Related papers: Learning Generalized Hamiltonians using fully Symp…

We show that the massive noncommutative U(1) theory is embedded in a gauge theory using an alternative systematic way, which is based on the symplectic framework. The embedded Hamiltonian density is obtained after a finite number of steps…

A well-specified parametrization for single-input/single-output (SISO) linear port-Hamiltonian systems amenable to structure-preserving supervised learning is provided. The construction is based on controllable and observable normal form…

Explicit and semi-explicit geometric integration schemes for dissipative perturbations of Hamiltonian systems are analyzed. The dissipation is characterized by a small parameter $\epsilon$, and the schemes under study preserve the…

In this work we show the equivalence between Hamiltonian mechanics and conservation of information entropy. We will show that distributions with coordinate independent values for information entropy require that the manifold on which the…

Recurrent neural networks (RNNs) have gained a great deal of attention in solving sequential learning problems. The learning of long-term dependencies, however, remains challenging due to the problem of a vanishing or exploding hidden…

Learned world models excel at interpolative generalization but fail at extrapolative generalization to novel physical properties. This limitation arises because they learn statistical correlations rather than the environment's underlying…

Neural networks that synergistically integrate data and physical laws offer great promise in modeling dynamical systems. However, iterative gradient-based optimization of network parameters is often computationally expensive and suffers…

Embedding non-restrictive prior knowledge, such as energy conservation laws, into learning methods is a key motive to construct physically consistent dynamics models from limited data, relevant for, e.g., model-based control. Recent work…

Characterizing noisy quantum devices requires methods for learning the underlying quantum Hamiltonian which governs their dynamics. Often, such methods compare measurements to simulations of candidate Hamiltonians, a task which requires…

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.…

This paper presents a new method for learning dissipative Hamiltonian dynamics from a limited and noisy dataset. The method uses the Helmholtz decomposition to learn a vector field as the sum of a symplectic and a dissipative vector field.…

Hamiltonian systems describe a broad class of dynamical systems governed by Hamiltonian functions, which encode the total energy and dictate the evolution of the system. Data-driven approaches, such as symbolic regression and neural…

Training deep neural networks (DNNs) can be difficult due to the occurrence of vanishing/exploding gradients during weight optimization. To avoid this problem, we propose a class of DNNs stemming from the time discretization of Hamiltonian…

Gaussian process regression is increasingly applied for learning unknown dynamical systems. In particular, the implicit quantification of the uncertainty of the learned model makes it a promising approach for safety-critical applications.…

This paper proposes Hamiltonian Learning, a novel unified framework for learning with neural networks "over time", i.e., from a possibly infinite stream of data, in an online manner, without having access to future information. Existing…

Classical Hamiltonian mechanics, characterized by a single conserved Hamiltonian (energy) and symplectic geometry, `hides' other invariants into symmetries of the Hamiltonian or into the kernel of the Poisson tensor. Nambu mechanics aims to…

Conservation of energy is at the core of many physical phenomena and dynamical systems. There have been a significant number of works in the past few years aimed at predicting the trajectory of motion of dynamical systems using neural…

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…

Port-Hamiltonian systems are pertinent representations of many nonlinear physical systems. In this study, we formulate and analyse a general class of stochastic car-following models with a systematic port-Hamiltonian structure. The model…

Hamiltonian Monte Carlo is a prominent Markov Chain Monte Carlo algorithm, which employs symplectic integrators to sample from high dimensional target distributions in many applications, such as statistical mechanics, Bayesian statistics…