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Nanopore sequencing enables direct, single-molecule interrogation of biopolymers and shows promise for analyzing not only DNA and RNA but also chemically modified bases, proteins, and other polymers. Expanded DNA alphabets, such as those found in xenonucleic acids (XNAs), open new possibilities for diagnostics, therapeutics, data storage, and engineered biology. However, robust sequencing strategies for these modified molecules remain lacking. While nanopore-based tools exist for some noncanonical bases, they often require extensive experimental calibration by measuring each base across many sequence contexts, which limits scalability and increases cost. In this work, we investigate computational methods for predicting the ionic current signals produced during nanopore sequencing of DNA containing noncanonical XNA bases, aiming to reduce the need for experimental calibration. We compare a sequence-based predictive model with two structure-aware approaches: one using graph-based molecular representations and another adapting a generative language model to molecular SMILES. Our findings show that while sequence context captures much of the signal variability, incorporating structural and chemical information improves predictive accuracy in specific cases. These results highlight the value of structural data representations and model design in scaling XNA sequencing, and suggest this framework could extend to modeling ionic currents from other complex biomolecules, such as proteins.