GeoLAMP Solves PDEs in Complex Geometries with High Stability

Solving multiphysics partial differential equations (PDEs) in highly intricate, micro-scale geometries, common in energy and chemical engineering, presents a significant computational challenge. Traditional scientific computing methods often struggle with the complexity and tortuosity of such domains. To address this, a new model called GeoLAMP (Geometry-aware Latent Autoregressive generative Model for PDEs) has been developed. GeoLAMP employs a dual-encoder architecture that operates on graph representations, allowing it to simultaneously capture both the global topology and fine-scale geometric features of complex structures. This enables an effective transformation of real-space physical fields into compact latent representations. Within this latent space, a causal self-attention transformer, combined with flow matching, models temporal dynamics, facilitating stable and scalable block-wise autoregressive predictions. A flexible decoder then reconstructs high-resolution physical fields at arbitrary points. The researchers established three new multiphysics benchmark datasets covering reactive flow, heat convection, and elasticity in complex geometries. GeoLAMP consistently demonstrated the most stable autoregression performance on these datasets, maintaining low errors throughout extended simulation horizons, offering new insights into geometry-aware learning for PDEs.