Geometry-aware Latent Autoregressive Generative Model for PDEs in Complex Domains

תקציר מקורי באנגליתarXiv:2609.00297v2 Announce Type: replace-cross Abstract: Solving multiphysics partial differential equations (PDEs) remains a major challenge in scientific computing, especially for highly complex $\mu$m-scale tortuous geometries critical to energy and chemical engineering. We address this challenge by proposing a Geometry-aware Latent Autoregressive generative Model for PDEs (GeoLAMP), which solves physics within highly irregular and tortuous structures by decoupling flow and transport physics. GeoLAMP introduces a dual-encoder architecture on graph representations to jointly capture global topology and fine-scale geometric features, enabling an effective transition from real-space fields to compact latent representations. In the latent space, we propose a causal self-attention transform