Related papers: Symplectic Neural Flows for Modeling and Discovery

The guiding center approximation represents a very powerful tool for analyzing and modeling a charged particle motion in strong magnetic fields. This approximation is based on conservation of the adiabatic invariant, magnetic moment.…

An explicit high-order noncanonical symplectic algorithm for ideal two-fluid systems is developed. The fluid is discretized as particles in the Lagrangian description, while the electromagnetic fields and internal energy are treated as…

Simulating trajectories of dynamical systems is a fundamental problem in a wide range of fields such as molecular dynamics, biochemistry, and pedestrian dynamics. Machine learning has become an invaluable tool for scaling physics-based…

In this paper we will explore fundamental constraints on the evolution of certain symplectic subvolumes possessed by any Hamiltonian phase space. This research has direct application to optimal control and control of conservative mechanical…

The dynamics of physical systems is often constrained to lower dimensional sub-spaces due to the presence of conserved quantities. Here we propose a method to learn and exploit such symmetry constraints building upon Hamiltonian Neural…

We present a new existence mechanism, based on symplectic topology, for orbits of Hamiltonian flows connecting a pair of disjoint subsets in the phase space. The method involves function theory on symplectic manifolds combined with rigidity…

We describe a symplectic approach towards thermodynamics in which thermodynamic transformations are described by (symplectic) Hamiltonian dynamics. Upon identifying the spaces of equilibrium states with Lagrangian submanifolds of a…

Modern learning systems act on internal representations of data, yet how these representations encode underlying physical or statistical structure is often left implicit. In physics, conservation laws of Hamiltonian systems such as…

This paper presents a mathematically rigorous framework for brain-inspired representation learning founded on the interplay between persistent topological structures and cohomological flows. Neural computation is reformulated as the…

Dynamists have been studying Hamiltonian systems for a long time. However, many physical systems are dissipative and do not preserve a symplectic form. This is the case, for example, with systems involving friction, which multiply the…

We present SymFlux, a novel deep learning framework that performs symbolic regression to identify Hamiltonian functions from their corresponding vector fields on the standard symplectic plane. SymFlux models utilize hybrid CNN-LSTM…

We present the Hamiltonian formalism for the Euler equation of symplectic fluids, introduce symplectic vorticity, and study related invariants. In particular, this allows one to extend D.Ebin's long-time existence result for geodesics on…

We propose a parametric hyperbolic conservation law (SymCLaw) for learning hyperbolic systems directly from data while ensuring conservation, entropy stability, and hyperbolicity by design. Unlike existing approaches that typically enforce…

While Hamiltonian mechanics provides a powerful inductive bias for neural networks modeling dynamical systems, Hamiltonian Neural Networks and their variants often fail to capture complex temporal dynamics spanning multiple timescales. This…

Symplectic integrators for Hamiltonian systems have been quite successful for studying few-body dynamical systems. These integrators are frequently derived using a formalism built on symplectic maps. There have been recent efforts to extend…

Relativistic dynamics of a charged particle in time-dependent electromagnetic fields has theoretical significance and a wide range of applications. It is often multi-scale and requires accurate long-term numerical simulations using…

This paper introduces equivariant hamiltonian flows, a method for learning expressive densities that are invariant with respect to a known Lie-algebra of local symmetry transformations while providing an equivariant representation of the…

Neural networks are a central technique in machine learning. Recent years have seen a wave of interest in applying neural networks to physical systems for which the governing dynamics are known and expressed through differential equations.…

The high volatility of renewable energies calls for more energy efficiency. Thus, different physical systems need to be coupled efficiently although they run on various time scales. Here, the port-Hamiltonian (pH) modeling framework comes…

The existence of explicit symplectic integrators for general nonseparable Hamiltonian systems is an open and important problem in both numerical analysis and computing in science and engineering, as explicit integrators are usually more…