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Neural-Network supported 3DVar

Ground Truth vs. Analysis. Compare the true Lorenz-63 trajectory to estimates from classical 3D-Var and a learned increment model. Use the legend to toggle series and drag to zoom.

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How to read the chart

  • Lines: Truth vs. Analysis (3D-Var / Pred-Inc).
  • Goal: analysis should “hug” the truth—divergence shows error.
  • Tip: zoom into intervals where curves split to compare methods.

Key metrics (this run)

Best validation MSE (MLP): — | Seed: —

Mean L2 error / cycle

  • 3D-Var: —
  • Pred-Inc: —

Observation noise variance (R): —

Experiment setup & methods

  • System: Lorenz-63 (\( \sigma = \)—, \( \rho = \)—, \( \beta = \)—)
  • Integration: \( \Delta t = \)—, horizon \( T = \)—, assimilation every — steps
  • Observations: full state (\( H = I_3 \)), Gaussian noise (variance \( R \) above)
  • 3D-Var: static \( B \), Kalman-type gain \( K \); analysis \( x_a = x_b + K(y - Hx_b) \)
  • Predicted-Increment (MLP): learns \( \delta \) from [background, observation]; apply \( x_a = x_b + \hat{\delta} \)

Downloads

CSV and metadata powering the plot:

Series (x) RMSE Run metadata (JSON)