Efficient higher-order multi-scale method and its convergence estimate for dynamic nonlinear hygro-thermo-mechanical coupling problems of heterogeneous structures

What the math gives to ML

The paper develops a two-scale asymptotic decomposition in which a coarse homogenized solution is corrected by explicitly parameterized first- and second-order local fluctuation fields. The transferable asset is not the hygro-thermo-mechanical physics itself, but the separation between slowly varying macroscopic derivatives and rapidly varying coefficient-dependent correctors, together with an offline-online computational split. This suggests neural operators that predict a cheap coarse field and reconstruct fine resolution through derivative-conditioned local bases, rather than learning every fine-scale degree of freedom directly. A second useful transfer is to make the corrector basis depend on a low-dimensional state such as temperature or material context, enabling conditional multiscale modules with substantially fewer parameters than a full-resolution network.