Related papers: Variational Learning of Euler-Lagrange Dynamics fr…
A variational method is used to derive a self-consistent macro-particle model for relativistic electromagnetic kinetic plasma simulations. Extending earlier work [E. G. Evstatiev and B. A. Shadwick, J. Comput. Phys., vol. 245, pp. 376-398,…
A dual formalism for Lagrange multipliers is developed. The formalism is used to minimize an action function $S(q_2,q_1,T)$ without any dynamical input other than that $S$ is convex. All the key equations of analytical mechanics -- the…
Model generalization of the underlying dynamics is critical for achieving data efficiency when learning for robot control. This paper proposes a novel approach for learning dynamics leveraging the symmetry in the underlying robotic system,…
We present the principle of virtual action as a foundation of continuum mechanics. Used mainly in relativity, the method has a useful application in classical mechanics and places the notion of action as the basic concept of dynamics. The…
We propose to compute approximations to general invariant sets in dynamical systems by minimizing the distance between an appropriately selected finite set of points and its image under the dynamics. We demonstrate, through computational…
High dimensional time series are endemic in applications of machine learning such as robotics (sensor data), computational biology (gene expression data), vision (video sequences) and graphics (motion capture data). Practical nonlinear…
Temporal variations in biological systems and more generally in natural sciences are typically modelled as a set of Ordinary, Partial, or Stochastic Differential or Difference Equations. Algorithms for learning the structure and the…
Human mobility, enabled by diverse transportation modes, is fundamental to urban functionality. Studying these movements across scales-from microscopic to macroscopic-yields valuable insights into urban dynamics. Local adaptation and…
We construct several variational integrators--integrators based on a discrete variational principle--for systems with Lagrangians of the form L = L_A + epsilon L_B, with epsilon << 1, where L_A describes an integrable system. These…
We develop in this paper a new framework for discrete calculus of variations when the actions have densities involving an arbitrary discretization operator. We deduce the discrete Euler-Lagrange equations for piecewise continuous critical…
We propose a thermodynamics-based learning strategy for non-equilibrium evolution equations based on Onsager's variational principle, which allows to write such PDEs in terms of two potentials: the free energy and the dissipation potential.…
We investigate the existence of minimizers of variational models with Eulerian-Lagrangian formulations. We consider energy functionals depending on the deformation of a body, defined on its reference configuration, and an Eulerian map…
This paper is devoted to the study of directional minimal time functions that specify the minimal time for a vector to reach an object following its given direction. We provide a careful analysis of general and generalized differentiation…
We propose a systematic method for learning stable and physically interpretable dynamical models using sampled trajectory data from physical processes based on a generalized Onsager principle. The learned dynamics are autonomous ordinary…
Time-invariant linear dynamical system arises in many real-world applications,and its usefulness is widely acknowledged. A practical limitation with this model is that its latent dimension that has a large impact on the model capability…
There is a growing attention given to utilizing Lagrangian and Hamiltonian mechanics with network training in order to incorporate physics into the network. Most commonly, conservative systems are modeled, in which there are no frictional…
We study the evolution of observables of dynamical systems. For linear systems, we show that observables satisfy a closed differential equation whose minimal order is determined by the dynamical system and observation operator. This yields…
This paper is a contribution to the general program of embedding theories of dynamical systems. Following our previous work on the Stochastic embedding theory developed with S. Darses, we define the fractional embedding of differential…
This paper is concerned with analyzing a class of fractional calculus of variations problems and their associated Euler-Lagrange (fractional differential) equations. Unlike the existing fractional calculus of variations which is based on…
Hydrodynamic equations for a one-component plasma are derived as a generalization of the Euler equations to include the effects of the long-range Coulomb interaction. By using a variational principle, these equations self-consistently unify…