Artificial neural network approximations of Cauchy inverse problem for linear PDEs
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Publication:2247118
DOI10.1016/j.amc.2021.126678OpenAlexW3206803216WikidataQ114210967 ScholiaQ114210967MaRDI QIDQ2247118
Publication date: 16 November 2021
Published in: Applied Mathematics and Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.amc.2021.126678
Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Numerical methods for partial differential equations, boundary value problems (65Nxx) Miscellaneous topics in partial differential equations (35Rxx)
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Radial basis function neural network (RBFNN) approximation of Cauchy inverse problems of the Laplace equation ⋮ An artificial neural network approach to identify the parameter in a nonlinear subdiffusion model
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Cites Work
- Unnamed Item
- A variational-type method of fundamental solutions for a Cauchy problem of Laplace's equation
- Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems
- Numerical solution for high order differential equations using a hybrid neural network-optimization method
- Two regularization methods for the Cauchy problems of the Helmholtz equation
- An alternating iterative algorithm for the Cauchy problem associated to the Helmholtz equation
- Numerical linear algebra for reconstruction inverse problems.
- Multilayer feedforward networks are universal approximators
- Multiscale topology optimization using neural network surrogate models
- DGM: a deep learning algorithm for solving partial differential equations
- Iterative Tikhonov regularization for the Cauchy problem for the Helmholtz equation
- An accelerated alternating procedure for the Cauchy problem for the Helmholtz equation
- Adaptive multi-fidelity polynomial chaos approach to Bayesian inference in inverse problems
- Data driven governing equations approximation using deep neural networks
- PDE-Net 2.0: learning PDEs from data with a numeric-symbolic hybrid deep network
- A machine learning framework for data driven acceleration of computations of differential equations
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- An inverse time-dependent source problem for a time-space fractional diffusion equation
- Uniqueness of solutions of the Cauchy problem for parabolic equations
- Hierarchical Bayesian inference for ill-posed problems via variational method
- Backus-Gilbert algorithm for the Cauchy problem of the Laplace equation
- Solution of the Cauchy problem using iterated Tikhonov regularization
- Augmented Tikhonov regularization
- Approximations for a Cauchy problem for the heat equation
- A Computational Quasi-Reversibility Method for Cauchy Problems for Laplace’s Equation
- Stability and Regularization of a Discrete Approximation to the Cauchy Problem for Laplace's Equation
- Neural‐network‐based approximations for solving partial differential equations
- The Cauchy problem for Laplace's equation via the conjugate gradient method
- A dynamical regularization algorithm for solving inverse source problems of elliptic partial differential equations
- Solving the quantum many-body problem with artificial neural networks
- Convergence of an Alternating Method to Solve the Cauchy Problem for Poisson's Equation
- A novel coupled complex boundary method for solving inverse source problems
- Tikhonov Regularization by a Reproducing Kernel Hilbert Space for the Cauchy Problem for an Elliptic Equation
- fPINNs: Fractional Physics-Informed Neural Networks
- SwitchNet: A Neural Network Model for Forward and Inverse Scattering Problems
- Solving a Cauchy problem for a 3D elliptic PDE with variable coefficients by a quasi-boundary-value method
- A mixed formulation of quasi-reversibility to solve the Cauchy problem for Laplace's equation
- Convergence analysis for finite element approximation to an inverse Cauchy problem
- The Cauchy Problem for the Heat Equation
- Inverse problems for partial differential equations
- Approximation by superpositions of a sigmoidal function
- Neural network method for solving partial differential equations
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