Data-driven rogue waves and parameters discovery in nearly integrable \(\mathcal{PT}\)-symmetric Gross-Pitaevskii equations via PINNs deep learning
DOI10.1016/j.physd.2022.133430zbMath1496.35373OpenAlexW4288032460WikidataQ113866764 ScholiaQ113866764MaRDI QIDQ2167994
Shou-Fu Tian, Zhenya Yan, Ming Zhong, Shibo Gong
Publication date: 1 September 2022
Published in: Physica D (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.physd.2022.133430
generalized Gross-Pitaevskii equationcomplex \(\mathcal{PT}\)-symmetric potentialsdata-driven rogue waves and parameters discoveryphysics-informed deep neural networks
Artificial neural networks and deep learning (68T07) PDEs in connection with fluid mechanics (35Q35) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Inverse problems for PDEs (35R30) NLS equations (nonlinear Schrödinger equations) (35Q55)
Related Items (7)
Uses Software
Cites Work
- Unnamed Item
- Solving forward and inverse problems of the logarithmic nonlinear Schrödinger equation with \(\mathcal{PT}\)-symmetric harmonic potential via deep learning
- Rogue wave formation and interactions in the defocusing nonlinear Schrödinger equation with external potentials
- PPINN: parareal physics-informed neural network for time-dependent PDEs
- \textit{hp}-VPINNs: variational physics-informed neural networks with domain decomposition
- Multi-component nonlinear Schrödinger equations with nonzero boundary conditions: higher-order vector Peregrine solitons and asymptotic estimates
- Data-driven peakon and periodic peakon solutions and parameter discovery of some nonlinear dispersive equations via deep learning
- B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data
- A two-stage physics-informed neural network method based on conserved quantities and applications in localized wave solutions
- When and why PINNs fail to train: a neural tangent kernel perspective
- \(N\)-double poles solutions for nonlocal Hirota equation with nonzero boundary conditions using Riemann-Hilbert method and PINN algorithm
- Multi-dimensional stable fundamental solitons and excitations in \(\mathcal{PT}\)-symmetric harmonic-Gaussian potentials with unbounded gain-and-loss distributions
- Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems
- Adaptive activation functions accelerate convergence in deep and physics-informed neural networks
- Data-driven rogue waves and parameter discovery in the defocusing nonlinear Schrödinger equation with a potential using the PINN deep learning
- A nonlocal physics-informed deep learning framework using the peridynamic differential operator
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations
- Julia: A Fresh Approach to Numerical Computing
- Financial Rogue Waves
- Nonlinear Waves in Integrable and Nonintegrable Systems
- Large Sample Properties of Simulations Using Latin Hypercube Sampling
- Real Spectra in Non-Hermitian Hamiltonians Having<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="bold-script">P</mml:mi><mml:mi mathvariant="bold-script">T</mml:mi></mml:math>Symmetry
- Effect of PT symmetry on nonlinear waves for three-wave interaction models in the quadratic nonlinear media
- Versatile rogue waves in scalar, vector, and multidimensional nonlinear systems
- On stable solitons and interactions of the generalized Gross-Pitaevskii equation with PT- and non-PT-symmetric potentials
- The nonlinear Schrödinger equation with generalized nonlinearities and PT-symmetric potentials: Stable solitons, interactions, and excitations
- 𝓟𝓣-symmetric quantum mechanics
- Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks
- DeepXDE: A Deep Learning Library for Solving Differential Equations
- Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations
- fPINNs: Fractional Physics-Informed Neural Networks
- Oceanic Rogue Waves
- Deep learning neural networks for the third-order nonlinear Schrödinger equation: bright solitons, breathers, and rogue waves
- Solving second-order nonlinear evolution partial differential equations using deep learning
- A physics-constrained deep residual network for solving the sine-Gordon equation
- A deep learning method for solving third-order nonlinear evolution equations
This page was built for publication: Data-driven rogue waves and parameters discovery in nearly integrable \(\mathcal{PT}\)-symmetric Gross-Pitaevskii equations via PINNs deep learning