Related papers: On the arbitrarily long-term stability of conserva…
We study the stability of randomized Taylor schemes for ODEs. We consider three notions of probabilistic stability: asymptotic stability, mean-square stability, and stability in probability. We prove fundamental properties of the…
Time delays are a common perturbation in systems with many states, such as networked, distributed, or decentralized systems. Current methods analyzing the stability of large systems with time delay typically produce very conservative…
Computable estimates for the error of finite element discretisations of parabolic problems in the $L^\infty(0,T; L^2)$ norm are developed, which exhibit constant effectivities (the ratio of the estimated error to the true error) with…
In this paper, we propose a new approach to prove stability of non-linear discrete-time systems. After introducing the new concept of stability contractor, we show that the interval centred form plays a fundamental role in this context and…
Conservation and consistency are fundamental properties of discretizations of systems of hyperbolic conservation laws. Here, these concepts are extended to the realm of iterative methods by formally defining locally conservative and flux…
In numerous robotics and mechanical engineering applications, among others, data is often constrained on smooth manifolds due to the presence of rotational degrees of freedom. Common datadriven and learning-based methods such as neural…
Reinforcement learning algorithms typically consider discrete-time dynamics, even though the underlying systems are often continuous in time. In this paper, we introduce a model-based reinforcement learning algorithm that represents…
In this paper an asymptotic expansion of the global error on the stepsize for partitioned linear multistep methods is proved. This provides a tool to analyse the behaviour of these integrators with respect to error growth with time and…
We study the stability of non-conservative deterministic cross diffusion models and prove that they are approximated by stochastic population models when the populations become locally large. In this model, the individuals of two species…
Research of delayed neural networks with variable self-inhibitions, inter-connection weights, and inputs is an important issue. %In the real world, self-inhibitions, %inter-connection weights, and inputs should vary through time. In In this…
This paper proposes a self-supervised objective for learning representations that localize objects under occlusion - a property known as object permanence. A central question is the choice of learning signal in cases of total occlusion.…
This paper investigates the global stability and the global asymptotic stability independent of the sizes of the delays of linear time-varying Caputo fractional dynamic systems of real fractional order possessing internal point delays. The…
This paper presents finite-time and fixed-time stabilization results for inhomogeneous abstract evolution problems, extending existing theories. We prove well-posedness for strong and weak solutions, and estimate upper bounds for settling…
In this paper we first obtain local contraction results in a Hm-norm with respect to time and space for a local scheme. We show that a global controlled scheme preserves higher order regularity with respect to the spatial variables together…
We develop a numerical algorithm for identifying approximately conserved quantities in models perturbed away from integrability. In the long-time regime, these quantities fully determine correlation functions of local observables. Applying…
We investigate the uniform stability properties of discrete-time linear switched systems subject to arbitrary switching, focusing on the "marginally unstable" regime in which the system is not Lyapunov stable but in which trajectories…
Uniform stability of a learning algorithm is a classical notion of algorithmic stability introduced to derive high-probability bounds on the generalization error (Bousquet and Elisseeff, 2002). Specifically, for a loss function with range…
Deep learning has been proposed as an efficient alternative for the numerical approximation of PDE solutions, offering fast, iterative simulation of PDEs through the approximation of solution operators. However, deep learning solutions have…
We study the uniform ergodicity property for non-invertible topological and measure-preserving dynamical systems. It is shown that for topological dynamical systems uniform ergodicity is equivalent to eventually periodicity and that for…
We propose a novel second-order ODE as the continuous-time limit of a Riemannian accelerated gradient-based method on a manifold with curvature bounded from below. This ODE can be seen as a generalization of the ODE derived for Euclidean…