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PEINR: A Physics-enhanced Implicit Neural Representation for High-Fidelity Flow Field Reconstruction
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Introduces HFR-Bench, a 5.4 TB CFD dataset of unsteady 2D/3D flow fields at multiple grid resolutions and WENO precisions, and PEINR, an INR with Gaussian/kernel-PCA temporal encoding, localized stencil-style spatial encoding, and a transformer spatiotemporal fuser for predicting the low-to-high fidelity error field.
Problem
High-fidelity flow field reconstruction from low-fidelity CFD data: lack of standard benchmarks, grid-independence assumption of INR methods, spectral bias, and imbalance between temporal and spatial complexity lead to poor fine-scale and temporal reconstruction.
Approach
Decouple temporal and spatial encoding (RBF-kernel plus Kernel PCA temporal features, neighbor-based stencil spatial coordinates), fuse them with a transformer block containing ResuMLP, multi-head attention and a spectral (FFT) block, and learn the error between bicubic-upscaled low-fidelity and high-fidelity fields rather than the field itself.
Key results
- On RT with α=16, β=1, PEINR reaches 26.96 PSNR and 7.76 DD versus 23.33 PSNR and 10.25 DD for CoordNet.
- On FFS with α=16, β=1, PEINR reaches 74.15 PSNR and 4.61 DD versus 42.71 PSNR and 98.46 DD for CoordNet.
- PEINR is slightly below CoordNet in PSNR on the RM dataset (α=16, β=1: 44.22 vs 45.34), which the authors attribute to discontinuities.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use PEINR instead of CoordNet | flow-field reconstruction · RM α=16 β=1 | PSNR: 45.34 -> 44.22 | Hurt |
| use PEINR instead of CoordNet | flow-field reconstruction · FFS α=16 β=1 | PSNR: 42.71 -> 74.15 | Helped |
| add physical encoding (ablation) | PEINR · RT, RM, FFS, Cylinder and SV | DD | Helped |
| add spectral block (ablation) | PEINR without physical encoding (PEINR1) · RT, RM, FFS, Cylinder and SV | PSNR | Helped |
| remove physical encoding and spectral block (ablation) | PEINR · Cylinder α=4 β=1.4 | PSNR: 35.7 -> 40.34 | Hurt |
| remove physical encoding (ablation) | PEINR · SV α=64 β=1.4 | PSNR: 43.55 -> 45.26 | Hurt |
| remove physical encoding and spectral block (ablation) | PEINR · SV α=64 β=1.4 | DD: 9.91 -> 4.21 | Hurt |
Surprising findings
- PEINR is slightly inferior to CoordNet in PSNR on the Riemann (RM) dataset, which the authors attribute to discontinuous flows.
Limitations
- PEINR is tailored to particular flow scenarios and may not generalize to out-of-distribution flows.
- Slightly lower PSNR than CoordNet on the Riemann discontinuous-flow dataset.
Experimental setup
Datasets: HFR-Bench
Benchmarks: HFR-Bench
Metrics: PSNR SSIM CORR DD
Baselines: Bicubic interpolation NIF CoordNet
Builds on: NIF CoordNet ResuMLP SIREN spectral block
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