmission responses into spectral amplitude and frequency-warping components. DEAN employs a shared geometric encoder with dual probabilistic heads to separately model resonance morphology and frequency shifts across topologies and between fidelity levels. To mitigate experimental data sparsity, we introduce an augmented transfer learning strategy in which the model is first trained on a large set of low-fidelity (LF) simulations and subsequently fine-tuned using a combined dataset of high-fidelity (HF) experimental data and EFDA-generated augmented data. The study uses 72 experimentally evaluated designs together with 510 simulated designs, resulting in a highly sparse experimental regime relative to the broader simulation design space. The baseline discrepancy between the LF and HF datasets corresponds to a normalized mean absolute error (NMAE) of 0.142 and a coefficient of determination ($R^2$) of 0.355. Under the augmented transfer learning strategy, DEAN achieves the strongest aggregate global accuracy among the evaluated models, with the level-set variant reaching a test-set NMAE of 0.055 and an $R^2$ of 0.858, while the multihot variant remains close with an NMAE of 0.059 and $R^2$ of 0.843. Fisher-Rao distance analysis and joint-density evaluation of peak deviations demonstrate improved preservation of resonance morphology and peak characteristics when using the DEAN framework. These findings indicate that explicitly modeling amplitude and frequency-warping variability enhances predictive reliability under sparse experimental data conditions. The proposed framework provides a structured, experimentally grounded surrogate for data-efficient modeling and candidate screening of elastic metamaterials under uncertain constitutive and manufacturing conditions.

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• Elasticity
• Inverse problems
• Stress propagation
• Artificial neural networks
• Lattices
• Mechanical metamaterials
• Machine learning