15 citations · 63 across the 15 of their papers we have counts for
15 papers
Numerical approaches to entangling dynamics from variational principles
Christian Offen, Boris Wembe, Laura Ares +2
In this work, we address the numerical identification of entanglement in dynamical scenarios. To this end, we consider different programs based on the restriction of the evolution…
Multiphoton, multimode state classification for nonlinear optical circuits
Denis A. Kopylov, Christian Offen, Laura Ares +5
We introduce a new classification of multimode states with a fixed number of photons. This classification is based on the factorizability of homogeneous multivariate polynomials an…
Adaptive higher order reversible integrators for memory efficient deep learning
Sofya Maslovskaya, Sina Ober-Blöbaum, Christian Offen +2
The depth of networks plays a crucial role in the effectiveness of deep learning. However, the memory requirement for backpropagation scales linearly with the number of layers, whi…
Commutator-free Cayley methods
Boris Wembe, Christian Offen, Sofya Maslovskaya +2
Differential equations posed on quadratic matrix Lie groups arise in the context of classical mechanics and quantum dynamical systems. Lie group numerical integrators preserve the…
Machine learning of discrete field theories with guaranteed convergence and uncertainty quantification
Christian Offen
We introduce a method based on Gaussian process regression to identify discrete variational principles from observed solutions of a field theory. The method is based on the data-ba…
Machine learning of continuous and discrete variational ODEs with convergence guarantee and uncertainty quantification
Christian Offen
The article introduces a method to learn dynamical systems that are governed by Euler--Lagrange equations from data. The method is based on Gaussian process regression and identifi…
Learning of discrete models of variational PDEs from data
Christian Offen, Sina Ober-Blöbaum
We show how to learn discrete field theories from observational data of fields on a space-time lattice. For this, we train a neural network model of a discrete Lagrangian density s…
Hamiltonian Neural Networks with Automatic Symmetry Detection
Eva Dierkes, Christian Offen, Sina Ober-Blöbaum +1
Recently, Hamiltonian neural networks (HNN) have been introduced to incorporate prior physical knowledge when learning the dynamical equations of Hamiltonian systems. Hereby, the s…
Backward error analysis for conjugate symplectic methods
Robert I McLachlan, Christian Offen
The numerical solution of an ordinary differential equation can be interpreted as the exact solution of a nearby modified equation. Investigating the behaviour of numerical solutio…
Variational Learning of Euler-Lagrange Dynamics from Data
Sina Ober-Blöbaum, Christian Offen
The principle of least action is one of the most fundamental physical principle. It says that among all possible motions connecting two points in a phase space, the system will exh…
Bifurcation preserving discretisations of optimal control problems
Christian Offen, Sina Ober-Blöbaum
The first order optimality conditions of optimal control problems (OCPs) can be regarded as boundary value problems for Hamiltonian systems. Variational or symplectic discretisatio…
Detection of high codimensional bifurcations in variational PDEs
Lisa Maria Kreusser, Robert I McLachlan, Christian Offen
We derive bifurcation test equations for A-series singularities of nonlinear functionals and, based on these equations, we propose a numerical method for detecting high codimension…
Symplectic integration of PDEs using Clebsch variables
Robert I McLachlan, Christian Offen, Benjamin K Tapley
Many PDEs (Burgers' equation, KdV, Camassa-Holm, Euler's fluid equations,...) can be formulated as infinite-dimensional Lie-Poisson systems. These are Hamiltonian systems on manifo…
Hamiltonian boundary value problems, conformal symplectic symmetries, and conjugate loci
Robert I McLachlan, Christian Offen
In this paper we continue our study of bifurcations of solutions of boundary-value problems for symplectic maps arising as Hamiltonian diffeomorphisms. These have been shown to be…
Bifurcation of solutions to Hamiltonian boundary value problems
Robert I McLachlan, Christian Offen
A bifurcation is a qualitative change in a family of solutions to an equation produced by varying parameters. In contrast to the local bifurcations of dynamical systems that are of…