Related papers: On Learning Hamiltonian Systems from Data
Local Hamiltonians arise naturally in physical systems. Despite its seemingly `simple' local structure, exotic features such as nonlocal correlations and topological orders exhibit in eigenstates of these systems. Previous studies for…
Stability and safety are critical properties for successful deployment of automatic control systems. As a motivating example, consider autonomous mobile robot navigation in a complex environment. A control design that generalizes to…
We propose a formalism for extracting molecular Hamiltonian structure from inversion of time-dependent fluorescence intensity data. The proposed method requires a minimum of \emph{a priori} knowledge about the system and allows for…
We present a method for learning generalized Hamiltonian decompositions of ordinary differential equations given a set of noisy time series measurements. Our method simultaneously learns a continuous time model and a scalar energy function…
In many real-world settings, image observations of freely rotating 3D rigid bodies may be available when low-dimensional measurements are not. However, the high-dimensionality of image data precludes the use of classical estimation…
Despite the availability of ever more data enabled through modern sensor and computer technology, it still remains an open problem to learn dynamical systems in a sample-efficient way. We propose active learning strategies that leverage…
Dynamic Bayesian networks provide a compact and natural representation for complex dynamic systems. However, in many cases, there is no expert available from whom a model can be elicited. Learning provides an alternative approach for…
Microscopically conserving reduced models of many-body systems have a long, highly successful history. Established theories of this type are the random-phase approximation for Coulomb fluids and the particle-particle ladder model for…
Implicit representations of finite-dimensional port-Hamiltonian systems are studied from the perspective of their use in numerical simulation and control design. Implicit representations arise when a system is modeled in Cartesian…
To understand the mechanism allowing for the long-term storage of excess energy in proteins, we study a Hamiltonian system consisting of several coupled pendula in partial contact with a heat bath. It is found that energy storage is…
We propose an efficient quantum algorithm for simulating the dynamics of general Hamiltonian systems. Our technique is based on a power series expansion of the time-evolution operator in its off-diagonal terms. The expansion decouples the…
The unprecedented predictive success of deep generative models in complex many-body systems, such as AlphaFold3, raises an epistemological question: do these networks merely memorize data distributions via high-dimensional interpolation, or…
Learning and predicting the dynamics of physical systems requires a profound understanding of the underlying physical laws. Recent works on learning physical laws involve generalizing the equation discovery frameworks to the discovery of…
This paper reports a development in the proper symplectic decomposition (PSD) for model reduction of forced Hamiltonian systems. As an analogy to the proper orthogonal decomposition (POD), PSD is designed to build a symplectic subspace to…
The Hopfield model is a paradigmatic model of neural networks that has been analyzed for many decades in the statistical physics, neuroscience, and machine learning communities. Inspired by the manifold hypothesis in machine learning, we…
Time-driven quantum systems are important in many different fields of physics like cold atoms, solid state, optics, etc. Many of their properties are encoded in the time evolution operator which is calculated by using a time-ordered product…
The dynamics of the spin-boson Hamiltonian is considered in the stochastic approximation. The Hamiltonian describes a two-level system coupled to an environment and is widely used in physics, chemistry and the theory of quantum measurement.…
We develop a physics-informed learning framework for energy-shaping control of port-Hamiltonian (pH) systems from trajectory data. The proposed approach co-learns a pH system model and an optimal energy-balancing passivity-based controller…
In recent years, the application of machine learning to physics has been actively explored. In this paper, we study a method for estimating the ground-state energy of quantum Hamiltonians by applying data-driven Koopman analysis within the…
A great number of works is devoted to qualitative investigation of Hamiltonian systems. One of tools of such investigation is the method of skew-symmetric differential forms. In present work, under investigation Hamiltonian systems in…