We introduce a method for training exactly conservative physics-informed neural networks
and physics-informed deep operator networks for dynamical systems, that is, for ordinary …

The main result of this paper is the discretization of second-order Hamiltonian systems of the
form $\ddot x=-K\nabla W (x) $, where K is a constant symmetric matrix and …

We develop a variational integrator for the shallow‐water equations on a rotating sphere.
The variational integrator is built around a discretization of the continuous Euler–Poincaré …

We present a machine learning based method for learning first integrals of systems of
ordinary differential equations from given trajectory data. The method is model-agnostic in …

This work proposes a suite of numerical techniques to facilitate the design of structure-
preserving integrators for nonlinear dynamics, with particular emphasis on many-body …

We show the arbitrarily long-term stability of conservative methods for autonomous ODEs.
Given a system of autonomous ODEs with conserved quantities, if the preimage of the …

A new technique has been recently introduced to define finite difference schemes that
preserve local conservation laws. So far, this approach has been applied to find parametric …

We propose a novel algorithmic method for constructing invariant variational schemes of
systems of ordinary differential equations that are the Euler–Lagrange equations of a …

Conservative symmetric second–order one–step schemes are derived for dynamical
systems describing various many–body systems using the Discrete Multiplier Method. This …

In this paper we introduce a procedure, based on the method of equivariant moving frames,
for formulating continuous Galerkin finite element schemes that preserve the Lie point …