Related papers: Learning of Hamiltonian Dynamics with Reproducing …

We introduce a novel numerical method to integrate partial differential equations representing the Hamiltonian dynamics of field theories. It is a multi-symplectic integrator that locally conserves the stress-energy tensor with an excellent…

We use machine learning to classify rational two-dimensional conformal field theories. We first use the energy spectra of these minimal models to train a supervised learning algorithm. We find that the machine is able to correctly predict…

The Hamiltonian Mean Field (HMF) model of coupled inertial, Hamiltonian rotors is a prototype for conservative dynamics in systems with long-range interactions. We consider the case where the interactions between the rotors are governed by…

We present a new approach to simulating Hamiltonian dynamics based on implementing linear combinations of unitary operations rather than products of unitary operations. The resulting algorithm has superior performance to existing simulation…

Identifying the dynamics of physical systems requires a machine learning model that can assimilate observational data, but also incorporate the laws of physics. Neural Networks based on physical principles such as the Hamiltonian or…

The modal analysis is revisited through the symplectic formalism, what leads to two intertwined eigenproblems. Studying the properties of the solutions, we prove that they form a canonical basis. The method is general and works even if the…

In a previous paper [3] we have studied flows defined on polytopes, presenting a new method to encapsulate its asymptotic dynamics along the edge-vertex heteroclinic network. These results apply to the class of polymatrix replicator…

We construct a space of vector fields that are normal to differentiable curves in the plane. Its basis functions are defined via saddle point variational problems in reproducing kernel Hilbert spaces (RKHSs). First, we study the properties…

Hidden Markov models (HMMs) and partially observable Markov decision processes (POMDPs) form a useful tool for modeling dynamical systems. They are particularly useful for representing environments such as road networks and office…

Recent work in reinforcement learning has leveraged symmetries in the model to improve sample efficiency in training a policy. A commonly used simplifying assumption is that the dynamics and reward both exhibit the same symmetry; however,…

Geometric aspects play an important role in the construction and analysis of structure-preserving numerical methods for a wide variety of ordinary and partial differential equations. Here we review the development and theory of symplectic…

We present a new machine learning technique which calculates a real-valued, time independent, finite dimensional Hamiltonian matrix from only experimental data. A novel cost function is given along with a proof that the cost function has…

We address the problem of safely learning controlled stochastic dynamics from discrete-time trajectory observations, ensuring system trajectories remain within predefined safe regions during both training and deployment. Safety-critical…

Characterizing time-periodic Hamiltonians is pivotal for validating and controlling driven quantum platforms, yet prevailing and unadjusted reconstruction methods demand dense time-domain sampling and heavy post-processing. We introduce a…

Variational integrators are derived for structure-preserving simulation of stochastic Hamiltonian systems with a certain type of multiplicative noise arising in geometric mechanics. The derivation is based on a stochastic discrete…

We study the Hamiltonian dynamics of a spaceship in the background of Alcubierre and G\"odel metrics. We derive the Hamiltonian vector fields governing the system evolution, construct and discuss related recursion operators generating the…

It is natural to measure the observables from the Hamiltonian-based quantum dynamics, and its inverse process that Hamiltonians are estimated from the measured data also is a vital topic. In this work, we propose a recurrent neural network…

There is an important difference between Hamiltonian-like vector fields in an almost-symplectic manifold $(M,\sigma)$, compared to the standard case of a symplectic manifold: in the almost-symplectic case, a vector field such that the…

This paper investigates the problem of data-driven modeling of port-Hamiltonian systems while preserving their intrinsic Hamiltonian structure and stability properties. We propose a novel neural-network-based port-Hamiltonian modeling…

The capabilities of image probe experiments are rapidly expanding, providing new information about quantum materials on unprecedented length and time scales. Many such materials feature inhomogeneous electronic properties with intricate…