Structure-preserving deep learning
From MaRDI portal
Publication:5014474
DOI10.1017/S0956792521000139WikidataQ124988461 ScholiaQ124988461MaRDI QIDQ5014474
Christian Etmann, Carola-Bibiane Schönlieb, Ferdia Sherry, Elena Celledoni, Brynjulf Owren, Matthias J. Ehrhardt, Robert I. Mclachlan
Publication date: 8 December 2021
Published in: European Journal of Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2006.03364
Artificial neural networks and deep learning (68T07) Numerical methods for ordinary differential equations (65Lxx) Numerical methods in optimal control (49Mxx) Numerical methods for mathematical programming, optimization and variational techniques (65Kxx)
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Cites Work
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- Continuum limit of total variation on point clouds
- Geometric integration of non-autonomous linear Hamiltonian problems
- Neural learning by geometric integration of reduced `rigid-body' equations
- An introduction to Lie group integrators - basics, new developments and applications
- Runge-Kutta methods in optimal control and the transformed adjoint system
- Forward stability of ResNet and its variants
- Deep neural networks motivated by partial differential equations
- Deep learning as optimal control problems: models and numerical methods
- A mean-field optimal control formulation of deep learning
- Shape analysis on Lie groups with applications in computer animation
- Geometry of matrix decompositions seen through optimal transport and information geometry
- Second order conformal symplectic schemes for damped Hamiltonian systems
- A proposal on machine learning via dynamical systems
- Inverse Problems
- log det A = tr log A
- Flat Minima
- Solving Ordinary Differential Equations I
- Generalized canonical transformations for time-dependent systems
- Splitting methods
- Geometric integration using discrete gradients
- Trust Region Methods
- Stable architectures for deep neural networks
- Optimal Approximation with Sparsely Connected Deep Neural Networks
- Layer-Parallel Training of Deep Residual Neural Networks
- Port-Hamiltonian Systems Theory: An Introductory Overview
- Total Variation Regularization for Manifold-Valued Data
- Solving Ordinary Differential Equations II
- Analysis of the BFGS Method with Errors
- Equivalence of approximation by convolutional neural networks and fully-connected networks
- Solving inverse problems using data-driven models
- Neural networks and physical systems with emergent collective computational abilities.
- Geometric Numerical Integration
- Understanding Machine Learning
- Stochastic Quasi-Newton Methods for Nonconvex Stochastic Optimization
- A stochastic estimator of the trace of the influence matrix for laplacian smoothing splines
- A Stochastic Approximation Method
- Conformal symplectic and relativistic optimization
- Approximation by superpositions of a sigmoidal function
- Riemannian geometry
- Conformal Hamiltonian systems
