Related papers: Dynamics on Lie groups with applications to attitu…
We show that the behavior of stochastic gradient descent is related to Bayesian statistics by showing that SGD is effectively diffusion on a fractal landscape, where the fractal dimension can be accounted for in a purely Bayesian way. By…
A method for sequential Bayesian inference of the static parameters of a dynamic state space model is proposed. The method is based on the observation that many dynamic state space models have a relatively small number of static parameters…
Stochastic differential equations (SDEs) have been shown recently to characterize well the dynamics of training machine learning models with SGD. When the generalization error of the SDE approximation closely aligns with that of SGD in…
The filtering distribution captures the statistics of the state of a dynamical system from partial and noisy observations. Classical particle filters provably approximate this distribution in quite general settings; however they behave…
In this survey, we report on the state of the art of some of the fundamental problems in the Lie theory of Lie groups modeled on locally convex spaces, such as integrability of Lie algebras, integrability of Lie subalgebras to Lie…
We will construct a theory which can explain the dynamics toward the steady state self-gravitating systems (SGSs) where many particles interact via the gravitational force. Real examples of SGS in the universe are globular clusters and…
By use of Lagrangian tracers propagated on 2D simulations of Scrape-Off Layer (SOL) turbulence, we are able to determine the non-local fractional-advection, fractional-diffusion equation (FADE) coefficients for a number of equilibrium…
The study of Large-Eddy Simulations (LES) in turbulent flows continues to be a critical area of research, particularly in understanding the behavior of small-scale turbulence structures and their impact on resolved scales. In this study, we…
Model misspecification constitutes a major obstacle to reliable inference in many inverse problems. Inverse problems in seismology, for example, are particularly affected by misspecification of wave propagation velocities. In this paper, we…
This paper presents a generalization of conventional sliding mode control designs for systems in Euclidean spaces to fully actuated simple mechanical systems whose configuration space is a Lie group for the trajectory-tracking problem. A…
Learning unknown stochastic differential equations (SDEs) from observed data is a significant and challenging task with applications in various fields. Current approaches often use neural networks to represent drift and diffusion functions,…
Models defined by stochastic differential equations (SDEs) allow for the representation of random variability in dynamical systems. The relevance of this class of models is growing in many applied research areas and is already a standard…
This paper deals with the state estimation of non-linear and non-Gaussian systems with an emphasis on the numerical solution to the Bayesian recursive relations. In particular, this paper builds upon the Lagrangian grid-based filter (GbF)…
Forecasting dynamic scenes remains a fundamental challenge in computer vision, as limited observations make it difficult to capture coherent object-level motion and long-term temporal evolution. We present Motion Group-aware Gaussian…
The paper is concerned with non-linear Gaussian filtering and smoothing in continuous-discrete state-space models, where the dynamic model is formulated as an It\^{o} stochastic differential equation (SDE), and the measurements are obtained…
We present a theory-first framework that interprets inference-time adaptation in large language models (LLMs) as online Bayesian state estimation. Rather than modeling rapid adaptation as implicit optimization or meta-learning, we formulate…
Boltzmann generators approach the sampling problem in many-body physics by combining a normalizing flow and a statistical reweighting method to generate samples of a physical system's equilibrium density. The equilibrium distribution is…
Estimating the statistics of the state of a dynamical system, from partial and noisy observations, is both mathematically challenging and finds wide application. Furthermore, the applications are of great societal importance, including…
Accurate prediction of structural dynamics is imperative for preserving digital twin fidelity throughout operational lifetimes. Parametric models with fixed nominal parameters often omit critical physical effects due to simplifications in…
Robust state estimation in coupled dynamical systems depends critically not only on sensor quality but on the structural alignment between observation channels and the system's intrinsic dynamics. This paper develops a rigorous framework…