GeoPI-LNODE: Geometry Conditioned Physics Informed Latent Neural ODEs for Long-Horizon Prediction

We propose a Geometry-conditioned Physics-Informed Latent Neural Ordinary Differential Equations (GeoPI-LNODE), a continuous-time surrogate modeling framework for long-term prediction of complex unsteady systems governed by known partial differential equations (PDEs). High-fidelity numerical simulations are essential for engineering analysis and design, but they often incur prohibitive computational costs, motivating the development of learning-based surrogate models to enable efficient prediction. However, accurate long-horizon prediction using surrogate models remains challenging due to accumulated rollout errors, physical inconsistencies, and difficulties in handling complex geometries. GeoPI-LNODE combines parameter- and boundary-conditioned latent dynamics, geometry-conditioned field reconstruction, and physics-informed regularization to model complex spatiotemporal dynamics while preserving physical consistency over long-horizon rollouts. A latent neural ODE evolves a low-dimensional state, while a coordinate-based decoder reconstructs physical fields and enables physics-informed regularization by using residuals from the governing equations to regularize the latent dynamics in physical space. We evaluate GeoPI-LNODE on coupled fluid–scalar transport, nonlinear hyperelastic dynamics, and three-dimensional aneurysm flow—challenging regimes involving tightly coupled processes, strong nonlinearities, and complex three-dimensional geometries, where surrogate models often struggle to maintain accurate and stable long-term predictions. Within each fixed computational domain, GeoPI-LNODE improves long-term prediction accuracy over representative surrogate baselines and approximately halves the flow-rate imbalance in the three-dimensional flow problem relative to the physics-informed variant without geometry conditioning. These results demonstrate the potential of physics-informed latent dynamics for accurate long-horizon surrogates.