HomPINNs: Homotopy physics-informed neural networks for learning multiple solutions of nonlinear elliptic differential equations
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Publication:2172562
DOI10.1016/j.camwa.2022.07.002OpenAlexW4285982480WikidataQ114952697 ScholiaQ114952697MaRDI QIDQ2172562
Wenrui Hao, Yao Huang, Guang Lin
Publication date: 16 September 2022
Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.camwa.2022.07.002
homotopy methodmultiple solutionsmachine learningphysics-informed neural networksnonlinear elliptic differential equationdata-driven computation
Artificial neural networks and deep learning (68T07) Numerical computation of solutions to systems of equations (65H10) Reaction-diffusion equations (35K57) Research exposition (monographs, survey articles) pertaining to numerical analysis (65-02) Finite difference methods for boundary value problems involving PDEs (65N06)
Related Items (2)
HomPINNs: homotopy physics-informed neural networks for solving the inverse problems of nonlinear differential equations with multiple solutions ⋮ A novel numerical scheme for fractional differential equations using extreme learning machine
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Cites Work
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- A three-dimensional steady-state tumor system
- Nonlinear effects in economic dynamic models
- A robust and efficient method for steady state patterns in reaction-diffusion systems
- A numerical method for the study of nucleation of ordered phases
- Numerical solution of nonlinear Volterra-Fredholm integro-differential equations via direct method using triangular functions
- Rational Legendre pseudospectral approach for solving nonlinear differential equations of Lane-Emden type
- Variational methods for non-differentiable functionals and their applications to partial differential equations
- A new augmented singular transform and its partial Newton-correction method for finding more solutions
- Multilayer feedforward networks are universal approximators
- The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
- Approximation rates for neural networks with general activation functions
- DGM: a deep learning algorithm for solving partial differential equations
- Structure probing neural network deflation
- Physics-informed neural networks for solving forward and inverse flow problems via the Boltzmann-BGK formulation
- Parallel physics-informed neural networks via domain decomposition
- Physics-informed neural networks for inverse problems in supersonic flows
- Physics-informed neural networks for high-speed flows
- Conservative physics-informed neural networks on discrete domains for conservation laws: applications to forward and inverse problems
- Adaptive activation functions accelerate convergence in deep and physics-informed neural networks
- A bootstrapping approach for computing multiple solutions of differential equations
- A homotopy method with adaptive basis selection for computing multiple solutions of differential equations
- Spatial pattern formation in reaction-diffusion models: a computational approach
- An adaptive homotopy method for computing bifurcations of nonlinear parametric systems
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- Nonlinear simulations of solid tumor growth using a mixture model: invasion and branching
- Numerical algebraic geometry
- Structure of multiple solutions for nonlinear differential equations
- A bifurcation method for solving multiple positive solutions to the boundary value problem of the Hénon equation on a unit disk
- Recent Developments in Numerical Methods for Fully Nonlinear Second Order Partial Differential Equations
- Spectral Methods
- Numerical algebraic geometry and algebraic kinematics
- Monge Ampère Equation: Applications to Geometry and Optimization
- Neural‐network‐based approximations for solving partial differential equations
- Parallel Newton--Krylov--Schwarz Algorithms for the Transonic Full Potential Equation
- Introduction to Numerical Continuation Methods
- Two-Level Spectral Methods for Nonlinear Elliptic Equations with Multiple Solutions
- Nonlinearly Preconditioned Inexact Newton Algorithms
- A Product-Decomposition Bound for Bezout Numbers
- A review of numerical methods for nonlinear partial differential equations
- Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks
- Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations
- Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks
- fPINNs: Fractional Physics-Informed Neural Networks
- The Numerical Solution of Systems of Polynomials Arising in Engineering and Science
- Deflation Techniques for Finding Distinct Solutions of Nonlinear Partial Differential Equations
- Boundary integral methods for multicomponent fluids and multiphase materials.
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