相关论文: Curve-Induced Dynamical Systems on Riemannian Mani…

We focus on a class of non-smooth optimization problems over the Stiefel manifold in the decentralized setting, where a connected network of $n$ agents cooperatively minimize a finite-sum objective function with each component being weakly…

In dynamical systems characterized by separation of time scales, the approximation of so called ``slow manifolds'', on which the long term dynamics lie, is a useful step for model reduction. Initializing on such slow manifolds is a useful…

Modern computational science and engineering applications are being improved by the advances in scientific machine learning. Data-driven methods such as Dynamic Mode Decomposition (DMD) can extract coherent structures from spatio-temporal…

Covariance matrices have attracted attention for machine learning applications due to their capacity to capture interesting structure in the data. The main challenge is that one needs to take into account the particular geometry of the…

Dynamic Mode Decomposition (DMD) is a powerful data-driven method used to extract spatio-temporal coherent structures that dictate a given dynamical system. The method consists of stacking collected temporal snapshots into a matrix and…

We introduce a dynamical-systems approach for the study of the Sard problem in sub-Riemannian Carnot groups. We show that singular curves can be obtained by concatenating trajectories of suitable dynamical systems. As an applications, we…

State-space models (SSMs) offer a powerful framework for dynamical system analysis, wherein the temporal dynamics of the system are assumed to be captured through the evolution of the latent states, which govern the values of the…

Dynamic mode decomposition (DMD) is an emerging methodology that has recently attracted computational scientists working on nonintrusive reduced order modeling. One of the major strengths that DMD possesses is having ground theoretical…

Mirror Descent (MD) is a scalable first-order method widely used in large-scale optimization, with applications in image processing, policy optimization, and neural network training. This paper generalizes MD to optimization on Riemannian…

We propose Lie group embedded dynamical neural networks (LieEDNN) and the corresponding learning algorithms based on gradient descent and metric projection on smooth manifold, where we treat Lie group as an intrinsic representation for…

Multiscale stochastic dynamical systems have been widely adopted to a variety of scientific and engineering problems due to their capability of depicting complex phenomena in many real world applications. This work is devoted to…

Subspace clustering is a classical technique that has been widely used for human motion segmentation and other related tasks. However, existing segmentation methods often cluster data without guidance from prior knowledge, resulting in…

In this article we extend the computational geometric curve reconstruction approach to curves in Riemannian manifolds. We prove that the minimal spanning tree, given a sufficiently dense sample, correctly reconstructs the smooth arcs and…

Adaptive stochastic gradient algorithms in the Euclidean space have attracted much attention lately. Such explorations on Riemannian manifolds, on the other hand, are relatively new, limited, and challenging. This is because of the…

Real-time motion generation -- which is essential for achieving reactive and adaptive behavior -- under kinodynamic constraints for high-dimensional systems is a crucial yet challenging problem. We address this with a two-step approach:…

Accurate models of robot dynamics are critical for safe and stable control and generalization to novel operational conditions. Hand-designed models, however, may be insufficiently accurate, even after careful parameter tuning. This…

Simultaneous Localization and Mapping (SLAM) plays an important role in many robotics fields, including social robots. Many of the available visual SLAM methods are based on the assumption of a static world and struggle in dynamic…

Capturing both geometry and rigid motion for structured dynamic objects, like multi-part assemblies or jointed mechanisms, remains a key challenge. Existing dynamic methods, such as deformable meshes or 3DGS, rely on unstructured…

Recent advances in motion diffusion models have substantially improved the realism of human motion synthesis. However, existing approaches either rely on full-sequence diffusion models with bidirectional generation, which limits temporal…

How to improve the ability of scene representation is a key issue in vision-oriented decision-making applications, and current approaches usually learn task-relevant state representations within visual reinforcement learning to address this…