Learning-informed parameter identification in nonlinear time-dependent PDEs
From MaRDI portal
Publication:6073849
DOI10.1007/s00245-023-10044-yarXiv2202.10915MaRDI QIDQ6073849
Martin Holler, Christian Aarset, Tram Thi Ngoc Nguyen
Publication date: 18 September 2023
Published in: Applied Mathematics and Optimization (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2202.10915
neural networksparameter identificationnonlinearityTikhonov regularizationmachine learningPDEsall-at-once formulation
Related Items (2)
Relaxation approach for learning neural network regularizers for a class of identification problems ⋮ On the identification and optimization of nonsmooth superposition operators in semilinear elliptic PDEs
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Discovering governing equations from data by sparse identification of nonlinear dynamical systems
- Local convergence of the steepest descent method in Hilbert spaces
- Iterative regularization methods for nonlinear ill-posed problems
- Nonlinear hemivariational inequalities with eigenvalues near zero
- Semigroups of linear operators and applications to partial differential equations
- Multilayer feedforward networks are universal approximators
- Optimal control of a non-smooth semilinear elliptic equation
- Design of the monodomain model by artificial neural networks
- The modern mathematics of deep learning
- Preconditioned all-at-once methods for large, sparse parameter estimation problems
- Regularization Based on All-At-Once Formulations for Inverse Problems
- Integration based profile likelihood calculation for PDE constrained parameter estimation problems
- The Tangential Cone Condition for Some Coefficient Identification Model Problems in Parabolic PDEs
- Coupled regularization with multiple data discrepancies
- Landweber–Kaczmarz for parameter identification in time-dependent inverse problems: all-at-once versus reduced version
- Learning partial differential equations via data discovery and sparse optimization
- All-at-once versus reduced iterative methods for time dependent inverse problems
- Optimization with learning-informed differential equation constraints and its applications
- MultiComposite Nonconvex Optimization for Training Deep Neural Networks
- Deep Network Approximation for Smooth Functions
- Solving inverse problems using data-driven models
- A convergence rates result for Tikhonov regularization in Banach spaces with non-smooth operators
- Goal oriented adaptivity in the IRGNM for parameter identification in PDEs: II. all-at-once formulations
- Neural network approximation
- Nonlinear partial differential equations with applications
- An introduction to the mathematical theory of inverse problems
This page was built for publication: Learning-informed parameter identification in nonlinear time-dependent PDEs
