相关论文: A note on the efficient implementation of Hamilton…

We consider the problem of optimizing hybrid structures (mixture of discrete and continuous input variables) via expensive black-box function evaluations. This problem arises in many real-world applications. For example, in materials design…

In this paper we promote the use of Support Vector Machines (SVM) as a machine learning tool for searches in high-energy physics. As an example for a new- physics search we discuss the popular case of Supersymmetry at the Large Hadron…

The past few years have witnessed an increased interest in learning Hamiltonian dynamics in deep learning frameworks. As an inductive bias based on physical laws, Hamiltonian dynamics endow neural networks with accurate long-term…

We define a numerical scheme that allows to approximate a given Hamiltonian by an effective one, by requiring several constraints determined by exact properties of generic ''short range'' Hamiltonians. In this way the standard lattice fixed…

The Hamiltonian structures of several hybrid kinetic-fluid models are identified explicitly, upon considering collisionless Vlasov dynamics for the hot particles interacting with a bulk fluid. After presenting different pressure-coupling…

The use of near-term quantum devices that lack quantum error correction, for addressing quantum chemistry and physics problems, requires hybrid quantum-classical algorithms and techniques. Here we present a process for obtaining the…

Energy-based models (EBMs) implement inference as gradient descent on a learned Lyapunov function, yielding interpretable, structure-preserving alternatives to black-box neural ODEs and aligning naturally with physical AI. Yet their use in…

We propose a perturbation algorithm for Hamiltonian systems on a Lie algebra $\mathbb{V}$, so that it can be applied to non-canonical Hamiltonian systems. Given a Hamiltonian system that preserves a subalgebra $\mathbb{B}$ of $\mathbb{V}$,…

We investigate integrable 2-dimensional Hamiltonian systems with scalar and vector potentials, admitting second invariants which are linear or quadratic in the momenta. In the case of a linear second invariant, we provide some examples of…

We present a new class of exponential integrators for ordinary differential equations. They are locally exact, i.e., they preserve the linearization of the original system at every point. Their construction consists in modifying existing…

We study the quantum version of a simplified model of optimization problems, where quantum fluctuations are introduced by a transverse field acting on the qubits. We find a complex low-energy spectrum of the quantum Hamiltonian,…

This work discusses the model reduction problem for large-scale multi-symplectic PDEs with cubic invariants. For this, we present a linearly implicit global energy-preserving method to construct reduced-order models. This allows to…

Extremal principles can generally be divided into two rather distinct classes. There are, on the one hand side, formulations based on the Lagrangian or Hamiltonian mechanics, respectively, dealing with time dependent problems, but…

Locally exact integrators preserve linearization of the original system at every point. We construct energy-preserving locally exact discrete gradient schemes for arbitrary multidimensional canonical Hamiltonian systems by modifying…

A method of exactly solving the master equation is presented in this letter. The explicit form of the solution is determined by the time evolution of a composite system including an auxiliary system and the open system in question. The…

The paper deals with numerical discretizations of separable nonlinear Hamiltonian systems with additive noise. For such problems, the expected value of the total energy, along the exact solution, drifts linearly with time. We present and…

Hamiltonian dynamics has been applied to study the slip-stacking dynamics. The canonical-perturbation method is employed to obtain the second-harmonic correction term in the slip-stacking Hamiltonian. The Hamiltonian approach provides a…

Reduced basis methods are popular for approximately solving large and complex systems of differential equations. However, conventional reduced basis methods do not generally preserve conservation laws and symmetries of the full order model.…

We present a novel positive kinetic scheme built on the efficient collide-and-stream algorithm of the lattice Boltzmann method (LBM) to address hyperbolic conservation laws. We focus on the compressible Euler equations with strong…

In this paper, we use support vector machines (SVM) to develop a machine learning framework to discover phase space structures that distinguish between distinct reaction pathways. The SVM model is trained using data from trajectories of…