A Physics-Informed Machine Learning Framework for Modeling Biaxial Strain-Induced Band Gap Variation in Zig-Zag Single-Walled Carbon Nanotubes.

Understanding the strain-dependent electronic response of carbon nanotubes is important for nanoelectronic applications in which mechanical deformation serves as a functional tuning mechanism. This study developed a physics-informed machine learning framework for modeling biaxial strain-induced band gap variation in zig-zag single-walled carbon nanotubes (SWCNTs). A traceable density functional theory/Perdew-Burke-Ernzerhof (DFT/PBE) dataset was reconstructed from published band gap curves and comprised 144 records representing 16 zig-zag SWCNT chirality groups, from (8,0) to (23,0), at nine nominal biaxial strain levels between -10% and +10%. The absolute band gap was reformulated as a baseline-relative target (ΔEg) representing the strain-induced variation from the chirality-specific unstrained state; this formulation assumes that the corresponding unstrained band gap is available for each chirality before prediction. Physics-informed descriptors included the chirality-derived diameter, chirality family, nominal strain, squared strain, and family-strain interaction terms. Predefined linear and nonlinear regression models were evaluated using repeated shuffled five-fold cross-validation, while transfer to unseen chirality groups was assessed using leave-one-chirality-out (LOCO) validation. Sensitivity analyses were additionally conducted to evaluate baseline uncertainty and digitization confidence. Within the represented chirality-strain domain, the best nonlinear configuration-support vector regression using diameter, squared strain, and family-strain descriptors-achieved a mean cross-validated coefficient of determination (R2) of 0.880 for ΔEg, compared with 0.786 for absolute Eg. Ridge regression using family-strain descriptors achieved a mean R2 of 0.527, demonstrating that the baseline-relative target also contained an interpretable linear response component. The benefit of target reformulation was most evident in explained variance and fold-level stability, whereas differences in absolute error metrics were comparatively small. The best ΔEg model achieved a mean LOCO R2 of 0.636, although substantial fold-level variation indicated that transfer remained strongly dependent on the held-out chirality group. The findings remained stable under chirality-specific Eg0 perturbations of up to ±0.020 eV and after exclusion of three low-confidence digitized records. Overall, baseline-relative target formulation and chirality-aware descriptor design improved the modeling of strain-induced electronic responses under limited-data conditions. The results should nevertheless be interpreted as a proof of concept within the represented zig-zag SWCNT domain rather than as a universal predictor across the complete CNT design space.