Explicit Reduced-Order Modeling and Data-Efficient Physics-Informed Inverse Design of Laminated Non-Pneumatic Tires

Efficient forward and inverse design of laminated non-pneumatic tires requires repeated evaluation of their load-bearing and tire–ground contact responses. The high-fidelity laminated beam–grounding analysis (LB-GA) formulation captures the coupled band and spoke mechanics but requires iterative solution of 18 differential equations with unknown regional boundaries. This study derives explicit reduced-order relations for vertical stiffness and average contact pressure by combining laminated curved-beam mechanics with double-sided compression-ring theory. Joint fitting to 500 high-fidelity LB-GA solutions yields the empirical screening criterion $R_{\mathrm{opt}}=N^{0.68}{n}^{0.83}>40$. In an additional set of 5000 independently generated cases spanning the investigated design and material domain, 97.68% of the cases satisfying this criterion have a maximum response error no greater than 10%. The explicit relations are subsequently used as a domain-masked mechanics constraint in a multi-fidelity physics-informed neural network trained with independent high-fidelity labels. With $5\times {10}^5$ labels, the model gives stiffness and pressure NRMSEs of 4.47% and 4.68%, whereas a data-driven model using $5\times {10}^6$ labels gives 5.00% and 8.37%. Model-preparation time decreases from 220.1 to 32.5 h. Multiobjective inverse design, a newly manufactured-tire experiment, and six reconstructed finite-element designs produce validation errors below 10%. The framework therefore enables accurate tire design with substantially fewer high-fidelity numerical labels.