8 papers
Dirac Structures and Reduction of Optimal Control Problems with Symmetries
A. Ibort, M. Leok, R. Salmoni +1
We study the symmetry reduction of optimal control problems using Dirac structures. The first-order conditions of the Pontryagin Maximum Principle are written as an implicit Dirac…
A Morse-Family Integrator for Hamilton--Jacobi Dynamics Across Caustics
F. Jiménez Alburquerque, M. Leok, C. Sardón +1
We develop a geometric framework for implicit discrete Hamiltonian systems based on discrete Morse families, Lagrangian relations, and discrete analogues of Tulczyjew's triple. The…
Symplectic Neural Networks for Learning Non-Separable Hamiltonians
Harsh Choudhary, Vyacheslav Kungurtsev, Chandan Gupta +2
Hamiltonian Neural Networks (HNNs) integrate physical priors into neural models by learning a system's Hamiltonian, improving generalization and sample efficiency. Identifying the…
Noether-Type Theorems and the Generalized Herglotz Principle in -Contact Geometry
Melvin Leok, Cristina Sardón, Xuefeng Zhao
We develop a unified geometric framework for dissipative mechanical systems based on uniform -contact manifolds, which provide an extended phase space equipped with multiple con…
Integration on -Cosymplectic Manifolds
M. Leok, C. Sardón, X. Zhao
This paper presents a unified framework for studying dynamics and integration on -cosymplectic manifolds. After outlining the geometric foundations of -cosymplectic structure…
q-Cosymplectic Geometry, Integrability and Reduction
Melvin Leok, Cristina Sardón, Xuefeng Zhao
In the present paper, we define the concept of a \( q \)-cosymplectic manifold, on which we study the Hamiltonian, gradient, local gradient, and \( q \)-evolution vector fields. Se…
Learning Generalized Hamiltonians using fully Symplectic Mappings
Harsh Choudhary, Chandan Gupta, Vyacheslav Kungurtsev +2
Many important physical systems can be described as the evolution of a Hamiltonian system, which has the important property of being conservative, that is, energy is conserved thro…
Nearly-periodic maps and geometric integration of noncanonical Hamiltonian systems
J. W. Burby, E. Hirvijoki, M. Leok
M. Kruskal showed that each continuous-time nearly-periodic dynamical system admits a formal symmetry, generated by the so-called roto-rate. When the nearly-periodic system…