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The Calderón's problem via DeepONets - MaRDI portal

The Calderón's problem via DeepONets (Q6570540)

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scientific article; zbMATH DE number 7879436

Language	Label	Description	Also known as
English	The Calderón's problem via DeepONets	scientific article; zbMATH DE number 7879436

Statements

scholarly article

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The Calderón's problem via DeepONets (English)

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Nicolás Valenzuela

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Vietnam Journal of Mathematics

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publication date

10 July 2024

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zbMATH Keywords

inverse problems

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Calderón's problem

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deep learning

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operator learning

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approximation

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numerical analysis

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MaRDI profile type

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Singular solutions of elliptic equations and the determination of conductivity by boundary measurements

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Calderón's inverse conductivity problem in the plane

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Physics Informed Neural Networks (PINNs) For Approximating Nonlinear Dispersive PDEs

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Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations

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Overcoming the curse of dimensionality in the numerical approximation of Allen-Cahn partial differential equations via truncated full-history recursive multilevel Picard approximations

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Model reduction and neural networks for parametric PDEs

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Global Uniqueness in the Impedance-Imaging Problem for Less Regular Conductivities

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RECOVERING A POTENTIAL FROM PARTIAL CAUCHY DATA

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On an inverse boundary value problem

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GLOBAL UNIQUENESS FOR THE CALDERÓN PROBLEM WITH LIPSCHITZ CONDUCTIVITIES

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Deep learning schemes for parabolic nonlocal integro-differential equations

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The Kolmogorov infinite dimensional equation in a Hilbert space via deep learning methods

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Deep learning architectures for nonlinear operator functions and nonlinear inverse problems

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Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations

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Multilevel Picard iterations for solving smooth semilinear parabolic heat equations

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Solving electrical impedance tomography with deep learning

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Solving high-dimensional partial differential equations using deep learning

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Uniqueness in Calderón's problem for conductivities with unbounded gradient

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Uniqueness in Calderón's problem with Lipschitz conductivities

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Deep backward schemes for high-dimensional nonlinear PDEs

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Overcoming the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equations

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A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations

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The Calderón problem with partial data in two dimensions

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On uniqueness in inverse problems for semilinear parabolic equations

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The Calderón problem with partial data

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Determining conductivity by boundary measurements

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Error estimates for DeepONets: a deep learning framework in infinite dimensions

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NETT: solving inverse problems with deep neural networks

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Physics-informed neural networks for high-speed flows

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The Calderón problem for quasilinear elliptic equations

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Reconstructions from boundary measurements

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fPINNs: Fractional Physics-Informed Neural Networks

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Hidden physics models: machine learning of nonlinear partial differential equations

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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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DGM: a deep learning algorithm for solving partial differential equations

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A uniqueness theorem for an inverse boundary value problem in electrical prospection

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A global uniqueness theorem for an inverse boundary value problem

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Electrical impedance tomography and Calderón's problem

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Error bounds for approximations with deep ReLU networks

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Identifiers

zbMATH Open document ID

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Mathematics Subject Classification ID

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zbMATH DE Number

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10.1007/S10013-023-00674-8

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Sitelinks

Mathematics(1 entry)

mardi Publication:6570540

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