Table 2 Applied Hyper-parameters for the WSS.

Input features

N_modes=5 N

≥ 95% energy for pressure/WSS often with < 10 modes; keeps model small.

Sequence/window length

20 time steps

Matches earlier pipeline; ~⅓–1 cardiac cycle of history if 60–80 steps/cycle.

Forecast horizon

1 step (autoregressive for multi-step)

Stable rollouts; can extend to 5 with scheduled sampling.

LSTM layers

2

Enough depth for nonlinearity without overfitting.

Hidden units

128

Good bias–variance tradeoff for small datasets.

Bidirectional

No

Causal forecasting.

Dropout

0.2 (between layers)

Regularization for small data.

Recurrent dropout

0.1

Regularizes hidden-to-hidden dynamics.

Output head

MLP(128→64→N_modes), activation ReLU then Linear

Light nonlinearity before linear projection.

Activation (LSTM)

tanh (cell), sigmoid (gates)

Standard LSTM.

Loss

MSE on POD coeffs; report RMSE/MAE in physical space after reconstruction

Training on coeffs is stable; evaluate fields too.

Optimizer

Adam

Robust default.

Initial LR

1e-3

Common starting point.

LR schedule

ReduceLROnPlateau (factor 0.5, patience 8, min LR 1e-6)

Adapts to plateaus.

Weight decay

1e-4

Mild regularization.

Gradient clipping

1.0 (global-norm)

Prevents exploding gradients.

Batch size

32

Fits typical GPU/CPU memory; stable grads.

Epochs

200 max, Early stopping patience 20 (monitor val RMSE)

Avoids overfitting.

Train/val/test split

70/15/15% by time (no leakage)

Preserves chronology.

Normalization

Z-score per coefficient using train stats

Required for stable training.

Seed

42 (fixed)

Reproducibility.