Table 5 Summary of hyperparameters and neural network configurations for all numerical experiments.
Models | Initial conditions | Library order | Iterations | \(\#\)hidden layers, \(\#\)neurons and activation functions | Learning Rates | \(\lambda\) |
|---|---|---|---|---|---|---|
Linear damped oscillator | \(\begin{bmatrix}2.0&0.0\end{bmatrix}^{T}\) | 3 | \([15000]+2\times [1000]\) | \(4\times [32]\), Tanh | (0.01, 0.001) | 0.05 |
Linear damped oscillator with noise | \(\begin{bmatrix}2.0&0.0\end{bmatrix}^{T}\) | 3 | \([20000]+2\times [2000]\) | \(4\times [32]\), Tanh | (0.005, 0.0001) | 0.06 |
Cubic damped oscillator | \(\begin{bmatrix}2.0&0.0\end{bmatrix}^{T}\) | 3 | \([15000]+2\times [1000]\) | \(4\times [32]\), Tanh | (0.01, 0.001) | 0.05 |
FitzHugh-Nagumo | \(\begin{bmatrix}0.0&0.0\end{bmatrix}^{T}\) | 3 | \([20000]+7\times [1000]\) | \(4\times [32]\), Tanh | (0.001, 0.0001) | 0.01 |
Lorenz attractor | \(\begin{bmatrix}-8&7&27\end{bmatrix}^{T}\) | 3 | \([20000]+2\times [2000]\) | \(1\times [256]\), SIREN | (0.5, 0.0001) | 0.5 |
Lorenz attractor with noise | \(\begin{bmatrix}-8&7&27\end{bmatrix}^{T}\) | 3 | \([20000]+2\times [2000]\) | \(1\times [256]\), SIREN | (0.1, 0.0001) | 0.5 |
Lotka-Volterra | \(\begin{bmatrix}1.8&1.8\end{bmatrix}^{T}\) | 2 | \([25000]+2\times [6000]\) | \(2\times [64]\), SIREN | (0.001, 0.0001) | 0.1 |
Logistic growth | 0.1 | 2 | \([20000]+2\times [5000]\) | \(3\times [32]\), Tanh | \((0.001, 0.0001)\) | 0.025 |
