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Generating Full-field Evolution of Physical Dynamics from Irregular Sparse Observations
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Proposes SDIFT, which encodes sparse off-grid physical observations into a functional Tucker latent space and runs a Gaussian-process-based sequential diffusion model with message-passing posterior sampling to reconstruct full-field dynamics.
Problem
Reconstructing continuous multidimensional physical dynamics from sparse, irregular, off-grid observations, where observations exist only at a few time steps and the full spatiotemporal field must be generated.
Approach
Combines a functional Tucker model (with a universal approximation proof) as latent representation, a GP-noise sequential diffusion over Tucker core sequences, and message-passing posterior sampling that propagates guidance from observed time steps to unobserved ones via GP regression.
Key results
- On Supernova Explosion under observation setting 1 with 1% observations, SDIFT w/ MPDPS achieves VRMSE 0.283 vs 0.561 for CoNFiLD.
- Under observation setting 2 (half time steps observed), SDIFT w/ MPDPS reaches 0.433 VRMSE on Supernova (1%) where CoNFiLD gets 0.757.
- Sampling time drops from 31.3s (CoNFiLD) to 2.23s (SDIFT w/ MPDPS) on Supernova at 1% observation ratio on an RTX 4090.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use MPDPS instead of DPS (ablation) | SDIFT · Supernova Explosion, observation setting 1 | VRMSE: 0.339 ± 0.116 -> 0.283 ± 0.026 (ρ=1%); 0.291 ± 0.033 -> 0.272 ± 0.025 (ρ=3%) | Helped |
| use MPDPS instead of DPS (ablation) | SDIFT · Ocean Sound Speed, observation setting 1 | VRMSE: 0.194 ± 0.073 -> 0.146 ± 0.046 (ρ=1%); 0.160 ± 0.035 -> 0.108 ± 0.043 (ρ=3%) | Helped |
| use MPDPS instead of DPS (ablation) | SDIFT · Active Matter, observation setting 1 | VRMSE: 0.298 ± 0.065 -> 0.215 ± 0.068 (ρ=1%); 0.174 ± 0.043 -> 0.156 ± 0.046 (ρ=3%) | Helped |
| use MPDPS instead of DPS (ablation) | SDIFT · Supernova Explosion, observation setting 2 | VRMSE: 0.659 ± 0.057 -> 0.433 ± 0.163 (ρ=1%); 0.6450 ± 0.054 -> 0.335 ± 0.122 (ρ=3%) | Helped |
| use MPDPS instead of DPS (ablation) | SDIFT · Ocean Sound Speed, observation setting 2 | VRMSE: 0.412 ± 0.156 -> 0.181 ± 0.084 (ρ=1%); 0.407 ± 0.136 -> 0.165 ± 0.041 (ρ=3%) | Helped |
| use MPDPS instead of DPS (ablation) | SDIFT · Active Matter, observation setting 2 | VRMSE: 0.674 ± 0.153 -> 0.296 ± 0.096 (ρ=1%); 0.637 ± 0.113 -> 0.256 ± 0.087 (ρ=3%) | Helped |
Surprising findings
- MPDPS outperforms standard DPS even when all target time steps are observed, attributed to smoothing across time steps.
Limitations
- No explicit incorporation of physical laws into modeling.
- Baselines' hyperparameters tuned on limited ranges; results reported as averages over 10 runs with high variance in some settings.
Experimental setup
Datasets: Supernova Explosion (The Well) Ocean Sound Speed (HYCOM) Active Matter (The Well)
Benchmarks: Supernova Explosion Ocean Sound Speed Active Matter
Metrics: VRMSE sampling time
Baselines: Senseiver CoNFiLD LRTFR DEMOTE NONFAT DPS
Builds on: diffusion posterior sampling EDM functional Tucker decomposition functional diffusion model CoNFiLD
Closest papers by meaning
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