相关论文: An efficient jet marcher for computing the quasipo…
Latent class model (LCM), which is a finite mixture of different categorical distributions, is one of the most widely used models in statistics and machine learning fields. Because of its non-continuous nature and the flexibility in shape,…
\textbf{Objective: }To develop a real-time method for designing gradient waveforms for arbitrary $k$-space trajectories that are time-optimal and hardware-compliant. \textbf{Methods: }The gradient waveform is solved recursively under both…
Stochastic Differential Equations (SDEs) serve as a powerful modeling tool in various scientific domains, including systems science, engineering, and ecological science. While the specific form of SDEs is typically known for a given…
We propose a numerical algorithm for the computation of multi-marginal optimal transport (MMOT) problems involving general probability measures that are not necessarily discrete. By developing a relaxation scheme in which marginal…
We develop the theory of Energy Conserving Descent (ECD) and introduce ECDSep, a gradient-based optimization algorithm able to tackle convex and non-convex optimization problems. The method is based on the novel ECD framework of…
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…
Unmapped areas and aerodynamic disturbances render autonomous navigation with quadrotors extremely challenging. To fly safely and efficiently, trajectory planners and trackers must be able to navigate unknown environments with unpredictable…
The unmanned aerial vehicle (UAV) based multi-access edge computing (MEC) appears as a popular paradigm to reduce task processing latency. However, the secure offloading is an important issue when occurring aerial eavesdropping. Besides,…
We study a class of nonsmooth stochastic optimization problems on Riemannian manifolds. In this work, we propose MARS-ADMM, the first stochastic Riemannian alternating direction method of multipliers with provable near-optimal complexity…
We study multivalued stochastic differential equations (MSDEs) with maximal monotone operators driven by semimartingales with jumps. We discuss in detail some methods of approximation of solutions of MSDEs based on discretization of…
We propose a probabilistic numerical algorithm to solve Backward Stochastic Differential Equations (BSDEs) with nonnegative jumps, a class of BSDEs introduced in [9] for representing fully nonlinear HJB equations. In particular, this allows…
Planning the trajectory of the controlled ego vehicle is a key challenge in automated driving. As for human drivers, predicting the motions of surrounding vehicles is important to plan the own actions. Recent motion prediction methods…
We introduce the multivariate decomposition finite element method (MDFEM) for solving elliptic PDEs with uniform random diffusion coefficients. We show that the MDFEM can be used to reduce the computational complexity of estimating the…
In this paper, we present a bilevel optimal motion planning (BOMP) model for autonomous parking. The BOMP model treats motion planning as an optimal control problem, in which the upper level is designed for vehicle nonlinear dynamics, and…
First-order optimization methods, such as SGD and Adam, are widely used for training large-scale deep neural networks due to their computational efficiency and robust performance. However, relying solely on gradient information, these…
With much research has been conducted into trajectory planning for quadrotors, planning with spatial and temporal optimal trajectories in real-time is still challenging. In this paper, we propose a framework for generating large-scale…
Bilevel hyperparameter optimization has received growing attention thanks to the fast development of machine learning. Due to the tremendous size of data sets, the scale of bilevel hyperparameter optimization problem could be extremely…
We study the discretization of the Escape Time problem: find the length of the shortest path joining an arbitrary point of a domain, to the domain's boundary. Path length is measured locally via a Finsler metric, potentially asymmetric and…
This paper considers estimating the parameters in a regime-switching stochastic differential equation(SDE) driven by Normal Inverse Gaussian(NIG) noise. The model under consideration incorporates a continuous-time finite state Markov chain…
We describe a mesh-free three-dimensional numerical scheme for solving the incompressible semi-geostrophic equations based on semi-discrete optimal transport techniques. These results generalise previous two-dimensional implementations. The…