Incorporating prior knowledge of physics laws and structural properties of dynamical
systems into the design of deep learning architectures has proven to be a powerful …

It was shown recently by W. Su, S. Boyd, and E. Candes, J. Mach. Learn. Res., 17 (2016),
pp. 1--43 that Nesterov's accelerated gradient method for minimizing a smooth convex …

Geometric numerical integration has recently been exploited to design symplectic
accelerated optimization algorithms by simulating the Bregman Lagrangian and Hamiltonian …

Neural differential equations offer a powerful approach for learning dynamics from data.
However, they do not impose known constraints that should be obeyed by the learned …

Motivated by recent developments in Hamiltonian variational principles, Hamiltonian
variational integrators, and their applications such as to optimization and control, we present …

This article considers the problem of modeling mechanical systems using classical
integrators, such as Runge-Kutta method or explicit Euler method, associated with the decay …

In this paper, explicit stable integrators based on symplectic and contact geometries are
proposed for a family of non-autonomous ordinarily differential equations (ODEs) found in …

Symplectic numerical integrators for Hamiltonian systems form the paramount class of
geometric numerical integrators, and have been very well investigated in the past forty …

Recent research on accelerated gradient methods of use in optimization has demonstrated
that these methods can be derived as discretizations of dynamical systems. This, in turn, has …