Related papers: Time-adaptive SympNets for separable Hamiltonian s…

We study time-uniform statistical inference for parameters in stochastic approximation (SA), which encompasses a bunch of applications in optimization and machine learning. To that end, we analyze the almost-sure convergence rates of the…

There has been increasing interest in methodologies that incorporate physics priors into neural network architectures to enhance their modeling capabilities. A family of these methodologies that has gained traction are Hamiltonian neural…

Following the development of weighted asymptotic approximation properties of matrices, we introduce the analogous uniform approximation properties (that is, study the improvability of Dirichlet's Theorem). An added feature is the use of…

Inductive Recommender Systems are capable of recommending for new users and with new items thus avoiding the need to retrain after new data reaches the system. However, these methods are still trained on all the data available, requiring…

We construct a symplectic integrator for non-separable Hamiltonian systems combining an extended phase space approach of Pihajoki and the symmetric projection method. The resulting method is semiexplicit in the sense that the main time…

Singular theories, characterised by the presence of degeneracies in their Lagrangian or Hamiltonian descriptions, require the systematic implementation of constraints in order to obtain well-defined dynamics. While the symplectic framework…

Hierarchical Bayesian models are increasingly used in large, inhomogeneous complex network dynamical systems by modeling parameters as draws from a hyperparameter-governed distribution. However, theoretical guarantees for these estimates as…

We reveal the symplectic nature of parameter-drift maps by embedding them into extended phase space. Applying the embedding to the parameter-drift standard nontwist map, our construction yields an autonomous symplectic map in extended phase…

We introduce an adaptive scattered data fitting scheme as extension of local least squares approximations to hierarchical spline spaces. To efficiently deal with non-trivial data configurations, the local solutions are described in terms of…

The kinetic term of the $N$-body Hamiltonian system defined on the surface of the sphere is non-separable. As a result, standard explicit symplectic integrators are inapplicable. We exploit an underlying hierarchy in the structure of the…

The similarity of graph structures, such as Meaning Representations (MRs), is often assessed via structural matching algorithms, such as Smatch (Cai and Knight, 2013). However, Smatch involves a combinatorial problem that suffers from…

The capability of recurrent neural networks to approximate trajectories of a random dynamical system, with random inputs, on non-compact domains, and over an indefinite or infinite time horizon is considered. The main result states that…

In this paper we prove a KAM-like theorem of symplectic algorithms for nearly integrable Hamiltonian systems which generalises the result of \cite{r1} and \cite{r6} for the case of integrable systems.

We study the performance of asymptotic and approximate consensus algorithms under harsh environmental conditions. The asymptotic consensus problem requires a set of agents to repeatedly set their outputs such that the outputs converge to a…

Symplectic integrators for Hamiltonian systems have been quite successful for studying few-body dynamical systems. These integrators are frequently derived using a formalism built on symplectic maps. There have been recent efforts to extend…

In this paper, further extensions of the result of the paper "A successive approximation method in functional spaces for hierarchical optimal control problems and its application to learning, arXiv:2410.20617 [math.OC], 2024" concerning a…

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…

Irregular sampling occurs in many time series modeling applications where it presents a significant challenge to standard deep learning models. This work is motivated by the analysis of physiological time series data in electronic health…

Systems of a large number N of globally coupled maps have become popular as a relatively simple prototype of high-dimensional dynamics, showing many interesting and typical phenomena like synchronisation, cluster formation and…

The non-Hermitian models, which are symmetric under parity (P) and time-reversal (T) operators, are the cornerstone for the fabrication of new ultra-sensitive optoelectronic devices. However, providing the gain in such systems usually…