A New Artificial Neural Network Method for Solving Schrödinger Equations on Unbounded Domains
From MaRDI portal
Publication:5045673
DOI10.4208/cicp.OA-2022-0135zbMath1498.65189OpenAlexW4312298021MaRDI QIDQ5045673
Weizhong Dai, Aniruddha Bora, Joshua P. Wilson, Jacob C. Boyt
Publication date: 7 November 2022
Published in: Communications in Computational Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.4208/cicp.oa-2022-0135
convergencelinear and nonlinear Schrödinger equationsartificial neural network methodsoliton and particle propagations
Artificial neural networks and deep learning (68T07) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite difference methods for boundary value problems involving PDEs (65N06)
Related Items (2)
A new absorbing layer approach for solving the nonlinear Schrödinger equation ⋮ PI-VEGAN: Physics Informed Variational Embedding Generative Adversarial Networks for Stochastic Differential Equations
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- A generalized finite-difference time-domain scheme for solving nonlinear Schrödinger equations
- A generalized finite-difference time-domain quantum method for the \(N\)-body interacting Hamiltonian
- Efficient finite difference solutions to the time-dependent Schrödinger equation
- A finite-difference method for solving the cubic Schrödinger equation
- Domain decomposition method and high-order absorbing boundary conditions for the numerical simulation of the time dependent Schrödinger equation with ionization and recombination by intense electric field
- Analysis of finite element method for one-dimensional time-dependent Schrödinger equation on unbounded domain
- The nonlinear Schrödinger equation. Self-focusing and wave collapse
- Inferring solutions of differential equations using noisy multi-fidelity data
- Hidden physics models: machine learning of nonlinear partial differential equations
- The finite difference scheme for nonlinear Schrödinger equations on unbounded domain by artificial boundary conditions
- Deep neural networks motivated by partial differential equations
- SciANN: a Keras/Tensorflow wrapper for scientific computations and physics-informed deep learning using artificial neural networks
- Lift \& learn: physics-informed machine learning for large-scale nonlinear dynamical systems
- PhyGeoNet: physics-informed geometry-adaptive convolutional neural networks for solving parameterized steady-state PDEs on irregular domain
- Data-driven rogue waves and parameter discovery in the defocusing nonlinear Schrödinger equation with a potential using the PINN deep learning
- An energy approach to the solution of partial differential equations in computational mechanics via machine learning: concepts, implementation and applications
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- Adaptive absorbing boundary conditions for Schrödinger-type equations: Application to nonlinear and multi-dimensional problems
- Absorbing boundary conditions for nonlinear scalar partial differential equations
- A perfectly matched layer approach to the nonlinear Schrödinger wave equations
- Neural algorithm for solving differential equations
- A new absorbing layer for simulation of wave propagation based on a KdV model on unbounded domain
- Numerical Gaussian Processes for Time-Dependent and Nonlinear Partial Differential Equations
- Split-Step Methods for the Solution of the Nonlinear Schrödinger Equation
- A Space-Time Finite Element Method for the Nonlinear Schrödinger Equation: The Continuous Galerkin Method
- Discrete Absorbing Boundary Conditions for Schrödinger-Type Equations. Construction and Error Analysis
- Numerical schemes for the simulation of the two-dimensional Schrödinger equation using non-reflecting boundary conditions
- Solving Time Dependent Fokker-Planck Equations via Temporal Normalizing Flow
- DeepXDE: A Deep Learning Library for Solving Differential Equations
- Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networks
- fPINNs: Fractional Physics-Informed Neural Networks
- Generalized finite-difference time-domain method with absorbing boundary conditions for solving the nonlinear Schrödinger equation on a GPU
This page was built for publication: A New Artificial Neural Network Method for Solving Schrödinger Equations on Unbounded Domains
