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.