Correcting Neural Operator Spectral Bias via Diffusion Posterior Sampling with Sparse Observations
Neural operator surrogates (NO) approximate PDE solutions orders of magnitude faster than numerical solvers, but suffer from spectral bias: high-frequency content is systematically attenuated, limiting reliability where fine-scale structure matters. Sparse sensor measurements of the field are often available too, offering pointwise accuracy without spectral distortion but covering only a small fraction of the domain. We address this by treating NO predictions as auxiliary observations in a diffusion posterior sampling framework. Our method, FreqNO-DPS (https://github.com/niccoloperrone/FreqNO-DPS), combines an unconditional score-based diffusion prior, trained on high-fidelity simulations...
| Authors | Niccolò Perrone, Fanny Lehmann, Stefania Fresca et al. |
|---|---|
| Primary category | cs.LG |
| Published | 2 June 2026 |
| Last updated at source | 2 June 2026 |
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