Table 2 Linear damped oscillator: the discovered governing equations using IRK-SINDy in the approach of Newton’s iterations and fixed point iterations for various sample-size m.
Sample-size | Newton’s iterations | Fixed point iterations |
|---|---|---|
\(m = 801\) | \(\begin{array}{cc} \dot{x}_{1}(t) = -0.100 x_{1}(t) + 2.000 x_{2}(t)\\ \dot{x}_{2}(t) = -2.001 x_{1}(t) - 0.100 x_{2}(t) \end{array}\) | \(\begin{array}{cc} \dot{x}_{1}(t) = -0.100 x_{1}(t) + 2.000 x_{2}(t)\\ \dot{x}_{2}(t) = -2.001 x_{1}(t) - 0.100 x_{2}(t) \end{array}\) |
\(m = 201\) | \(\begin{array}{cc} \dot{x}_{1}(t) = -0.100 x_{1}(t) + 2.000 x_{2}(t)\\ \dot{x}_{2}(t) = -2.001 x_{1}(t) - 0.100 x_{2}(t) \end{array}\) | \(\begin{array}{cc} \dot{x}_{1}(t) = -0.100 x_{1}(t) + 2.000 x_{2}(t)\\ \dot{x}_{2}(t) = -2.001 x_{1}(t) - 0.100 x_{2}(t) \end{array}\) |
\(m = 41\) | \(\begin{array}{cc} \dot{x}_{1}(t) = -0.101 x_{1}(t) + 2.003 x_{2}(t)\\ \dot{x}_{2}(t) = -2.003 x_{1}(t) - 0.101 x_{2}(t) \end{array}\) | \(\begin{array}{cc} & \dot{x}_{1}(t) = -0.101 x_{1}(t) + 2.004 x_{2}(t)\\ & \dot{x}_{2}(t) = -2.004 x_{1}(t) - 0.101 x_{2}(t) \end{array}\) |
\(m = 31\) | \(\begin{array}{cc} \dot{x}_{1}(t) = -0.102 x_{1}(t) + 2.009 x_{2}(t)\\ \dot{x}_{2}(t) = -2.008 x_{1}(t) - 0.103 x_{2}(t) \end{array}\) | \(\begin{array}{cc} \dot{x}_{1}(t) = -0.100 x_{1}(t) + 2.015 x_{2}(t)\\ \dot{x}_{2}(t) = -2.014 x_{1}(t) - 0.100 x_{2}(t) \end{array}\) |
