AGODE: Adaptive Graph ODE for Grid-free Fluid Modeling and Domain Adaptation

摘要

This paper studies grid-free point process modeling under varying fluid parameters. Existing methods rely on grid-based approaches or fixed parameters, making it challenging to handle complex nonlinear dynamics and out-of-distribution (OOD) scenarios. To address this, we propose Adaptive Perturbation Graph ODE (AGODE), a novel framework that integrates three key innovations: (1) an adaptive conditioning mechanism for physical parameter adaptation(2) a continuous graph neural ODE for spatiotemporal evolution modeling, and (3) a perturbation module with mutual information maximization for uncertainty quantification. AGODE employs graph neural networks to encode unstructured point cloud data into latent dynamics governed by neural ODEs, where physical parameters are injected through context-aware conditioning vectors. The perturbation module generates diverse trajectory samples by introducing stochastic noise during ODE integration, while contrastive learning aligns predictions with physical contexts to filter implausible outcomes. Extensive experiments across five fluid dynamics benchmarks (Prometheus, Navier-Stokes, Spherical-SWE, 3D Reaction-Diffusion, ERA5) demonstrate AGODE's state-of-the-art performance. Specifically, AGODE achieves MSE of 0.0302/0.0312 (in-domain/OOD) on Prometheus, outperforming PURE by 6.5%/5.0%, and reduces Navier-Stokes errors by 28.1% compared to physics-informed NMO. Notably, AGODE maintains superior OOD generalization with only 2.9% average error increase versus 7.8% for baselines, while its uncertainty quantification improves prediction reliability by 41% (95% confidence interval coverage). These results validate AGODE's capabilities in continuous spatiotemporal modeling, multi-parameter adaptation, and robust uncertainty estimation for complex fluid systems.