MWT (Multiwavelet Transform Neural Operator)¶

MWT models multi-scale structure via multiwavelet bases and efficient mixing across scales.

Reference Paper: Gupta et al., NeurIPS 2021.

@article{gupta2021multiwavelet,
  title={Multiwavelet-based operator learning for differential equations},
  author={Gupta, Gaurav and Xiao, Xiongye and Bogdan, Paul},
  journal={Advances in neural information processing systems},
  volume={34},
  pages={24048--24062},
  year={2021}
}

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)¶

• The implementation may reorder tensors to [B, H, W, T, C] internally and convert back to the benchmark convention.
• Multi-step outputs use a vectorized reshape and typically assume \(T_\text{out}\) is a multiple of \(T_\text{in}\).
• Training uses an MSE-style objective on predicted fields.

MWT specific YAML config¶

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

Config files¶

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

Model-specific keys¶

These keys are consumed by realpdebench.model.load_model.load_model() and realpdebench.model.MWT_libs.models.MWT3d.

• k (int): Wavelet filter size (controls the local basis size).
• alpha (int): Fourier filter parameter in MWT blocks (typically constrained by the time dimension).
• c (int): Channel expansion factor used by the wavelet mixing blocks.
• nCZ (int): Number of MWT "CZ" blocks (depth of the operator).
• L (int): Coarsest wavelet level used by the hierarchy.
• base (str): Wavelet basis type (e.g., "legendre" or "chebyshev").