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Prometheus: Out-of-distribution Fluid Dynamics Modeling with Disentangled Graph ODE
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Introduces the Prometheus FDS fire-simulation dataset and a 13-baseline OOD benchmark, plus DGODE, a disentangled graph ODE that separates node and environment representations via VQ-based mutual information minimization.
Problem
Out-of-distribution generalization for fluid dynamics forecasting when system parameters (HRR, ventilation, etc.) shift across environments, with few large-scale OOD fluid datasets available.
Approach
Learns invariant node representations via temporal GNN plus frequency network, discretizes environment features with vector quantization, and minimizes an adversarially estimated mutual-information upper bound between them; these feed an environment-aware graph ODE where a virtual environment state interacts with all nodes, with environment-feature perturbation as a stability regularizer.
Key results
- DGODE achieves MSE 0.0344 on Prometheus-T without OOD vs. 0.0414 for the runner-up LSM (about 17% relative improvement).
- On Prometheus-P with OOD, DGODE reaches MSE 0.0413 on WeatherBench-T-style comparisons and 0.1087 on WeatherBench-W; reported improvements range 15.7% to 47.6% over second-best models.
- Removing the mutual information minimization loss increases Prometheus-T MSE from 0.0344 to 0.0367 (w/o OOD), about 22% degradation in the OOD setting per the paper.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use DGODE instead of the strongest baseline, LSM | Prometheus-T · Prometheus-T w/ OOD | MSE: 0.0456 -> 0.0359 | Helped |
| use DGODE instead of the strongest baseline, FNO | Prometheus-P · Prometheus-P w/ OOD | MSE: 0.0522 -> 0.0413 | Helped |
| use DGODE instead of the strongest baseline, Earth | WeatherBench-T · WeatherBench-T w/ OOD | MSE: 0.0952 -> 0.0883 | Helped |
| use DGODE instead of the strongest baseline, SGODE | WeatherBench-W · WeatherBench-W w/ OOD | MSE: 0.1301 -> 0.1087 | Helped |
| use DGODE instead of the strongest baseline, FNO | Navier–Stokes · Navier–Stokes w/ OOD | MSE: 0.1712 -> 0.0925 | Helped |
| add codebook loss Lcod (ablation) | DGODE · Prometheus-T w/ OOD | MSE: 0.0367 -> 0.0359 | Helped |
| add codebook loss Lcod (ablation) | DGODE · WeatherBench-T w/ OOD | MSE: 0.0901 -> 0.0883 | Helped |
| add stability loss Lsta (ablation) | DGODE · Prometheus-T w/ OOD | MSE: 0.0418 -> 0.0359 | Helped |
| add stability loss Lsta (ablation) | DGODE · WeatherBench-T w/ OOD | MSE: 0.0957 -> 0.0883 | Helped |
| add mutual-information loss Lmi (ablation) | DGODE · Prometheus-T w/ OOD | MSE: 0.0421 -> 0.0359 | Helped |
| add mutual-information loss Lmi (ablation) | DGODE · WeatherBench-T w/ OOD | MSE: 0.0973 -> 0.0883 | Helped |
Surprising findings
- Operator-learning and visual backbones such as FNO and Earthfarseer are competitive with several graph-based methods, while many GNN baselines degrade substantially under OOD shift.
Limitations
- Environment labels are unavailable, so the method relies on unsupervised discretization of environment features via vector quantization.
- Evaluation is limited to simulated fire, weather, and Navier-Stokes data; extension to rigid or molecular dynamics is left to future work.
Experimental setup
Datasets: Prometheus-T Prometheus-P WeatherBench-T WeatherBench-W Navier-Stokes
Benchmarks: Prometheus-T Prometheus-P WeatherBench-T WeatherBench-W Navier-Stokes
Metrics: MSE SSIM
Baselines: U-Net Swin Transformer Earthfarseer CLCRN MGNT EAGLE DGCRN MPNODE CG-ODE SGODE FNO F-FNO
Builds on: CG-ODE Fourier neural operator Geo-FNO Graph neural network message passing MINE mutual information estimation
Closest papers by meaning
- Learning Distributions of Complex Fluid Simulations with Diffusion Graph Networks (ICLR 2025 · similarity 0.88)
- PURE: Prompt Evolution with Graph ODE for Out-of-distribution Fluid Dynamics Modeling (NeurIPS 2024 · similarity 0.88)
- PhyMPGN: Physics-encoded Message Passing Graph Network for spatiotemporal PDE systems (ICLR 2025 · similarity 0.87)
- SEGNO: Generalizing Equivariant Graph Neural Networks with Physical Inductive Biases (ICLR 2024 · similarity 0.87)
- PIORF: Physics-Informed Ollivier-Ricci Flow for Long–Range Interactions in Mesh Graph Neural Networks (ICLR 2025 · similarity 0.86)
- Physics-Informed DeepONets for drift-diffusion on metric graphs: simulation and parameter identification (ICML 2025 · similarity 0.86)
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