Structure-preserving deep learning

Analysis of the BFGS Method with Errors

(2020) Yuchen Xie et al.   SIAM JOURNAL ON OPTIMIZATION

Conformal symplectic and relativistic optimization

(2020) Guilherme França et al.   JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT

Solving inverse problems using data-driven models

(2019) Simon Arridge et al.   ACTA NUMERICA

Forward Stability of ResNet and Its Variants

(2019) Linan Zhang et al.   JOURNAL OF MATHEMATICAL IMAGING AND VISION

Equivalence of approximation by convolutional neural networks and fully-connected networks

(2019) Philipp Petersen et al.   PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY

Stable architectures for deep neural networks

(2017) Eldad Haber et al.   INVERSE PROBLEMS

Stochastic Quasi-Newton Methods for Nonconvex Stochastic Optimization

(2017) Xiao Wang et al.   SIAM JOURNAL ON OPTIMIZATION

Shape analysis on Lie groups with applications in computer animation

(2016) Elena Celledoni et al.   Journal of Geometric Mechanics

Geometric integration of non-autonomous linear Hamiltonian problems

(2015) Håkon Marthinsen et al.   ADVANCES IN COMPUTATIONAL MATHEMATICS

Continuum Limit of Total Variation on Point Clouds

(2015) Nicolás García Trillos et al.   ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS

Second Order Conformal Symplectic Schemes for Damped Hamiltonian Systems

(2015) Ashish Bhatt et al.   JOURNAL OF SCIENTIFIC COMPUTING

Deep learning

(2015) Yann LeCun et al.   NATURE

Total Variation Regularization for Manifold-Valued Data

(2014) Andreas Weinmann et al.   SIAM Journal on Imaging Sciences

An introduction to Lie group integrators – basics, new developments and applications

(2013) Elena Celledoni et al.   JOURNAL OF COMPUTATIONAL PHYSICS