Related papers: Global Symplectic Uncertainty Propagation on SO(3)
We propose semiparametric estimators, called elliptical skew-(S)KEPTIC, for efficiently and robustly estimating non-Gaussian graphical models. Our approach extends the semiparametric elliptical framework to the meta skew-elliptical family,…
Unraveling real eigenfrequencies in non-Hermitian $\mathcal{PT}$-symmetric Hamiltonians has opened new avenues in quantum physics, photonics, and most recently, phononics. However, the existing literature squarely focuses on exploiting such…
Reparameterizable densities are an important way to learn probability distributions in a deep learning setting. For many distributions it is possible to create low-variance gradient estimators by utilizing a `reparameterization trick'. Due…
Cardiovascular simulations are increasingly used for non-invasive diagnosis of cardiovascular disease, to guide treatment decisions, and in the design of medical devices. Quantitative assessment of the variability of simulation outputs due…
We present a new approach to the proof of ergodic theorems for actions of free groups based on geometric covering and asymptotic invariance arguments. Our approach can be viewed as a direct generalization of the classical geometric covering…
We prove a Nekhoroshev-type theorem for nearly integrable symplectic map. As an application of the theorem, we obtain the exponential stability symplectic algorithms. Meanwhile, we can get the bounds for the perturbation, the variation of…
We present a structure preserving discretization of the fundamental spacetime geometric structures of fluid mechanics in the Lagrangian description in 2D and 3D. Based on this, multisymplectic variational integrators are developed for…
The existence of explicit symplectic integrators for general nonseparable Hamiltonian systems is an open and important problem in both numerical analysis and computing in science and engineering, as explicit integrators are usually more…
A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative…
The goal of this research is to derive an approach to assess uncertainty in an arbitrary volume conditioned by sampling data, without using geostatistical simulation. We have accomplished this goal by deriving an numerical tool suitable for…
We present a proximal algorithm that performs a variational recursion on the space of joint probability measures to propagate the stochastic uncertainties in power system dynamics over high dimensional state space. The proposed algorithm…
Stochastic hybrid systems are dynamic systems that undergo both random continuous-time flows and random discrete jumps. Depending on how randomness is introduced into the continuous dynamics, discrete transitions, or both, stochastic hybrid…
This paper introduces a new technique for learning probabilistic models of mass and friction distributions of unknown objects, and performing robust sliding actions by using the learned models. The proposed method is executed in two…
We introduce a novel formulation for geometry on discrete points. It is based on a universal differential calculus, which gives a geometric description of a discrete set by the algebra of functions. We expand this mathematical framework so…
This paper develops methods of distributed Bayesian hypothesis tests for fault detection and diagnosis that are based on belief propagation and optimization in graphical models. The main challenges in developing distributed statistical…
The Hamiltonian Monte Carlo method generates samples by introducing a mechanical system that explores the target density. For distributions on manifolds it is not always simple to perform the mechanics as a result of the lack of global…
Circular and non-flat data distributions are prevalent across diverse domains of data science, yet their specific geometric structures often remain underutilized in machine learning frameworks. A principled approach to accounting for the…
Iterative geostatistical seismic inversion integrates seismic and well data to infer the spatial distribution of subsurface elastic properties. These methods provide limited assessment to the spatial uncertainty of the inverted elastic…
A geometric representation for multivariate extremes, based on the shapes of scaled sample clouds in light-tailed margins and their so-called limit sets, has recently been shown to connect several existing extremal dependence concepts.…
Uncertainty analysis in the outcomes of model predictions is a key element in decision-based material design to establish confidence in the models and evaluate the fidelity of models. Uncertainty Propagation (UP) is a technique to determine…