\(PT\)-symmetric PINN for integrable nonlocal equations: forward and inverse problems (Q6554430)

scientific article; zbMATH DE number 7864182

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English	\(PT\)-symmetric PINN for integrable nonlocal equations: forward and inverse problems	scientific article; zbMATH DE number 7864182

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title

\(PT\)-symmetric PINN for integrable nonlocal equations: forward and inverse problems (English)

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12 June 2024

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Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

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Bound states of non-Hermitian quantum field theories

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Integrable \(\mathcal{PT}\)-symmetric local and nonlocal vector nonlinear Schrödinger equations: a unified two-parameter model

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Inverse scattering transform for the integrable nonlocal nonlinear Schrödinger equation

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Dynamics of high-order solitons in the nonlocal nonlinear Schrödinger equations

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Exotic vector freak waves in the nonlocal nonlinear Schrödinger equation

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Rogue waves in the ocean

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Water waves, nonlinear Schrödinger equations and their solutions

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Rogue wave solutions of AB system

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Rogue waves in the nonlocal \(\mathcal{PT}\)-symmetric nonlinear Schrödinger equation

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Dynamics of rogue waves in the partially \(\mathcal{PT}\)-symmetric nonlocal Davey-Stewartson systems

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Rogue waves of the nonlocal Davey–Stewartson I equation

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Darboux transformations and global solutions for a nonlocal derivative nonlinear Schrödinger equation

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Rational and semi‐rational solutions of a nonlocal (2 + 1)‐dimensional nonlinear Schrödinger equation

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Three-Wave Interaction Equations: Classical and Nonlocal

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Integrable nonlocal derivative nonlinear Schrödinger equations

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Approximation by superpositions of a sigmoidal function

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Q4558473

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Solving second-order nonlinear evolution partial differential equations using deep learning

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PINN deep learning method for the Chen-Lee-Liu equation: rogue wave on the periodic background

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VC-PINN: variable coefficient physics-informed neural network for forward and inverse problems of PDEs with variable coefficient

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\(N\)-double poles solutions for nonlocal Hirota equation with nonzero boundary conditions using Riemann-Hilbert method and PINN algorithm

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Data-driven rogue waves and parameters discovery in nearly integrable \(\mathcal{PT}\)-symmetric Gross-Pitaevskii equations via PINNs deep learning

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Predicting the dynamic process and model parameters of the vector optical solitons in birefringent fibers \textit{via} the modified PINN

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Data-driven vector soliton solutions of coupled nonlinear Schrödinger equation using a deep learning algorithm

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PT-symmetric solitons and parameter discovery in self-defocusing saturable nonlinear Schrödinger equation via LrD-PINN

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Deep learning soliton dynamics and complex potentials recognition for 1D and 2D \(\mathcal{PT}\)-symmetric saturable nonlinear Schrödinger equations

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Data driven soliton solution of the nonlinear Schrödinger equation with certain \(\mathcal{PT}\)-symmetric potentials via deep learning

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The line rogue wave solutions of the nonlocal Davey-Stewartson I equation with \textit{PT} symmetry based on the improved physics-informed neural network

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Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems

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

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Adaptive activation functions accelerate convergence in deep and physics-informed neural networks

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Enforcing continuous symmetries in physics-informed neural network for solving forward and inverse problems of partial differential equations

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On the limited memory BFGS method for large scale optimization

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Large Sample Properties of Simulations Using Latin Hypercube Sampling

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Identifiers

zbMATH Open document ID

1546.35181

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DOI

10.1063/5.0197939

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Mathematics Subject Classification ID

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Mathematics(1 entry)

mardi Publication:6554430