Related papers: Reverse-engineering invariant manifolds with asymp…
The hyperbolic manifold is a smooth manifold of negative constant curvature. While the hyperbolic manifold is well-studied in the literature, it has gained interest in the machine learning and natural language processing communities lately…
The aim of this work is to establish the existence of invariant manifolds in complex systems. Considering trajectory curves integral of multiple time scales dynamical systems of dimension two and three (predator-prey models, neuronal…
In this paper, we propose an approach to learn stable dynamical systems evolving on Riemannian manifolds. The approach leverages a data-efficient procedure to learn a diffeomorphic transformation that maps simple stable dynamical systems…
We construct finite-dimensional invariant manifolds in the phase space of the Navier-Stokes equation on R^2 and show that these manifolds control the long-time behavior of the solutions. This gives geometric insight into the existing…
We construct two examples of invariant manifolds that despite being locally unstable at every point in the transverse direction are globally stable. Using numerical simulations we show that these invariant manifolds temporarily repel nearby…
We show that one can obtain asymptotic evolving boost-invariant geometries in a simple manner from the corresponding static solutions. We exhibit the procedure in the case of a supergravity dual of R-charged hydrodynamics by turning on a…
We extend the theory of spectral submanifolds (SSMs) to general non-autonomous dynamical systems that are either weakly forced or slowly varying. Examples of such systems arise in structural dynamics, fluid-structure interactions and…
Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite dimensional autonomous deterministic systems, and for…
We use the invariant-based inverse engineering subject to the quasiadiabatic condition to produce robust and high fidelity coherent superposition of quantum states. The inverse engineering provides shortcuts to the desired quantum-state…
We consider the Cauchy problem for first order systems. Assuming that the set of the singular points of the characteristic variety is a smooth manifold and the characteristic values are real and semi-simple we introduce a new class which is…
Invariant manifolds are important constructs for the quantitative and qualitative understanding of nonlinear phenomena in dynamical systems. In nonlinear damped mechanical systems, for instance, spectral submanifolds have emerged as useful…
In order for a bimanual robot to manipulate an object that is held by both hands, it must construct motion plans such that the transformation between its end effectors remains fixed. This amounts to complicated nonlinear equality…
This paper analyses the stability of cycles within a heteroclinic network lying in a three-dimensional manifold formed by six cycles, for a one-parameter model developed in the context of game theory. We show the asymptotic stability of the…
Symmetry transformations induce invariances which are frequently described with deep latent variable models. In many complex domains, such as the chemical space, invariances can be observed, yet the corresponding symmetry transformation…
Many real-world networks exhibit hierarchical, tree-like structure and heavy-tailed degree distributions, phenomena not readily captured by standard statistical models for network data. Extensions of the popular continuous latent space…
Backward compatible representation learning enables updated models to integrate seamlessly with existing ones, avoiding to reprocess stored data. Despite recent advances, existing compatibility approaches in Euclidean space neglect the…
Recently developed reduced-order modeling techniques aim to approximate nonlinear dynamical systems on low-dimensional manifolds learned from data. This is an effective approach for modeling dynamics in a post-transient regime where the…
Attitude control systems naturally evolve on nonlinear configuration spaces, such as S^2 and SO(3). The nontrivial topological properties of these configuration spaces result in interesting and complicated nonlinear dynamics when studying…
We define a geometric quantity for asymptotically hyperbolic manifolds, which we call the volume-renormalized mass. It is essentially a linear combination of the ADM mass surface integral and a renormalization of the volume. We show that…
In this work, we address the design of tracking controllers that drive a mechanical system's state asymptotically towards a reference trajectory. Motivated by aerospace and robotics applications, we consider fully-actuated systems evolving…