WDNO (Wavelet Diffusion Neural Operator)¶

WDNO combines a diffusion model with a wavelet representation to model complex spatiotemporal dynamics, especially when abrupt changes are present.

Reference Paper: Hu et al., ICLR 2025.

@inproceedings{
hu2025wavelet,
title={Wavelet Diffusion Neural Operator},
author={Peiyan Hu and Rui Wang and Xiang Zheng and Tao Zhang and Haodong Feng and Ruiqi Feng and Long Wei and Yue Wang and Zhi-Ming Ma and Tailin Wu},
booktitle={The Thirteenth International Conference on Learning Representations},
year={2025}
}

RealPDEBench interface¶

• Input: x with shape [B, T_in, H, W, C_in]
• Output: predictions with shape [B, T_out, H, W, C_out]

Implementation notes (RealPDEBench)¶

• WDNO trains a diffusion model in wavelet-coefficient space on a concatenation of input and target information.
• Inference is performed by DDPM/DDIM-style sampling and can be slower than deterministic operator baselines due to multiple sampling steps.
• Conditioning uses wavelet coefficients derived from the input window.

WDNO specific YAML config¶

This baseline is enabled by model_name: "wdno" in the training YAML.

Config files¶

• Cylinder: realpdebench/configs/cylinder/wdno.yaml
• Controlled Cylinder: realpdebench/configs/controlled_cylinder/wdno.yaml
• FSI: realpdebench/configs/fsi/wdno.yaml
• Foil: realpdebench/configs/foil/wdno.yaml
• Combustion: realpdebench/configs/combustion/wdno.yaml

Model-specific keys¶

These keys are consumed by realpdebench.model.load_model.load_model() and realpdebench.model.wdno.WDNO.

• dim (int): Base channel width of the internal 3D U-Net used by the diffusion model.
• dim_mults (list[int]): Channel multipliers per resolution stage of the internal U-Net.
• wave_type (str): Wavelet family used for the wavelet decomposition (e.g., "bior1.1").
• pad_mode (str): Wavelet padding mode (e.g., "zero").
• beta_schedule (str): Diffusion beta schedule ("linear", "cosine", or "sigmoid").
• sampling_timesteps (int): Number of sampling steps for inference. If smaller than the diffusion training steps, WDNO uses DDIM-style fast sampling.
• ddim_sampling_eta (float): DDIM sampling noise parameter (controls stochasticity during DDIM sampling).