Research map / Probabilistic and scientific modeling / Differential equations and PDEs
PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solvers
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's title only (no summary yet). Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace one-step MSE with iterative PDE-Refiner training and inference | Modern U-Net · Kuramoto-Sivashinsky 1D | Corr. >0.8 time: 75.4 ± 1.1 -> 97.5 ± 0.5 | Helped |
| Use PDE-Refiner instead of MSE training | U-Net · Kolmogorov 2D Flow | Corr. >0.8 time: 9.663 ± 0.117 -> 10.659 ± 0.092 | Helped |
| Add an additional previous time step to the MSE model input (ablation) | MSE-trained Modern U-Net · Kuramoto-Sivashinsky 1D | Corr. >0.8 time: 75.4 ± 1.1 -> 61.7 ± 1.1 | Hurt |
| Increase the MSE model parameter count fourfold (ablation) | MSE-trained Modern U-Net · Kuramoto-Sivashinsky 1D | Corr. >0.8 time: 75.4 ± 1.1 -> 79.7 ± 0.7 | Helped |
| Average an ensemble of five MSE-trained models (ablation) | MSE-trained Modern U-Net · Kuramoto-Sivashinsky 1D | Corr. >0.8 time: 75.4 ± 1.1 -> 79.7 ± 0.0 | Helped |
| Use the pushforward trick during training (ablation) | MSE-trained Modern U-Net · Kuramoto-Sivashinsky 1D | Corr. >0.8 time: 75.4 ± 1.1 -> 75.4 ± 1.1 | No clear effect |
| Replace MSE with Sobolev norm loss, k=0 (ablation) | Modern U-Net · Kuramoto-Sivashinsky 1D | Corr. >0.8 time: 75.4 ± 1.1 -> 71.4 ± 2.9 | Hurt |
| Replace MSE with Sobolev norm loss, k=1 (ablation) | Modern U-Net · Kuramoto-Sivashinsky 1D | Corr. >0.8 time: 75.4 ± 1.1 -> 66.9 ± 1.8 | Hurt |
| Replace MSE with Sobolev norm loss, k=2 (ablation) | Modern U-Net · Kuramoto-Sivashinsky 1D | Corr. >0.8 time: 75.4 ± 1.1 -> 8.7 ± 0.9 | Hurt |
| Add Markov Neural Operator dissipativity regularization (ablation) | Modern U-Net · Kuramoto-Sivashinsky 1D | Corr. >0.8 time: 75.4 ± 1.1 -> 66.6 ± 1.0 | Hurt |
| Correct MSE predictions for known invariances (ablation) | MSE-trained Modern U-Net · Kuramoto-Sivashinsky 1D | Corr. >0.8 time: 75.4 ± 1.1 -> 74.8 ± 1.1 | No clear effect |
| Train a second model to predict the MSE model's errors (ablation) | MSE-trained Modern U-Net · Kuramoto-Sivashinsky 1D | Corr. >0.8 time: 75.4 ± 1.1 -> 75.7 ± 0.5 | No clear effect |
Closest papers by meaning
- MultiPDENet: PDE-embedded Learning with Multi-time-stepping for Accelerated Flow Simulation (ICML 2025 · similarity 0.91)
- CALM-PDE: Continuous and Adaptive Convolutions for Latent Space Modeling of Time-dependent PDEs (NeurIPS 2025 · similarity 0.89)
- Text2PDE: Latent Diffusion Models for Accessible Physics Simulation (ICLR 2025 · similarity 0.89)
- Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators (NeurIPS 2026 · similarity 0.89)
- P$^2$C$^2$Net: PDE-Preserved Coarse Correction Network for efficient prediction of spatiotemporal dynamics (NeurIPS 2024 · similarity 0.89)
- SineNet: Learning Temporal Dynamics in Time-Dependent Partial Differential Equations (ICLR 2024 · similarity 0.89)
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.