Research map / Probabilistic and scientific modeling / Differential equations and PDEs
PINP: Physics-Informed Neural Predictor with latent estimation of fluid flows
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 PINP, a physics-informed neural predictor that estimates latent velocity and pressure fields from observed concentration frames and advances them with a discretized advection-diffusion PDE plus a correction U-Net, trained with data, NS-residual and temporal-monotonicity losses.
Problem
Predicting future fluid/scalar evolution from observed concentration data alone, where latent physical quantities (velocity, pressure) are unobserved and standard neural operators lack physical grounding and generalize poorly for temporal extrapolation and spatial generalization.
Approach
Embed a discretized passive-scalar transport PDE (advection-diffusion, evaluated at an intermediate time t') directly into the predictor, use a 3D U-Net to infer velocity, pressure and Peclet/Reynolds numbers from past frames and spatial embeddings (SDF, boundary mask), and regularize with incompressible NS residuals and a temporal monotonicity constraint.
Key results
- On Flow 2D, PINP reaches MAE 0.0107 and MSE 0.0003 versus the second-best U-NO at MAE 0.0183 and MSE 0.0008.
- On SEVIR, PINP achieves the best CSI-M (0.3800) and high-threshold CSI (e.g., CSI-219 0.0989) but a worse MSE (4.1684e-3) than SimVP (3.8508e-3) and NowcastNet (3.8883e-3).
- On Smoke 3D, PINP reaches MAE 0.1073 and MSE 0.0249, beating the next-best F-FNO (0.1124 / 0.0250).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use PINP instead of U-NO | Flow 2D prediction · Flow 2D | MAE: 0.0183 -> 0.0107 | Helped |
| Use PINP instead of HelmFluid | Smoke 2D prediction · Smoke 2D | MAE: 0.0254 -> 0.0209 | Helped |
| Use PINP instead of F-FNO | Smoke 3D prediction · Smoke 3D | MAE: 0.1124 -> 0.1073 | Helped |
| Use PINP instead of NowcastNet | SEVIR nowcasting · SEVIR | CSI-M: 0.3743 -> 0.3800 | Helped |
| Use PINP instead of SimVP | SEVIR nowcasting · SEVIR | MSE (1e-3): 3.8508 -> 4.1684 | Hurt |
| Add the physical constraint (ablation) | PINP · Flow 2D | MAE: 0.0272 -> 0.0209 | Helped |
| Add the temporal constraint (ablation) | PINP · Flow 2D | MAE: 0.0293 -> 0.0209 | Helped |
| Add the velocity-pressure constraint (ablation) | PINP · Flow 2D | MAE: 0.0262 -> 0.0209 | Helped |
| Add the correction network (ablation) | PINP · Smoke 2D | MAE: 0.0316 -> 0.0209 | Helped |
| Use the original discrete PDE prediction operator instead of a changed operator (ablation) | PINP · Flow 2D | MAE: 0.0197 -> 0.0107 | Helped |
| Use c(t') instead of c(t_k) in the prediction operator (ablation) | PINP · Flow 2D | MAE: Inf -> 0.0107 | Helped |
Surprising findings
- Removing the temporal constraint or the correction network substantially worsens accuracy; replacing c(t') with c(t_k) produces infinite error.
- On SEVIR nowcasting, PINP does not lead in MSE or low-threshold CSI, winning only on CSI-M and high thresholds.
Limitations
- Velocity and pressure are recovered only up to an unknown scaling constant, requiring calibration with a true data point.
- Assumes passive scalar transport with no feedback on the flow; the NS constraints are not strictly satisfied in noisy nowcasting data.
- Mixed or weaker results on SEVIR MSE and low-threshold CSI.
Experimental setup
Datasets: Flow 2D (COMSOL-generated) Smoke 2D (PhiFlow-generated) Smoke 3D (FactFormer-generated) SEVIR
Benchmarks: Flow 2D Smoke 2D Smoke 3D SEVIR
Metrics: MSE MAE CSI correlation
Baselines: U-Net ResNet FNO F-FNO U-FNO U-NO LSM HelmFluid ConvLSTM PredRNN SimVP Earthformer
Builds on: Navier-Stokes equations Fourier neural operator HelmFluid NowcastNet
Closest papers by meaning
- PARCv2: Physics-aware Recurrent Convolutional Neural Networks for Spatiotemporal Dynamics Modeling (ICML 2024 · similarity 0.87)
- Sub-Sequential Physics-Informed Learning with State Space Model (ICML 2025 · similarity 0.87)
- Space and time continuous physics simulation from partial observations (ICLR 2024 · similarity 0.87)
- PINNsFormer: A Transformer-Based Framework For Physics-Informed Neural Networks (ICLR 2024 · similarity 0.87)
- MultiPDENet: PDE-embedded Learning with Multi-time-stepping for Accelerated Flow Simulation (ICML 2025 · similarity 0.86)
- Parameterized Physics-informed Neural Networks for Parameterized PDEs (ICML 2024 · 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.