Identifying Topological Invariants of Non-Hermitian Systems via Domain-Adaptive Multimodal Model for Mathematics
Identifying topological invariants are endowed with profound physical connotations in the fields of condensed matter physics. However, they are often limited by the failure of standard theorems and high computational costs. Traditional machine learning methods typically treat this problem as a black-box regression, which fails to learn the underlying mathematical structures of lattices. To this end, we propose a straightforward yet powerful multimodal model that fundamentally improves topological invariants discovery through two key methodological innovations. First, instead of feeding raw data into a standard network, our model introduces a dual-track alignment mechanism. This mechanism treats eigenvalues as context sequences and eigenvectors as matrix structures, enabling the model to naturally capture the interrelated algebraic and geometric properties of topological states. Second, to resolve the common problem where deep learning models make numerical mistakes in exact mathematical calculations, we use a tool-integrated reasoning paradigm. Within this paradigm, the neural network acts as a logical controller to calculate discrete topological indices. This design eliminates the uncertainty of deep learning, ensuring zero-error calculations from continuous physical data. We demonstrate that our model can accurately reconstruct complex three-dimensional generalized Brillouin zones and achieve 97% accuracy in calculating non-Bloch Chern numbers in long-range transition systems. By combining the flexible logic of multimodal artificial intelligence with the rigorous precision of symbolic computation, this work provides a reliable and highly versatile tool for exploring exotic topological phases.