Related papers: On Learning Hamiltonian Systems from Data
The Hamiltonian formalism plays a central role in classical and quantum physics. Hamiltonians are the main tool for modelling the continuous time evolution of systems with conserved quantities, and they come equipped with many useful…
Hamiltonian systems with multiple timescales arise in molecular dynamics, classical mechanics, and theoretical physics. Long-time numerical integration of such systems requires resolving fast dynamics with very small time steps, which…
The reduction of Hamiltonian systems aims to build smaller reduced models, valid over a certain range of time and parameters, in order to reduce computing time. By maintaining the Hamiltonian structure in the reduced model, certain…
Most classical mechanical systems are based on dynamical variables whose values are real numbers. Energy conservation is then guaranteed if the dynamical equations are phrased in terms of a Hamiltonian function, which then leads to…
Hamiltonian mechanics is an effective tool to represent many physical processes with concise yet well-generalized mathematical expressions. A well-modeled Hamiltonian makes it easy for researchers to analyze and forecast many related…
In this study we consider the Hamiltonian approach for the construction of a map for a system with nonlinear resonant interaction, including phase trapping and phase bunching effects. We derive basic equations for a single resonant…
Reconstructing the KAM dynamics diagram of Hamiltonian system from the time series of a limited number of parameters is an outstanding question in nonlinear science, especially when the Hamiltonian governing the system dynamics are unknown.…
Patterns arise spontaneously in a range of systems spanning the sciences, and their study typically focuses on mechanisms to understand their evolution in space-time. Increasingly, there has been a transition towards controlling these…
We introduce a data-driven method for learning the equations of motion of mechanical systems directly from position measurements, without requiring access to velocity data. This is particularly relevant in system identification tasks where…
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…
We introduce a methodology for seeking conservation laws within a Hamiltonian dynamical system, which we term ``neural deflation''. Inspired by deflation methods for steady states of dynamical systems, we propose to {iteratively} train a…
In this paper, we develop a neural network-based approach for time-series prediction in unknown Hamiltonian dynamical systems. Our approach leverages a surrogate model and learns the system dynamics using generalized coordinates (positions)…
Standandard Hamiltonian mechanics in its homogeneous formulation is applied to the study of discontinuities representing rapid changes of Hamiltonians. Different formulations of Hamiltonian mechanics are reviewed. An original representation…
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…
Correlated many-body problems ubiquitously appear in various fields of physics such as condensed matter physics, nuclear physics, and statistical physics. However, due to the interplay of the large number of degrees of freedom, it is…
The Hamiltonian of a quantum system governs the dynamics of the system via the Schrodinger equation. In this paper, the Hamiltonian is reconstructed in the Pauli basis using measurables on random states forming a time series dataset. The…
For Hamiltonian systems, simulation algorithms that exactly conserve numerical energy or pseudo-energy have seen extensive investigation. Most available methods either require the iterative solution of nonlinear algebraic equations at each…
Accurately learning the temporal behavior of dynamical systems requires models with well-chosen learning biases. Recent innovations embed the Hamiltonian and Lagrangian formalisms into neural networks and demonstrate a significant…
Machine learning methods are widely used in the natural sciences to model and predict physical systems from observation data. Yet, they are often used as poorly understood "black boxes," disregarding existing mathematical structure and…
We introduce a generalizable framework for learning to identify effective Hamiltonians directly from experimental data in solid-state quantum systems. Our approach is based on a physics-informed neural network architecture that embeds…