Related papers: Locating saddle points using gradient extremals on…
In this article we introduce a variational approach to collision avoidance of multiple agents evolving on a Riemannian manifold and derive necessary conditions for extremals. The problem consists of finding non-intersecting trajectories of…
We introduce and investigate stochastic processes designed to find local minimizers and saddle points of non-convex functions, exploring the landscape more efficiently than the standard noisy gradient descent. The processes switch between…
The high-index saddle dynamics (HiSD) method is a powerful approach for computing saddle points and solution landscape. However, its practical applicability is constrained by the need for the explicit energy function expression. To overcome…
Identifying hidden dynamics from observed data is a significant and challenging task in a wide range of applications. Recently, the combination of linear multistep methods (LMMs) and deep learning has been successfully employed to discover…
Bayesian change-point detection, together with latent variable models, allows to perform segmentation over high-dimensional time-series. We assume that change-points lie on a lower-dimensional manifold where we aim to infer subsets of…
Point cloud maps generated via LiDAR sensors using extensive remotely sensed data are commonly used by autonomous vehicles and robots for localization and navigation. However, dynamic objects contained in point cloud maps not only downgrade…
We model incompressible flows with an adaptive stabilized finite element method Stokes flows, which solves a discretely stable saddle-point problem to approximate the velocity-pressure pair. Additionally, this saddle-point problem delivers…
The Adam optimization method has achieved remarkable success in addressing contemporary challenges in stochastic optimization. This method falls within the realm of adaptive sub-gradient techniques, yet the underlying geometric principles…
Dynamical systems that describe the escape from the basins of attraction of stable invariant sets are presented and analyzed. It is shown that the stable fixed points of such dynamical systems are the index-1 saddle points. Generalizations…
Attitude control systems naturally evolve on nonlinear configuration spaces, such as S^2 and SO(3). The nontrivial topological properties of these configuration spaces result in interesting and complicated nonlinear dynamics when studying…
Adaptive Moment Estimation (Adam), which combines Adaptive Learning Rate and Momentum, would be the most popular stochastic optimizer for accelerating the training of deep neural networks. However, it is empirically known that Adam often…
Learning shared structure across environments facilitates rapid learning and adaptive behavior in neural systems. This has been widely demonstrated and applied in machine learning to train models that are capable of generalizing to novel…
This paper introduces a new method for robot motion planning and navigation in uneven environments through a surfel representation of underlying point clouds. The proposed method addresses the shortcomings of state-of-the-art navigation…
We introduce a nonlinear stochastic model reduction technique for high-dimensional stochastic dynamical systems that have a low-dimensional invariant effective manifold with slow dynamics, and high-dimensional, large fast modes. Given only…
The paper presents a simple and effective learning-based method for computing a discriminative 3D point cloud descriptor for place recognition purposes. Recent state-of-the-art methods have relatively complex architectures such as…
Discovering the governing equations of a dynamical system from observed trajectories provides deeper insight into its structure than mere prediction of future states. We present a data-driven approach to model discovery based on…
In part I we considered the problem of convergence to a saddle point of a concave-convex function via gradient dynamics and an exact characterization was given to their asymptotic behaviour. In part II we consider a general class of…
This work presents a numerical analysis of computing transition states of semilinear elliptic partial differential equations (PDEs) via the index-1 saddle dynamics, or equivalently, the gentlest ascent dynamics. To establish clear…
In this paper, we give explicit descriptions of versions of (Local-) Backtracking Gradient Descent and New Q-Newton's method to the Riemannian setting.Here are some easy to state consequences of results in this paper, where X is a general…
Primal-dual gradient dynamics that find saddle points of a Lagrangian have been widely employed for handling constrained optimization problems. Building on existing methods, we extend the augmented primal-dual gradient dynamics (Aug-PDGD)…