相关论文: Dynamic interpolation for obstacle avoidance on Ri…

This paper studies path synthesis for nonholonomic mobile robots moving in two-dimensional space. We first address the problem of interpolating paths expressed as sequences of straight line segments, such as those produced by some planning…

In this work we study the asymptotic behavior of solutions of the incompressible two-dimensional Euler equations in the exterior of a single smooth obstacle when the obstacle becomes very thin tending to a curve. We extend results by…

Narrow passage path planning is a prevalent problem from industrial to household sites, often facing difficulties in finding feasible paths or requiring excessive computational resources. Given that deep penetration into the environment can…

Modern generative models hold great promise for accelerating diverse tasks involving the simulation of physical systems, but they must be adapted to the specific constraints of each domain. Significant progress has been made for…

We formulate the Bergman-type interpolation problem on finite open Riemann surfaces covered by the unit disk. Our version of the interpolation problem generalizes Bergman-type interpolation problems previously studied by Seip, Berntsson,…

Spline interpolation is a widely used class of methods for solving interpolation problems by constructing smooth interpolants that minimize a regularized energy functional involving the Laplacian operator. While many existing approaches…

In this paper we design a neural interpolation operator to improve the boundary data for regional weather models, which is a challenging problem as we are required to map multi-scale dynamics between grid resolutions. In particular, we…

We study a class of design problems in solid mechanics, leading to a variation on the classical question of equi-dimensional embeddability of Riemannian manifolds. In this general new context, we derive a necessary and sufficient existence…

Interpolating between points is a problem connected simultaneously with finding geodesics and study of generative models. In the case of geodesics, we search for the curves with the shortest length, while in the case of generative models we…

Finite-dimensional dissipative dynamical systems with multiple time-scales are obtained when modeling chemical reaction kinetics with ordinary differential equations. Such stiff systems are computationally hard to solve and therefore,…

Riemannian submanifold optimization with momentum is computationally challenging because, to ensure that the iterates remain on the submanifold, we often need to solve difficult differential equations. Here, we simplify such difficulties…

Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data…

In this paper, we investigate the multi-objective optimal control problem of ordinary differential equations on Riemannian manifolds. We first obtain the second-order necessary conditions for weak Pareto optimal solutions for…

The techniques and analysis presented in this thesis provide new methods to solve optimization problems posed on Riemannian manifolds. These methods are applied to the subspace tracking problem found in adaptive signal processing and…

In this paper we study nonconvex and nonsmooth multi-block optimization over Riemannian manifolds with coupled linear constraints. Such optimization problems naturally arise from machine learning, statistical learning, compressive sensing,…

We consider the approximation of minimal geodesics between two closed sets in $\mathbb{R}^D$ endowed with a smooth Riemannian metric. The continuous problem is formulated as the minimization of the energy functional over piecewise smooth…

Autonomous driving requires reliable collision avoidance in dynamic environments. Nonlinear Model Predictive Controllers (NMPCs) are suitable for this task, but struggle in time-critical scenarios requiring high frequency. To meet this…

We present a novel approach to Riemannian interpolation on the Grassmann manifold. Instead of relying on the Riemannian normal coordinates, i.e. the Riemannian exponential and logarithm maps, we approach the interpolation problem with an…

In this two-parts paper, we present a systematic procedure to extend the known Hamiltonian model of ideal inviscid fluid flow on Riemannian manifolds in terms of Lie-Poisson structures to a port-Hamiltonian model in terms of Stokes-Dirac…

The present contribution investigates shape optimisation problems for a class of semilinear elliptic variational inequalities with Neumann boundary conditions. Sensitivity estimates and material derivatives are firstly derived in an…