arXiv research

In integrable hydrodynamic systems, coordinates exist where generators and symmetries are simple.

In this paper we analyze the tangential symmetries of Darboux integrable decomposable exterior differential systems. The decomposable systems generalize the notion of a hyperbolic exterior differential system and include the classic notion of Darboux integrability for first order systems and second order scalar equatio…

Transferable Boltzmann Generators learn to sample unseen molecules efficiently.

New method to derive integrable systems from existing Lax systems.

Complex frequency generalizes eigenvalues in LTI systems.

Generative models speed up complex system simulations.

Elliptic systems are characterized by Darboux integrability.

Meta learning enables cross-domain Hamiltonian dynamics.

A solution for the Weinstein's Problem in the general framework of generalized Lie algebroids is the target of this paper. We present the mechanical systems called by use, mechanical (?; ?)-systems, Lagrange mechanical (?; ?)-systems or Finsler mechanical (?; ?)-systems and we develop their geometries. We obtain the ca…

In this paper, a new deep reinforcement learning based augmented general sequence tagging system is proposed. The new system contains two parts: a deep neural network (DNN) based sequence tagging model and a deep reinforcement learning (DRL) based augmented tagger. The augmented tagger helps improve system performance …

Mixed superposition rules, i.e., functions describing the general solution of a system of first-order differential equations in terms of a generic family of particular solutions of first-order systems and some constants, are studied. The main achievement is a generalization of the celebrated Lie-Scheffers Theorem, char…

The paper provides a non-asymptotic error bound for linear system identification under nonlinear policies.

The paper develops methods to derive mixed superposition rules for Lie systems and applies them to various physical systems.

We study integrable geodesic flows on Stiefel varieties $V_{n,r}=SO(n)/SO(n-r)$ given by the Euclidean, normal (standard), Manakov-type, and Einstein metrics. We also consider natural generalizations of the Neumann systems on $V_{n,r}$ with the above metrics and proves their integrability in the non-commutative sense b…

Maps dBKP solutions to MS system solutions, defining Einstein-Weyl structures.

Simplified proof of mass center system's uniqueness and generalized Pappus' theorem across Euclidean, spherical, and hyperbolic geometries.

CoDA adapts dynamics models to new physical systems by conditioning on context.

Unified approach to deform Lie-Hamilton systems using Poisson-Hopf algebra.

With the growth of renewable generation (RG) and the development of associated ride through curves serving as operating limits, during disturbances, on violation of these limits, the power system is at risk of losing large amounts of generation. In order to identify preventive control measures that avoid such scenarios…

The paper proved that every $C^2$-solution of a given first order PDEs system, regarded on the jet fibre bundle of order one $J^1(T,M)$, may be viewed as a "generalized harmonic map", via the least squares variational method. Our ideas are structured in the following way: 1) we find a suitable geometrical structure on …

We give necessary and sufficient geometric conditions for a distribution (or a Pfaffian system) to be locally equivalent to the canonical contact system on Jn(R,Rm), the space of n-jets of maps from R into Rm. We study the geometry of that class of systems, in particular, the existence of corank one involutive subdistr…

This paper presents a new causal network learning algorithm (FSNN, Feedback System Neural Network) based on the construction and analysis of a non-linear system of Ordinary Differential Equations (ODEs). The constructed system provides insight into the mechanisms responsible for generating the past and potential future…

In this paper, we consider a generalization of variational calculus which allows us to consider in the same framework different cases of mechanical systems, for instance, Lagrangian mechanics, Hamiltonian mechanics, systems subjected to constraints, optimal control theory and so on. This generalized variational calculu…

Speaker verification (SV) systems using deep neural network embeddings, so-called the x-vector systems, are becoming popular due to its good performance superior to the i-vector systems. The fusion of these systems provides improved performance benefiting both from the discriminatively trained x-vectors and generative …

New explanation of reservoir computing using random projections.

The paper studies random dynamical systems of polynomial automorphisms on C^2 and finds mean stability.

Category theory generalizes finite type invariants using diagrams systems.

Arnold-Liouville systems cannot be bi-Hamiltonian generically.

We provide a general Doob-Meyer decomposition for $g$-supermartingale systems, which does not require any right-continuity on the system. In particular, it generalizes the Doob-Meyer decomposition of Mertens (1972) for classical supermartingales, as well as Peng's (1999) version for right-continuous $g$-supermartingale…

The paper studies bifurcations in discrete dynamical systems on manifolds.

DeepONet models system discrepancies with low data.

Framework predicts nonlinear system responses using GFDT and generative models.

Although conservative Hamiltonian systems with constraints can be formulated in terms of Dirac structures, a more general framework is necessary to cover also dissipative systems such as gradient and metriplectic systems with constraints. We define Leibniz-Dirac structures which lead to a natural generalization of Dira…

We find the complete set of fundamental invariants for systems of ordinary differential equations of order $\ge 4$ under the group of point transformations generalizing similar results for contact invariants of a single ODE and point invariants of systems of the second and the third order. It turns out that starting fr…

A new description, different by the classical theory of Hamiltonian Mechanics, in the general framework of generalized Lie algebroids is presented. In the particular case of Lie algebroids, new and important results are obtained. We present the \emph{dual mechanical systems} called by use, \emph{dual mechanical}$(ρ,η) …

In this paper we prove a version of Lie-Bäcklund theorem for overdetermined systems of scalar PDEs, whose general solution depends on 1 function of 1 variable. This generalizes the case of involutive system of the second order on the plane treated by E.Cartan in 1910. Many examples are provided.

Study Toda systems blowup masses linked to Weyl groups.

This work introduces a method to learn dynamical systems from noisy sensor measurements using multiple shooting.

Among the machine learning applications to business, recommender systems would take one of the top places when it comes to success and adoption. They help the user in accelerating the process of search while helping businesses maximize sales. Post phenomenal success in computer vision and speech recognition, deep learn…

The paper generalizes Hodge theory to semisimple local systems and proves a geometric Decomposition theorem.

In this paper we present a far-reaching generalization of E. Vessiot's analysis of the Darboux integrable partial differential equations in one dependent and two independent variables. Our approach provides new insights into this classical method, uncovers the fundamental geometric invariants of Darboux integrable syst…

The paper extends static Systemic Risk Measures to a conditional setting.

The performance of fully synchronized distributed systems has faced a bottleneck due to the big data trend, under which asynchronous distributed systems are becoming a major popularity due to their powerful scalability. In this paper, we study the generalization performance of stochastic gradient descent (SGD) on a dis…

Overview of integrable systems with symmetries, focusing on toric and semitoric systems.

Paper explores foundation models for dynamical systems using synthetic data.

This paper considers control systems defined on Lie algebroids. After deriving basic controllability tests for general control systems, we specialize our discussion to the class of mechanical control systems on Lie algebroids. This class of systems includes mechanical systems subject to holonomic and nonholonomic const…

Fault detection problem for closed loop uncertain dynamical systems, is investigated in this paper, using different deep learning based methods. Traditional classifier based method does not perform well, because of the inherent difficulty of detecting system level faults for closed loop dynamical system. Specifically, …

sFML learns stochastic dynamical systems from data.