Research map / Probabilistic and scientific modeling / Dynamical systems
FlowDAS: A Stochastic Interpolant-based Framework for Data Assimilation
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Proposes FlowDAS, a data assimilation framework that learns short-step state transitions with stochastic interpolants and injects observations at each interpolation step via a Monte Carlo conditional score estimate.
Problem
Data assimilation for stochastic PDE-governed and chaotic dynamical systems when true dynamics are partly or wholly unknown; existing model-driven filters need known dynamics and deterministic neural operators or all-at-once score-based diffusion models lack step-wise stochastic transitions and meas
Approach
Treat a learned stochastic interpolant between adjacent states as the forward model, and add an observation-conditioned drift term estimated by self-normalized Monte Carlo over endpoint samples, so observations are assimilated at every interpolation step at inference without retraining.
Key results
- On Navier-Stokes 1.5625% sparse observation, FlowDAS RMSE 0.123 vs SDA 0.258, FNO-DA 0.183, Transolver-DA 0.180.
- On Lorenz-63 over 15 steps, FlowDAS RMSE 0.202 vs BPF 0.270 and SDA 1.114; BPF retains a slightly higher log-prior (17.88 vs 17.29).
- On SEVIR VIL weather forecasting, FlowDAS RMSE 0.053 and CSI(tau40) 0.614 vs Transolver-DA 0.499 and SDA 0.387.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use observation-conditioned FlowDAS instead of SDA | Lorenz-63 · Lorenz-63 | RMSE: 1.114 -> 0.202 | Helped |
| Use FlowDAS instead of BPF | Lorenz-63 · Lorenz-63 | log-prior: 17.88 -> 17.29 | Hurt |
| Use FlowDAS instead of SDA | Navier-Stokes super-resolution and sparse observation · Navier-Stokes | RMSE: 0.073 -> 0.038; 0.133 -> 0.067; 0.251 -> 0.071; 0.258 -> 0.123 | Helped |
| Use FlowDAS instead of Transolver-DA | SEVIR VIL sparse-observation forecasting · SEVIR VIL sparse observation 10% | RMSE: 0.062±0.001 -> 0.053±0.004 | Helped |
| Replace unbiased Monte Carlo estimation with Jensen-based biased estimation (ablation) | FlowDAS · Lorenz-63 | RMSE: 0.202 -> 0.363 | Hurt |
| Increase Monte Carlo sampling count from J=3 to J=50 (ablation) | FlowDAS · Lorenz-63 | RMSE: 0.167 -> 0.138 | Helped |
| Use 2nd-order stochastic Runge-Kutta instead of 1st-order Milstein posterior estimation (ablation) | FlowDAS · Navier-Stokes super-resolution 32^2 → 128^2 | RMSE: 0.048 -> 0.038 | Helped |
| Use 2nd-order stochastic Runge-Kutta instead of 1st-order Milstein posterior estimation (ablation) | FlowDAS · Navier-Stokes super-resolution 16^2 → 128^2 | RMSE: 0.101 -> 0.067 | Helped |
| Remove observation correction during forecasting (ablation) | FlowDAS · Navier-Stokes super-resolution 32^2 → 128^2 | RMSE: 0.038 -> 0.206 | Hurt |
| Remove observation correction during forecasting (ablation) | FlowDAS · Navier-Stokes super-resolution 16^2 → 128^2 | RMSE: 0.067 -> 0.206 | Hurt |
| Use FlowDAS instead of Transolver-DA | SEVIR VIL sparse-observation forecasting · SEVIR VIL sparse observation 10% | CSI(τ20): 0.663±0.001 -> 0.746±0.022 | Helped |
| Use FlowDAS instead of Transolver-DA | SEVIR VIL sparse-observation forecasting · SEVIR VIL sparse observation 10% | CSI(τ40): 0.499±0.002 -> 0.614±0.044 | Helped |
Surprising findings
- Biased Jensen-based gradient estimate of the observation likelihood degraded performance relative to the unbiased Monte Carlo estimate.
- Particle filter BPF, which uses the true transition equations, achieves a higher log-prior than FlowDAS on Lorenz-63.
Limitations
- BPF not evaluated on high-dimensional Navier-Stokes or weather tasks due to exponential particle requirements, so comparison is limited.
- Inference requires J Monte Carlo samples per interpolation step and extra gradient computations, adding cost.
- Weather experiment uses a single SEVIR product with 10% random sparse observations.
Experimental setup
Datasets: Lorenz-63 simulated trajectories Navier-Stokes simulated vorticity fields SEVIR VIL
Benchmarks: Lorenz-63 DA Navier-Stokes super-resolution and inpainting SEVIR VIL weather forecasting
Metrics: RMSE W1 distance log-likelihood CSI kinetic energy spectrum
Baselines: SDA BPF FNO-DA Transolver-DA
Builds on: stochastic interpolants score-based data assimilation diffusion posterior sampling Fourier neural operator
Closest papers by meaning
- Learning semilinear neural operators: A unified recursive framework for prediction and data assimilation. (ICLR 2024 · similarity 0.88)
- DiffDA: a Diffusion model for weather-scale Data Assimilation (ICML 2024 · similarity 0.88)
- Probabilistic Forecasting with Stochastic Interpolants and Föllmer Processes (ICML 2024 · similarity 0.87)
- On conditional diffusion models for PDE simulations (NeurIPS 2024 · similarity 0.87)
- Deep Bayesian Filter for Bayes-Faithful Data Assimilation (ICML 2025 · similarity 0.87)
- Mesh-Free Convolution: Learned Spectral Attenuation and Transport (NeurIPS 2026 · similarity 0.86)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.