Table 1 Simulation performance the data-driven models

From: Online calibration of deep learning sub-models for hybrid numerical modeling systems

Model

Exponents

Dimension

True gradient

(0.90 −0.01 −14.57)  ±  (0.02 0.01 0.02)

2.061  ±  0.001

Static approximation

(0.91 −0.01 −14.57)  ±  (0.02 0.01 0.02)

2.061  ±  0.001

Ensemble approximation

(0.91 −0.01 −14.56)  ±  (0.02 0.01 0.02)

2.061  ±  0.001

Physical core

(−0.03 −4.99 −5.98)  ±  (0.01 1.43 1.42)

0

  1. full Lyapunov spectrum and Lyapunov dimension of the tested models. The Lyapunov spectrum of the true Lorenz 63 system is (0.91, 0.0, −14.57) and it’s dimension is estimated to be 2.06457. The Lyapunov spectrum was estimated using the Gram-Schmidt orthonormalization technique, starting from initial conditions in the test set. The reported values correspond to the average Lyapunov spectrum after convergence, with the errors representing the standard deviation.
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