25 citations · 68 across the 9 of their papers we have counts for
9 papers
Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves
Christian Offen, Sina Ober-Blöbaum
The article shows how to learn models of dynamical systems from data which are governed by an unknown variational PDE. Rather than employing reduction techniques, we learn a discre…
Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery
Yana Lishkova, Paul Scherer, Steffen Ridderbusch +4
By one of the most fundamental principles in physics, a dynamical system will exhibit those motions which extremise an action functional. This leads to the formation of the Euler-L…
Symplectic integration of learned Hamiltonian systems
Christian Offen, Sina Ober-Blöbaum
Hamiltonian systems are differential equations which describe systems in classical mechanics, plasma physics, and sampling problems. They exhibit many structural properties, such a…
Efficient time stepping for numerical integration using reinforcement learning
Michael Dellnitz, Eyke Hüllermeier, Marvin Lücke +4
Many problems in science and engineering require an efficient numerical approximation of integrals or solutions to differential equations. For systems with rapidly changing dynamic…
Learning ODE Models with Qualitative Structure Using Gaussian Processes
Steffen Ridderbusch, Christian Offen, Sina Ober-Blöbaum +1
Recent advances in learning techniques have enabled the modelling of dynamical systems for scientific and engineering applications directly from data. However, in many contexts exp…
Backward error analysis for variational discretisations of partial differential equations
Robert I McLachlan, Christian Offen
In backward error analysis, an approximate solution to an equation is compared to the exact solution to a nearby modified equation. In numerical ordinary differential equations, th…
Local intersections of Lagrangian manifolds correspond to catastrophe theory
Christian Offen
Two smooth map germs are right-equivalent if and only if they generate two Lagrangian submanifolds in a cotangent bundle which have the same contact with the zero-section. In this…
Symplectic integration of boundary value problems
Robert I McLachlan, Christian Offen
Symplectic integrators can be excellent for Hamiltonian initial value problems. Reasons for this include their preservation of invariant sets like tori, good energy behaviour, none…
Preservation of bifurcations of Hamiltonian boundary value problems under discretisation
Robert I McLachlan, Christian Offen
We show that symplectic integrators preserve bifurcations of Hamiltonian boundary value problems and that nonsymplectic integrators do not. We provide a universal description of th…