Related papers: A Partial Hamiltonian Approach for Current Value H…
We consider non-stationary dynamical systems with one-and-a-half degrees of freedom. We are interested in algorithmic construction of rich classes of Hamilton's equations with the Hamiltonian H=p^2/2+V(x,t) which are Liouville integrable.…
We introduce an efficient variational hybrid quantum-classical algorithm designed for solving Caputo time-fractional partial differential equations. Our method employs an iterable cost function incorporating a linear combination of overlap…
The physics of a closed quantum mechanical system is governed by its Hamiltonian. However, in most practical situations, this Hamiltonian is not precisely known, and ultimately all there is are data obtained from measurements on the system.…
In this paper, we consider a Bayesian inverse problem modeled by elliptic partial differential equations (PDEs). Specifically, we propose a data-driven and model-based approach to accelerate the Hamiltonian Monte Carlo (HMC) method in…
We develop circuit implementations for digital-level quantum Hamiltonian dynamics simulation algorithms suitable for implementation on a reconfigurable quantum computer, such as trapped ions. Our focus is on the co-design of a problem, its…
Hamilton-Jacobi partial differential equations (HJ PDEs) play a central role in many applications such as economics, physics, and engineering. These equations describe the evolution of a value function which encodes valuable information…
We derive the dynamics of several rigid bodies of arbitrary shape in a 2-dimensional inviscid and incompressible fluid, whose vorticity field is given by point vortices. We adopt the idea of Vankerschaver et al. (2009) to derive the…
The fractional Hamiltonian analysis of 1+1 dimensional field theory is investigated and the fractional Ostrogradski's formulation is obtained. The fractional path integral of both simple harmonic oscillator with an acceleration-squares part…
We consider the problem of parameter estimation in dynamic systems described by ordinary differential equations. A review of the existing literature emphasizes the need for deterministic global optimization methods due to the nonconvex…
We consider the task of approximating the ground state energy of two-local quantum Hamiltonians on bounded-degree graphs. Most existing algorithms optimize the energy over the set of product states. Here we describe a family of shallow…
An extension of Riewe's fractional Hamiltonian formulation is presented for fractional constrained systems. The conditions of consistency of the set of constraints with equations of motion are investigated. Three examples of fractional…
In this work we combine two distinct machine learning methodologies, sequential Monte Carlo and Bayesian experimental design, and apply them to the problem of inferring the dynamical parameters of a quantum system. We design the algorithm…
Quantum Hamiltonian identification is important for characterizing the dynamics of quantum systems, calibrating quantum devices and achieving precise quantum control. In this paper, an effective two-step optimization (TSO) quantum…
This paper can be seen as an attempt of rethinking the {\em Extra-Gradient Philosophy} for solving Variational Inequality Problems. We show that the properly defined {\em Reduced Gradients} can be used instead for finding approximate…
High-resolution simulations of particle-based kinetic plasma models typically require a high number of particles and thus often become computationally intractable. This is exacerbated in multi-query simulations, where the problem depends on…
Hybrid machine learning based on Hamiltonian formulations has recently been successfully demonstrated for simple mechanical systems, both energy conserving and not energy conserving. We introduce a pseudo-Hamiltonian formulation that is a…
Pricing financial derivatives, in particular European-style options at different time-maturities and strikes, means a relevant problem in finance. The dynamics describing the price of vanilla options when constant volatilities and interest…
We formulate an optimization problem of Hamiltonian design based on the variational principle. Given a variational ansatz for a Hamiltonian we construct a loss function to be minimised as a weighted sum of relevant Hamiltonian properties…
We present a novel statistical inference framework for convex empirical risk minimization, using approximate stochastic Newton steps. The proposed algorithm is based on the notion of finite differences and allows the approximation of a…
Hamiltonian systems are known to conserve the Hamiltonian function, which describes the energy evolution over time. Obtaining a numerical spatio-temporal scheme that accurately preserves the discretized Hamiltonian function is often a…