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...
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 ...
Gao, X., Zhang, H.Q.: Rogue waves for the Hirota equation on the Jacobi elliptic cn-function background. Nonlinear Dyn. 101, 1159–1168 (2020) Google Scholar Zhang, H.Q., Chen, F.: Rogue waves for the fourth-order nonlinear Schrödinger equation on the periodic background. Chaos ...
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The electrical conductivity of weight diluted and concentrated standard seawater as a function of salinity and temperature The ratios Rs,t,o of electrical conductivity of seawater samples of precisely known salinity to standard seawater at the same temperature have been measure... T Dauphinee,J Ancsi...
A layer is a nonlinear function of an input value, commonly represented as (2) where hi is the hidden layer i, represented by its weight matrix Wi and bias vector bi. Notice that the relationship among hi, Wi, and X is a simple linear regression. This is then evaluated in a ...
In addition, the tanh function has the best training effect by comparing eight common activation functions (e.g., ReLU (x) , ELU (x) , SiLU (x) , sigmoid (x) , swish (x) , sin (x) , cos (x) , and tanh (x) ). For the inverse problem, we invert the...
Such non-smooth equations, for instance, arise in the continuous representation of fractional deep neural networks (DNNs). Here the underlying non-differentiable function is the ReLU or max function. The control enters in a nonlinear and multiplicative manner and we additionally impose control ...
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 ...
We prove existence and uniqueness of entropy solutions for the quasilinear elliptic equation u - div a ( u , Du ) = v, where 0 v ∈ L 1 ( R N ) ∩ L ∞ ( R N ), a ( z , ξ ) = ξ f ( z , ξ ), and f is a convex function of ξ with linear growth as ∥ξ∥...