CNO (Convolutional Neural Operator)¶

CNO is a convolutional neural operator designed to learn robust operator mappings and avoid discretization artifacts.

Reference Paper: Raonic et al., NeurIPS 2023.

@article{raonic2023convolutional,
  title={Convolutional neural operators for robust and accurate learning of PDEs},
  author={Raonic, Bogdan and Molinaro, Roberto and De Ryck, Tim and Rohner, Tobias and Bartolucci, Francesca and Alaifari, Rima and Mishra, Siddhartha and de B{\'e}zenac, Emmanuel},
  journal={Advances in Neural Information Processing Systems},
  volume={36},
  pages={77187--77200},
  year={2023}
}

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)¶

• Internally, inputs may be permuted to [B, C, T, H, W] for 3D convolutions and then permuted back.
• If \(T_\text{out} > T_\text{in}\), the implementation expands the output feature dimension and reshapes back into the time dimension, so it assumes \(T_\text{out}\) is a multiple of \(T_\text{in}\).
• Training uses an MSE-style objective on predicted fields.

CNO specific YAML config¶

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

Config files¶

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

Model-specific keys¶

In the current reference implementation, realpdebench.model.load_model.load_model() constructs realpdebench.model.cno.CNO3d and only wires through:

• N_layers (int): Number of downsampling/upsampling stages (operator "depth").