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Space and time continuous physics simulation from partial observations
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Proposes a double-dynamical-system model (latent auto-regressive GNN plus a transformer/GRU continuous state observer) that predicts fluid dynamics at arbitrary space and time locations from sparse observations.
Problem
Simulating physical systems (fluid dynamics) continuously in space and time from sparse, regularly sampled observations, while generalizing to new initial conditions without retraining and without knowing the PDE.
Approach
Two interlinked dynamical systems: a discrete latent auto-regressive GNN (System 1) produces anchor states from the sparse initial condition, and a continuous-time state observer (System 2) implemented with Fourier-encoded query cross-attention over anchor states plus a GRU decodes the solution at arbitrary (x, t). Theory argues latent-space forecasting gives tighter error bounds than classic enco
Key results
- On Navier (High sparsity, in-X), the method reaches MSE 0.1989 (x1e-3) vs 1.557 for DINo and 1.913 for interpolated MGN over 20 frames.
- On Shallow Water Ext-X with Low sparsity, MSE 2.800 vs 21.55 for DINo and 8.187 for interpolated MGN.
- Time continuity on Navier with 1/4 temporal resolution: 0.4062 In-T vs 12.77 for interpolated MGN, 243.9 for MAgNet, and 46.02 for DINo (High-sparsity setting).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the proposed double-dynamical-system model instead of the strongest reported baseline | continuous space prediction · Navier, Shallow Water, and Eagle; Ext-X | MSE (× 10^-3): 1.600 -> 0.2029; 4.784 -> 0.2463; 14.80 -> 0.5601; 1.744 -> 0.4493; 13.40 -> 1.051; 8.187 -> 2.800; 173.4 -> 90.88; 241. | Helped |
| Use the proposed double-dynamical-system model instead of the strongest reported baseline | continuous time prediction · Navier, Shallow Water, and Eagle; Ext-T at 1/2 resolution | MSE (× 10^-3): 5.922 -> 0.2138; 1.287 -> 0.4326; 209.8 -> 119.9 | Helped |
| Use the proposed double-dynamical-system model instead of the strongest reported baseline | continuous time prediction · Navier, Shallow Water, and Eagle; Ext-T at 1/4 resolution | MSE (× 10^-3): 36.43 -> 11.36; 1.355 -> 0.4802; 263.8 -> 306.9 | Mixed |
Surprising findings
- Interpolated MeshGraphNet and the Time Oracle show close in/out-domain errors, and DINo and MAgNet fail on the most down-sampled Navier settings.
- The Eagle benchmark is hard mainly due to spatial interpolation error, and the method is not uniformly best there (e.g., 278.6 vs 225.8 for MAgNet at Low time 1/4 in-T).
Limitations
- Relies on regular time sampling and observability assumptions
- Does not incorporate physics priors
- Baseline MAgNet needs query chunking to perform well, increasing runtime
Experimental setup
Datasets: Navier Shallow Water Eagle
Benchmarks: Navier Shallow Water Eagle
Metrics: MSE
Baselines: Interpolated MeshGraphNet MAgNet DINo Time Oracle Spatial Oracle
Builds on: MeshGraphNet MAgNet DINo Neural ODE
Closest papers by meaning
- Breaking the Discretization Barrier of Continuous Physics Simulation Learning (NeurIPS 2025 · similarity 0.91)
- Symmetric Basis Convolutions for Learning Lagrangian Fluid Mechanics (ICLR 2024 · similarity 0.88)
- ODEWorld: A Continuous Predictive Architecture via Physical-Time Flow (NeurIPS 2026 · similarity 0.87)
- PINP: Physics-Informed Neural Predictor with latent estimation of fluid flows (ICLR 2025 · similarity 0.87)
- CALM-PDE: Continuous and Adaptive Convolutions for Latent Space Modeling of Time-dependent PDEs (NeurIPS 2025 · similarity 0.87)
- Universal Physics Transformers: A Framework For Efficiently Scaling Neural Operators (NeurIPS 2024 · similarity 0.87)
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