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

We establish three multiphysics benchmark datasets in complex geometries, covering reactive flow, heat convection, and elasticity. It comes from a paper posted to arXiv on 1 October 2026. 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 transformer with flow matching to model temporal dynamics, allowing stable and scalable block-wise autoregressive prediction. In addition, we propose a grid-graph data fusion scheme that projects low-resolution grid-based approximate priors onto graph representations, improving prediction of flow in tortuous structures. GeoLAMP consistently achieves the most stable autoregression performance on these datasets. Our results provide a systematic study of geometry-aware learning for PDEs in $\mu$m-scale complex geometries and offer new insights into block-wise time marching of latent autoregressive PDE modeling via a flow matching framework.

Why it counts

We establish three multiphysics benchmark datasets in complex geometries, covering reactive flow, heat convection, and elasticity.

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