Related papers: Finding geodesics with the Deep Ritz method
We consider the proximal gradient method on Riemannian manifolds for functions that are possibly not geodesically convex. Starting from the forward-backward-splitting, we define an intrinsic variant of the proximal gradient method that uses…
We study planar domains $G$ equipped with a hyperbolic type metric and approximate geodesics that join two points $x,y \in G$ and their lengths. We present an algorithm that enables one to approximate the shortest distance in polygonal…
Deep learning based localization and mapping has recently attracted significant attention. Instead of creating hand-designed algorithms through exploitation of physical models or geometric theories, deep learning based solutions provide an…
We solve the geodesic deviation equations for the orbital motions in the Schwarzschild metric which are close to a circular orbit. It turns out that in this particular case the equations reduce to a linear system, which after…
We derive a general system of ODEs and associated explicit solutions in a special case for geodesics between full rank matrices in the deep linear network geometry. In the process, we find horizontal straight lines in the invariant balanced…
Training a neural network requires navigating a high-dimensional, non-convex loss surface to find parameters that minimize this loss. In many ways, it is surprising that optimizers such as stochastic gradient descent and ADAM can reliably…
Search-based methods that use motion primitives can incorporate the system's dynamics into the planning and thus generate dynamically feasible MAV trajectories that are globally optimal. However, searching high-dimensional state lattices is…
Applying robust optimization often requires selecting an appropriate uncertainty set both in shape and size, a choice that directly affects the trade-off between average-case and worst-case performances. In practice, this calibration is…
Deep distance metric learning (DDML), which is proposed to learn image similarity metrics in an end-to-end manner based on the convolution neural network, has achieved encouraging results in many computer vision tasks.$L2$-normalization in…
Optimizing energy consumption for robot navigation in fields requires energy-cost maps. However, obtaining such a map is still challenging, especially for large, uneven terrains. Physics-based energy models work for uniform, flat surfaces…
Finding solutions to the classical transportation problem is of great importance, since this optimization problem arises in many engineering and computer science applications. Especially the Earth Mover's Distance is used in a plethora of…
We consider the problem of inferring the topology of a network using the measurements available at the end nodes, without cooperation from the internal nodes. To this end, we provide a simple method to obtain path interference which…
We consider the following problem : we have a high-resolution street network of a given city, and low-resolution measurements of traffic within this city. We want to associate to each measurement the set of streets corresponding to the…
The observation of the motion of particles and light near a gravitating object is until now the only way to explore and to measure the gravitational field. In the case of exact black hole solutions of the Einstein equations the…
Industrial robots are widely used in various manufacturing environments due to their efficiency in doing repetitive tasks such as assembly or welding. A common problem for these applications is to reach a destination without colliding with…
The geometry of weight spaces and functional manifolds of neural networks play an important role towards 'understanding' the intricacies of ML. In this paper, we attempt to solve certain open questions in ML, by viewing them through the…
The outdoor navigation capabilities of ground robots have improved significantly in recent years, opening up new potential applications in a variety of settings. Cost-based representations of the environment are frequently used in the path…
We analyze the disordered Riemannian geometry resulting from random perturbations of the Euclidean metric. We focus on geodesics, the paths traced out by a particle traveling in this quenched random environment. By taking the point of the…
GipsyX/RTGx is the Jet Propulsion Laboratory's (JPL) next generation software package for positioning, navigation, timing, and Earth science using measurements from three geodetic techniques: Global Navigation Satellite Systems (GNSS),…
Trajectory optimization offers mature tools for motion planning in high-dimensional spaces under dynamic constraints. However, when facing complex configuration spaces, cluttered with obstacles, roboticists typically fall back to…