Related papers: Global Symplectic Uncertainty Propagation on SO(3)
In this paper, we consider the problem of propagating an uncertain distribution by a possibly non-linear function and quantifying the resulting uncertainty. We measure the uncertainty using the Wasserstein distance, and for a given input…
Symplectic integrators are a foundation to the study of dynamical $N$-body phenomena, at scales ranging from from planetary to cosmological. These integrators preserve the Poincar\'e invariants of Hamiltonian dynamics. The $N$-body…
This paper presents a deterministic hybrid observer for the attitude dynamics of a rigid body that guarantees global asymptotical stability. Any smooth attitude observer suffers from the inherent topological restriction that it is…
Symplectic integrators are widely used for long-term integration of conservative astrophysical problems due to their ability to preserve the constants of motion; however, they cannot in general be applied in the presence of nonconservative…
Predictive uncertainty estimation remains a challenging problem precluding the use of deep neural networks as subsystems within safety-critical applications. Aleatoric uncertainty is a component of predictive uncertainty that cannot be…
This series of papers is devoted to an open-ended project aimed at the solution of Hilbert's sixth problem (concerning joint axiomatization of physics and probability theory) proposed to be constructed in the framework of an all-embracing…
Uncertainty quantification in medical images has become an essential addition to segmentation models for practical application in the real world. Although there are valuable developments in accurate uncertainty quantification methods using…
When propagating uncertainty in the data of differential equations, the probability laws describing the uncertainty are typically themselves subject to uncertainty. We present a sensitivity analysis of uncertainty propagation for…
In this paper we present a theoretical analysis of the global dynamics in a triaxial galactic system using a 3D integrable Hamiltonian as a simple representation. We include a thorough discussion on the effect of adding a generic…
We present a new framework for analyzing the evolution of information in geophysical systems. Understanding how information, and its counterpart, uncertainty, propagates is central to predictability studies and has significant implications…
Symplectic numerical schemes for reversible dynamical systems predict the solution reliably over large times as well, and are a good starting point for extension to schemes for simulating irreversible situations like viscoelastic wave…
Understanding the dynamics of multi--dimensional conservative dynamical systems (Hamiltonian flows or symplectic maps) is a fundamental issue of non-linear science. The Generalized ALignment Index (GALI), which was recently introduced and…
Probabilistic forecasting provides a principled framework for uncertainty quantification in dynamical systems by representing predictions as probability distributions rather than deterministic trajectories. However, existing forecasting…
We propose a new approach for propagating stable probability distributions through neural networks. Our method is based on local linearization, which we show to be an optimal approximation in terms of total variation distance for the ReLU…
Coupled partial differential equation (PDE) systems, which often represent multi-physics models, are naturally suited for modular numerical solution methods. However, several challenges yet remain in extending the benefits of modularization…
This paper presents global tracking strategies for the attitude dynamics of a rigid body. It is well known that global attractivity is prohibited for continuous attitude control systems on the special orthogonal group. Such topological…
Non-Hermitian systems exhibit a distinctive type of wave propagation, due to the intricate interplay of non-Hermiticity and disorder. Here, we investigate the spreading dynamics in the archetypal non-Hermitian Aubry-Andr\'e model with…
We develop Lie-Poisson integrators for general Hamiltonian systems on $\mathbf{R}^{3}$ equipped with the rigid body bracket. The method uses symplectic realisation of $\mathbf{R}^{3}$ on $T^{*}\mathbf{R}^{2}$ and application of symplectic…
This paper examines the global convergence problem of SLAM algorithms, an issue that faces topological obstructions. This is because the state-space of attitude dynamics is defined on a non-contractible manifold: the special orthogonal…
A novel method to propagate uncertainty through the soft-thresholding nonlinearity is proposed in this paper. At every layer the current distribution of the target vector is represented as a spike and slab distribution, which represents the…