Research map / Probabilistic and scientific modeling / Differential equations and PDEs
Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Prediction
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 |
|---|---|---|---|
| Add a differentiable coarse CFD simulator to the GCN for shock-heavy out-of-distribution prediction | GCN · Generalization | RMSE: $9.5 \cdot 10^{-2}$ -> $\mathbf{5.4 \cdot 10^{-2}}$ | Helped |
| Add a differentiable coarse CFD simulator to the GCN | GCN · Interpolation | RMSE: $\mathbf{1.4 \cdot 10^{-2}}$ -> $1.8 \cdot 10^{-2}$ | Hurt |
| Add GCN processing to the coarse simulation and upsampling (ablation) | Upsampled Coarse Mesh · Interpolation | RMSE: $4.0 \cdot 10^{-2}$ -> $1.8 \cdot 10^{-2}$ | Helped |
| Add GCN processing to the coarse simulation and upsampling (ablation) | Upsampled Coarse Mesh · Generalization | RMSE: $7.0 \cdot 10^{-2}$ -> $\mathbf{5.4 \cdot 10^{-2}}$ | Helped |
| Optimize the coarse mesh through gradients from the CFD simulation (ablation) | Frozen Mesh · Generalization | RMSE: $6.1 \cdot 10^{-2}$ -> $\mathbf{5.4 \cdot 10^{-2}}$ | Helped |
| Optimize the coarse mesh through gradients from the CFD simulation (ablation) | Frozen Mesh · Interpolation | RMSE: $1.8 \cdot 10^{-2}$ -> $1.8 \cdot 10^{-2}$ | No clear effect |
| Use CFD-GCN instead of a pure GCN | GCN · Generalization | Batch Prediction Time: 0.1 -> 2.0 | Hurt |
| Use CFD-GCN instead of a full fine-mesh simulation | Ground Truth Simulation · Fine-mesh simulation | Batch Prediction Time: 137 -> 2.0 | Helped |
| Project mesh updates to prevent element degeneration (ablation) | Coarse mesh optimization · Mesh optimization | Training loss stability | Helped |
Closest papers by meaning
- Graph Neural PDE Solvers with Conservation and Similarity-Equivariance (ICML 2024 · similarity 0.88)
- MultiPDENet: PDE-embedded Learning with Multi-time-stepping for Accelerated Flow Simulation (ICML 2025 · similarity 0.88)
- Learning Distributions of Complex Fluid Simulations with Diffusion Graph Networks (ICLR 2025 · similarity 0.87)
- MeshMask: Physics-Based Simulations with Masked Graph Neural Networks (ICLR 2025 · similarity 0.87)
- Finite Volume Features, Global Geometry Representations, and Residual Training for Deep Learning-based CFD Simulation (ICML 2024 · similarity 0.87)
- PhyMPGN: Physics-encoded Message Passing Graph Network for spatiotemporal PDE systems (ICLR 2025 · 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.