73 citations · 670 across the 56 of their papers we have counts for
63 papers
Learning Hamiltonians from Trajectory Data with Kernel Methods
Jianyu Hu, David Martin de Diego, Juan-Pablo Ortega +1
We study the recovery of a Hamiltonian from discrete trajectory observations using structure-preserving kernel methods. When exact-flow data are fitted through a symplectic one-ste…
A Unified Discrete Gradient-SAV Framework for Structure-Preserving Integration
Elena Celledoni, David Martín de Diego, Brynjulf Owren +1
We present a framework combining discrete gradient (DG) methods with the Scalar Auxiliary Variable (SAV) approach to construct structure-preserving integrators for dissipative and…
Discrete-time generalized canonical transformations for non-autonomous systems
Leonardo Colombo, David Martin de Diego, Riccardo Muradore +2
A dynamical system is said to be \emph{non-autonomous} when the differential equations describing its evolution depends explicitly on time. Among the various geometric approaches t…
Learning Forced Multibody Dynamics on Lie Groups
Martine Dyring Hansen, Marta Ghirardelli, Elena Celledoni +2
We propose an architecture for learning the dynamics of mechanical systems based on discrete forced Euler-Lagrange equations on Lie groups using only position data. By formulating…
Variational Inverse Problems for Second Order ODEs with and without Constraints
G. E. Prince, T. Mestdag, D. Martin de Diego
Many physical systems with or without nonholonomic constraints have a Lagrangian description. In the first case, the Lagrangian model can be represented by second-order ODEs that a…
Constructing Dynamic Feedback Linearizable Discretizations
Ashutosh Jindal, Florentina Nicolau, David Martin Diego +1
Dynamic feedback linearization-based methods allow us to design control algorithms for a fairly large class of nonlinear systems in continuous time. However, this feature does not…
Momentum-based gradient descent methods for Lie groups
Cédric M. Campos, David Martín de Diego, José Torrente-Teruel
Polyak's Heavy Ball (PHB; Polyak, 1964), a.k.a. Classical Momentum, and Nesterov's Accelerated Gradient (NAG; Nesterov, 1983) are well-established momentum-descent methods for opti…
Designing Poisson Integrators Through Machine Learning
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. We assume the Poisson manifold is integrable…
From retraction maps to symplectic-momentum numerical integrators
María Barbero-Liñán, Juan Carlos Marrero, David Martín de Diego
Retraction maps have been generalized to discretization maps in (Barbero Liñán and and Mart\'ın de Diego, 2022). Discretization maps are used to systematically derive numerical int…
Metriplectic Euler-Poincaré equations: smooth and discrete dynamics
Anthony Bloch, Marta Farré Puiggalí, David Martín de Diego
In this paper we will study some interesting properties of modifications of the Euler-Poincaré equations when we add a special type of dissipative force, so that the equations of m…
Completeness of Riemannian metrics: an application to the control of constrained mechanical systems
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 system…
Symmetry Preservation in Hamiltonian Systems: Simulation and Learning
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. This means…
A new perspective on symplectic integration of constrained mechanical systems via discretization maps
María Barbero Liñán, David Martín de Diego, Rodrigo T. Sato Martín de Almagro
A new geometric procedure to construct symplectic methods for constrained mechanical systems is developed in this paper. The definition of a map coming from the notion of retractio…
Higher-order retraction maps and construction of numerical methods for optimal control of mechanical systems
Alexandre Anahory Simoes, Maria Barbero Liñán, Leonardo Colombo +1
Retractions maps are used to define a discretization of the tangent bundle of the configuration manifold as two copies of the configuration manifold where the dynamics take place.…
Discrete gradient methods for irreversible port-Hamiltonian systems
Alexandre Anahory Simoes, David Martín de Diego, Bernhard Maschke
In this paper we introduce discrete gradient methods to discretize irreversible port-Hamiltonian systems showing that the main qualitative properties of the continuous system are p…
A parallel iterative method for variational integration
Sebastián J. Ferraro, David Martín de Diego, Rodrigo Takuro Sato Martín de Almagro
Discrete variational methods show excellent performance in numerical simulations of different mechanical systems. In this paper, we introduce an iterative procedure for the solutio…
A Discrete Variational Derivation of Accelerated Methods in Optimization
Cédric M. Campos, Alejandro Mahillo, David Martín de Diego
Many of the new developments in machine learning are connected with gradient-based optimization methods. Recently, these methods have been studied using a variational perspective.…
Retraction maps: a seed of geometric integrators
María Barbero Liñán, David Martín de Diego
The classical notion of retraction map used to approximate geodesics is extended and rigorously defined to become a powerful tool to construct geometric integrators and it is calle…
On the geometry of discrete contact mechanics
Alexandre Anahory Simoes, David Martín de Diego, Manuel de León +1
In this paper, we continue the construction of variational integrators adapted to contact geometry started in \cite{VBS}, in particular, we introduce a discrete Herglotz Principle…
Optimal Trajectory Tracking of Nonholonomic Mechanical Systems: a geometric approach
Aradhana Nayak, Rodrigo Sato Martín de Almagro, Leonardo Colombo +1
We study the tracking of a trajectory for a nonholonomic system by recasting the problem as an optimal control problem. The cost function is chosen to minimize the error in positio…
High-order geometric methods for nonholonomic mechanical systems
David Martín de Diego, Rodrigo T. Sato Martín de Almagro
In the last two decades, significant effort has been put in understanding and designing so-called structure-preserving numerical methods for the simulation of mechanical systems. G…
Lie-Poisson integrators
David Martin de Diego
In this paper, we discuss the geometric integration of hamiltonian systems on Poisson manifolds, in particular, in the case, when the Poisson structure is induced by a Lie algebra,…
Variational order for forced Lagrangian systems
D. Martín de Diego, R. Sato Martín de Almagro
We are able to derive the equations of motion for forced mechanical systems in a purely variational setting, both in the context of Lagrangian or Hamiltonian mechanics, by duplicat…
The interplay between Dirac systems, Morse families and Interconnection
M. Barbero-Liñán, H. Cendra, E. García-Toraño Andrés +1
We provide a generalization of the notion of Dirac system by using Morse families to intrinsically embrace the dynamics associated with different physical systems such as constrain…