A multiscale cross attention framework for predicting the electromagnetic coupling characteristics of low dimensional In-Pb heterostructures fabricated by hot pressing

Low dimensional In-Pb heterostructures fabricated by hot pressing offer distinctive potential in superconducting quantum devices, spintronics, and flexible electromagnetic functional materials. Their electromagnetic coupling response is governed by atomic layer spin-orbit coupling, the In-Pb interfacial proximity effect, mesoscale texture, and macroscopic processing conditions acting together, and a predictive framework combining physical consistency with inverse process design has been lacking. This study proposes the Multiscale Cross Attention Electromagnetic Coupling Network, MSCA-EMNet. A hierarchical encoder embeds the four scales into independent, nonoverlapping channels, and a bidirectional cross scale attention module, BS-CrossAttn, places the Query at scale $k$ and the Key and Value at scale $k\pm 1$ , running upward aggregation and downward constraint feedback in parallel. A FiLM mechanism maps hot pressing parameters and the applied magnetic field to channel level affine parameters supporting inverse determination of feasible windows, and a scale availability mask lets records of unequal scale coverage train together through a learnable absent process embedding. Onsager reciprocity and magnetoelectric reciprocity between the direct and converse responses keep the nine component tensor physically consistent, the tensor being defined at a specified magnetic field and including three components of the interfacial magnetoelectric susceptibility. On 1,200 samples from DFT calculations and hot pressing experiments, MSCA-EMNet reaches an overall normalized mean absolute error of 0.041 and a coefficient of determination of 0.948, improvements of 43% and 7.2% over the strongest baseline. The extrapolation degradation rate is 48.8%, the proportion of samples violating the Onsager relation falls from the baseline range of 12%-41% to 1.7%, and cross system transfer reaches 0.86 to 0.89. An inverse design case maps a target tensor to a window of 168°C-174 °C, 62-70 MPa, 25-35 min and 8-12 μm, and six confirmatory experiments reproduce the target within 7.6% on every component.