function, which keeps its profile during the propagation governed by the FSE-emulating setup. Note that the trajectory of the Airy pulse does not accelerate (the inset in the right panel of Fig.3a displays the propagation pattern up toz = 1000 m). With the increase ofα, a new ...
Although the approach is valid for any type of modelocking technique, from now on we focus on the case of active modelocking via amplitude modulation. The effect of the modulator is modeled through its transmission function, written as{e}^{-m(t)}, wherem(t)represents the modulator state. ...
The method is a discretization of an equivalent least-squares formulation in the set of neural network functions with the ReLU activation function. The method is capable of approximating the discontinuous interface of the underlying problem automatically through the free hyper-planes of the ReLU neural...
As activation functions, we use Exponential Linear Units (ELU) for their smooth function interpolation abilities. While one could readily use ReLU, Leaky-ReLU, tanh , or adaptive activation functions with learnable hyper-parameters, we find that ELU consistently performs best in the benchmark ...
We reformulated the given problem as a system of coupled PDEs to lower the impacts of automatic differentiation on the initial condition and the second-order time-derivative in the PDE. Various NN training were performed to choose the optimal hyper-parameter tuning such as activation function, ...
Choudhuri, A., Porsezian, K.: Dark-in-the-Bright solitary wave solution of higher-order nonlinear Schrödinger equation with non-Kerr terms. Opt. Commun. 285, 364–367 (2012) Google Scholar Triki, H., Azzouzi, F., Grelu, P.: Multipole solitary wave solutions of the higher-order ...
We here choose the basic solution matrix (84)Ξ3(λ)=Ξ2(λ)A2−1,and the spectral functions of spectral problems (4), (5) (85)Φ1(1)=Ξ3(λ)1,0,9/10,0T,Φ2(1)=Ξ3(λ)0,1,1,0T.Let λ=(1+i)f2+1. Expanding the vector function Φ1(1) and Φ2(1) at f=0, ...
In addition, the tanh function has the best training effect by comparing eight common activation functions (e.g., \\(extrm{ReLU}(extbf{x})\\), \\(extrm{ELU}(extbf{x})\\), \\(extrm{SiLU}(extbf{x})\\), \\(extrm{sigmoid}(extbf{x})\\), \\(extrm{...
6. The continuous part of NF spectrum is represented by the complex-valued function\(r(\xi ) \in {\mathbb {C}}\)of a real argument\(\xi \in {\mathbb {R}}\), where\(\xi\)is called the spectral parameter;\(r(\xi )\)is called the reflection coefficient, and\(\xi\)emerges ...
If p1=0 then the values of D1 and D2 are irrelevant, while p2=0 makes the values of D3 and D4 irrelevant. The loss column specifies the loss function, either MSE for mean squared error (α=2) or mean absolute error MAE (α=1), respectively (see Eq. (1)). The mean res, 99...