Momentum-based gradient descent methods for Lie groups

no code implementations • 14 Apr 2024 • Cédric M. Campos, David Martín de Diego, José Torrente

Polyak's Heavy Ball (PHB; Polyak, 1964), a. k. a.

Designing Poisson Integrators Through Machine Learning

no code implementations • 29 Mar 2024 • Miguel Vaquero, David Martín de Diego, Jorge Cortés

This paper presents a general method to construct Poisson integrators, i. e., integrators that preserve the underlying Poisson geometry.

Completeness of Riemannian metrics: an application to the control of constrained mechanical systems

no code implementations • 25 Nov 2023 • José Ángel Acosta, Anthony Bloch, David Martín de Diego

We introduce a mathematical technique based on modifying a given Riemannian metric and we investigate its applicability to controlling and stabilizing constrained mechanical systems.

Symmetry Preservation in Hamiltonian Systems: Simulation and Learning

no code implementations • 30 Aug 2023 • Miguel Vaquero, Jorge Cortés, David Martín de Diego

This work presents a general geometric framework for simulating and learning the dynamics of Hamiltonian systems that are invariant under a Lie group of transformations.

Variational integrators for non-autonomous systems with applications to stabilization of multi-agent formations

no code implementations • 3 Feb 2022 • Leonardo Colombo, Manuela Gamonal Fernández, David Martín de Diego

Numerical methods that preserve geometric invariants of the system, such as energy, momentum or the symplectic form, are called geometric integrators.

A Discrete Variational Derivation of Accelerated Methods in Optimization

no code implementations • 4 Jun 2021 • Cédric M. Campos, Alejandro Mahillo, David Martín de Diego

Many of the new developments in machine learning are connected with gradient-based optimization methods.