DMD (Dynamic Mode Decomposition)¶

DMD is a classical reduced-order modeling technique that extracts spatiotemporal coherent structures from time-series data via an SVD-based decomposition, then extrapolates dynamics using a linear evolution model.

Reference Paper: Kutz et al., Dynamic Mode Decomposition: Data-Driven Modeling of Complex Systems, 2016.

@book{kutz2016dynamic,
  title={Dynamic mode decomposition: data-driven modeling of complex systems},
  author={Kutz, J Nathan and Brunton, Steven L and Brunton, Bingni W and Proctor, Joshua L},
  year={2016},
  publisher={SIAM}
}

RealPDEBench interface¶

• Input: x with shape [B, T_in, H, W, C_in]
• Output: predictions with shape [B, T_out, H, W, C_out] (typically C_out == C_in for this baseline)

RealPDEBench usage notes¶

• No training stage: DMD is not trained with gradient descent. In the RealPDEBench paper tables, DMD occupies only the inference-only column and the training columns are left blank.
• Main knobs: n_modes (number of retained modes), n_predict (prediction horizon).
• Autoregressive rollout: N_autoregressive is a shared evaluation setting (not DMD-specific); see Getting Started → Evaluation settings.
• Modalities: if extra channels are zero-padded (unmeasured modalities), DMD is typically configured to use only the measured channels.

DMD specific YAML config¶

DMD is enabled by model_name: "dmd" in the YAML. Since it is a non-learning baseline, the YAML mainly controls how DMD is applied at evaluation time.

Config files¶

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

Model-specific keys¶

These keys are consumed by realpdebench.model.load_model.load_model() and realpdebench.model.dmd.DMD.

• n_modes (int): Number of retained DMD modes after truncation (higher can fit more dynamics, but may overfit/noise).
• n_predict (int): Number of future frames predicted per DMD forward call.
• input_feature (int): Number of channels used by DMD from the input tensor (useful when extra channels are zero-padded/unmeasured).