A two-stage physics-informed neural network method based on conserved quantities and applications in localized wave solutions

From MaRDI portal
Publication:2135816

DOI10.1016/j.jcp.2022.111053OpenAlexW3177788059MaRDI QIDQ2135816

Yong Chen, Shuning Lin

Publication date: 9 May 2022

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2107.01009




Related Items (27)

\(N\)-double poles solutions for nonlocal Hirota equation with nonzero boundary conditions using Riemann-Hilbert method and PINN algorithmData-driven rogue waves and parameters discovery in nearly integrable \(\mathcal{PT}\)-symmetric Gross-Pitaevskii equations via PINNs deep learningA deep learning method for solving high-order nonlinear soliton equationsMixed higher-order rogue waves and solitons for the coupled modified nonlinear Schrödinger equationVC-PINN: variable coefficient physics-informed neural network for forward and inverse problems of PDEs with variable coefficientEnforcing continuous symmetries in physics-informed neural network for solving forward and inverse problems of partial differential equationsData-driven soliton mappings for integrable fractional nonlinear wave equations via deep learning with Fourier neural operatorComplex dynamics on the one-dimensional quantum droplets via time piecewise PINNsDeep learning data-driven multi-soliton dynamics and parameters discovery for the fifth-order Kaup-Kuperschmidt equationPhysics-informed neural network methods based on Miura transformations and discovery of new localized wave solutionsNumber of solitons emerged in the initial profile of shallow water using convolutional neural networksPre-training physics-informed neural network with mixed sampling and its application in high-dimensional systemsParallel physics-informed neural networks method with regularization strategies for the forward-inverse problems of the variable coefficient modified KdV equationPhysics-informed neural networks with two weighted loss function methods for interactions of two-dimensional oceanic internal solitary wavesDeep neural networks learning forward and inverse problems of two-dimensional nonlinear wave equations with rational solitonsDeep learning soliton dynamics and complex potentials recognition for 1D and 2D \(\mathcal{PT}\)-symmetric saturable nonlinear Schrödinger equationsData-driven forward and inverse problems for chaotic and hyperchaotic dynamic systems based on two machine learning architecturesMulti-output physics-informed neural network for one- and two-dimensional nonlinear time distributed-order modelsExploring two-dimensional internal waves: a new three-coupled Davey-Stewartson system and physics-informed neural networks with weight assignment methodsGradient-enhanced physics-informed neural networks based on transfer learning for inverse problems of the variable coefficient differential equationsIs the neural tangent kernel of PINNs deep learning general partial differential equations always convergent?Data-driven nonparametric identification of material behavior based on physics-informed neural network with full-field dataPhysical informed neural networks with soft and hard boundary constraints for solving advection-diffusion equations using Fourier expansionsPhysics-informed neural networks based on adaptive weighted loss functions for Hamilton-Jacobi equationsData-driven discoveries of Bäcklund transformations and soliton evolution equations via deep neural network learning schemesPrediction of the number of solitons for initial value of nonlinear Schrödinger equation based on the deep learning methodThe nonlinear wave solutions and parameters discovery of the Lakshmanan-Porsezian-Daniel based on deep learning


Uses Software


Cites Work


This page was built for publication: A two-stage physics-informed neural network method based on conserved quantities and applications in localized wave solutions