Related papers: Global Symplectic Uncertainty Propagation on SO(3)

In this paper we consider the numerical approximation of systems of Boussinesq-type to model surface wave propagation. Some theoretical properties of these systems (multi-symplectic and Hamiltonian formulations, well-posedness and existence…

This paper addresses the limitations of standard uncertainty models, e.g., robust (norm-bounded) and stochastic (one fixed distribution, e.g., Gaussian), and proposes to model uncertainty via Optimal Transport (OT) ambiguity sets. These…

Geometry constitutes a core set of intuitions present in all humans, regardless of their language or schooling [1]. Could brain's built in machinery for processing geometric information take part in uncertainty representation? For decades…

Geographical data are generally autocorrelated. In this case, it is preferable to select spread units. In this paper, we propose a new method for selecting well-spread samples from a finite spatial population with equal or unequal inclusion…

In machine learning, accurately predicting the probability that a specific input is correct is crucial for risk management. This process, known as uncertainty (or confidence) estimation, is particularly important in mission-critical…

In order to perform numerical studies of long-term stability in nonlinear Hamiltonian systems, one needs a numerical integration algorithm which is symplectic. Further, this algorithm should be fast and accurate. In this paper, we propose…

This manuscript introduces novel approaches to three phenomena. First, we extend the algebraic formulation of kinetic theory within the contact framework by making explicit the gauge freedom, thereby obtaining a formulation in which the…

We present and compare different numerical schemes for the integration of the variational equations of autonomous Hamiltonian systems whose kinetic energy is quadratic in the generalized momenta and whose potential is a function of the…

In this paper, we argue for the utility of deterministic inference in the classical problem of numerical linear algebra, that of solving a linear system. We show how the Gaussian belief propagation solver, known to work for symmetric…

Well-spread samples are desirable in many disciplines because they improve estimation when target variables exhibit spatial structure. This paper introduces an integrated methodological framework for spreading samples over the population's…

It is shown that for any ensemble, whether classical or quantum, continuous or discrete, there is only one measure of the "volume" of the ensemble that is compatible with several basic geometric postulates. This volume measure is thus a…

Accurate modeling of contamination in subsurface flow and water aquifers is crucial for agriculture and environmental protection. Here, we demonstrate a parallel method to quantify the propagation of the uncertainty in the dispersal of…

We show that given a general uncoupled a priori unstable Hamiltonian \[ \frac12 p^2 + V(q) + G(I) + \epsilon h(p, q, I, \varphi, t), \] where $h$ is a generic Ma\~n\'e analytic function and $\epsilon$ is small enough, there is an orbit for…

Symplectic integration of autonomous Hamiltonian systems is a well-known field of study in geometric numerical integration, but for non-autonomous systems the situation is less clear, since symplectic structure requires an even number of…

Uncertainty propagation in nonlinear dynamic systems remains an outstanding problem in scientific computing and control. Numerous approaches have been developed, but are limited in their capability to tackle problems with more than a few…

We derive, and discuss the properties of, a symplectic map for the dynamics of bodies on nearly parabolic orbits. The orbits are perturbed by a planet on a circular, coplanar orbit interior to the pericenter of the parabolic orbit. The map…

We propose an implementation of symplectic implicit Runge-Kutta schemes for highly accurate numerical integration of non-stiff Hamiltonian systems based on fixed point iteration. Provided that the computations are done in a given floating…

This paper presents a geometric variational discretization of compressible fluid dynamics. The numerical scheme is obtained by discretizing, in a structure preserving way, the Lie group formulation of fluid dynamics on diffeomorphism groups…

This work proposes a scheme for significantly reducing the computational complexity of discretized problems involving the non-smooth forward propagation of uncertainty by combining the adaptive hierarchical sparse grid stochastic…

Uncertainty in large language model (LLM)-based systems is often studied at the level of a single model output, yet deployed LLM applications are compound systems in which uncertainty is transformed and reused across model internals,…