arXiv subjects

Ashish Kumar Pandey

Publications and source records attributed to Ashish Kumar Pandey.

22 records · Page 2Linked to original sources

arXiv2020

TanhSoft -- a family of activation functions combining Tanh and Softplus

Deep learning at its core, contains functions that are composition of a linear transformation with a non-linear function known as activation function. In past few years, there is an increasing interest in construction of novel activation functions resulting in better learning. In this work, we propose a family of novel activation functions, namely TanhSoft, with four undetermined hyper-parameters of the form tanh(αx+βe^{γx})ln(δ+e^x) and tune these hyper-parameters to obtain activation functions which are shown to outperform several well known activation functions. For instance, replacing ReLU with xtanh(0.6e^x)improves top-1 classification accuracy on CIFAR-10 by 0.46% for DenseNet-169 and 0.7% for Inception-v3 while with tanh(0.87x)ln(1 +e^x) top-1 classification accuracy on CIFAR-100 improves by 1.24% for DenseNet-169 and 2.57% for SimpleNet model.

cs.NE↗

arXiv2017

Comparison of modulational instabilities in full-dispersion shallow water models

We study the modulational instability of a shallow water model, with and without surface tension, which generalizes the Whitham equation to include bi-directional propagation. Without surface tension, the small amplitude periodic traveling waves are modulationally unstable if their wave number is greater than a critical wave number predicting a Benjamin-Feir type instability and the result qualitatively agrees with the shallow water model in [HP16]. With surface tension, the result qualitatively agrees with the physical problem except for the large surface tension limit which is accurately predicted by the shallow water model in [HP16]. We also compare the results with the Whitham and full-dispersion Camassa-Holm equations.

math.AP↗

arXiv2016

Modulational instability in a full-dispersion shallow water model

We propose a shallow water model which combines the dispersion relation of water waves and the Boussinesq equations, and which extends the Whitham equation to permit bidirectional propagation. We establish that its sufficiently small, periodic wave train is spectrally unstable to long wavelength perturbations, provided that the wave number is greater than a critical value, like the Benjamin-Feir instability of a Stokes wave. We verify that the asso- ciated linear operator possesses infinitely many collisions of purely imaginary eigenvalues, but they do not contribute to instability away from the origin in the spectral plane to the leading order in the amplitude parameter. We discuss the effects of surface tension on the modulational instability. The results agree with those from formal asymptotic expansions and numerical computations for the physical problem.

math.AP↗

arXiv2016

Modulational instability in nonlinear nonlocal equations of regularized long wave type

We study the stability and instability of periodic traveling waves in the vicinity of the origin in the spectral plane, for equations of Benjamin- Bona-Mahony (BBM) and regularized Boussinesq types permitting nonlocal dispersion. We extend recent results for equations of Korteweg-de Vries type and derive modulational instability indices as functions of the wave number of the underlying wave. We show that a sufficiently small, periodic traveling wave of the BBM equation is spectrally unstable to long wavelength perturbations if the wave number is greater than a critical value and a sufficiently small, periodic traveling wave of the regularized Boussinesq equation is stable to square integrable perturbations.

math.AP↗