Related papers: Data-driven discoveries of B\"acklund transforms a…

A couple of applications of B\"acklund transformations in the study of nonlinear evolution equations is here given. Specifically, we are concerned about third order nonlinear evolution equations. Our attention is focussed on one side, on…

We investigate the physics informed neural network method, a deep learning approach, to approximate soliton solution of the nonlinear Schr\"odinger equation with parity time symmetric potentials. We consider three different parity time…

In the process of the deep learning, we integrate more integrable information of nonlinear wave models, such as the conservation law obtained from the integrable theory, into the neural network structure, and propose a conservation-law…

We propose effective scheme of deep learning method for high-order nonlinear soliton equation and compare the activation function for high-order soliton equation. The neural network approximates the solution of the equation under the…

In this paper, we investigate the forward problems on the data-driven rational solitons for the (2+1)-dimensional KP-I equation and spin-nonlinear Schr\"odinger (spin-NLS) equation via the deep neural networks leaning. Moreover, the inverse…

Deep learning is computationally intensive, with significant efforts focused on reducing arithmetic complexity, particularly regarding energy consumption dominated by data movement. While existing literature emphasizes inference, training…

In this paper, we firstly extend the Fourier neural operator (FNO) to discovery the soliton mapping between two function spaces, where one is the fractional-order index space $\{\epsilon|\epsilon\in (0, 1)\}$ in the fractional integrable…

In this paper, we firstly extend the physics-informed neural networks (PINNs) to learn data-driven stationary and non-stationary solitons of 1D and 2D saturable nonlinear Schr\"odinger equations (SNLSEs) with two fundamental PT-symmetric…

Soliton pulsations are ubiquitous feature of non-stationary soliton dynamics in mode-locked lasers and many other physical systems. To overcome difficulties related to huge amount of necessary computations and low efficiency of traditional…

We put forth two physics-informed neural network (PINN) schemes based on Miura transformations and the novelty of this research is the incorporation of Miura transformation constraints into neural networks to solve nonlinear PDEs. The most…

The KdV eigenfunction equation is considered: some explicit solutions are constructed. These, to the best of the authors' knowledge, new solutions represent an example of the powerfulness of the method devised. Specifically, B\"acklund…

The numerical determination of solitary states is an important topic for such research areas as Bose-Einstein condensates, nonlinear optics, plasma physics, etc. In this paper, we propose a data-driven approach for identifying solitons…

The derivation of the Backlund transformations (BTs) is a standard problem of the theory of the integrable systems. Here, I discuss the equations describing the BTs for the Ablowitz-Ladik hierarchy (ALH), which have been already obtained by…

We introduce a deep learning framework designed to train smoothed elastoplasticity models with interpretable components, such as a smoothed stored elastic energy function, a yield surface, and a plastic flow that are evolved based on a set…

This paper introduces a deep learning system based on a quantum neural network for the binary classification of points of a specific geometric pattern (Two-Moons Classification problem) on a plane. We believe that the use of hybrid deep…

Deep learning has revolutionized the computer vision and image classification domains. In this context Convolutional Neural Networks (CNNs) based architectures are the most widely applied models. In this article, we introduced two…

In this work, we propose a novel backward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations (BSDEs), where the deep neural network (DNN) models are trained not only…

The use of implicit time-stepping schemes for the numerical approximation of solutions to stiff nonlinear time-evolution equations brings well-known advantages including, typically, better stability behaviour and corresponding support of…

This work contributes to the development of a new data-driven method (D-DM) of feedforward neural networks (FNNs) learning. This method was proposed recently as a way of improving randomized learning of FNNs by adjusting the network…

Magnetotelluric deep learning (DL) inversion methods based on joint data-driven and physics-driven have become a hot topic in recent years. When mapping observation data (or forward modeling data) to the resistivity model using neural…