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We present a stochastic descent algorithm for unconstrained optimization that is particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained optimization and…
We introduce an algorithm based on Generalized Dual Method (GDM) to efficiently study the dynamics of a particle in quasiperiodic environments without the need to use periodic approximations or to save the information of the vertices that…
We introduce a new numerical method to approximate the solutions of a class of stationary Hamilton-Jacobi (HJ) partial differential equations arising from minimum time optimal control problems. We rely on nested grid approximations, and…
This paper presents a formulation for deterministically calculating optimized paths for a multiagent system consisting of heterogeneous vehicles. The key idea is the calculation of the shortest time for each agent to reach every grid point…
In this article we expand and develop the authors' recent proposed methodology for efficient stochastic superparameterization (SP) algorithms for geophysical turbulence. Geophysical turbulence is characterized by significant intermittent…
Optimization problems with constraints in the form of a partial differential equation arise frequently in the process of engineering design. The discretization of PDE-constrained optimization problems results in large-scale linear systems…
Quasi-Monte Carlo (QMC) method is a useful numerical tool for pricing and hedging of complex financial derivatives. These problems are usually of high dimensionality and discontinuities. The two factors may significantly deteriorate the…
Data compression technology is able to reduce data size, which can be applied to lower the cost of task offloading in mobile edge computing (MEC). This paper addresses the practical challenges for robust trajectory and scheduling…
We propose a joint channel estimation and data detection (JED) algorithm for densely-populated cell-free massive multiuser (MU) multiple-input multiple-output (MIMO) systems, which reduces the channel training overhead caused by the…
Joint distribution matching (JDM) problem, which aims to learn bidirectional mappings to match joint distributions of two domains, occurs in many machine learning and computer vision applications. This problem, however, is very difficult…
We present the Continuous Empirical Cubature Method (CECM), a novel algorithm for empirically devising efficient integration rules. The CECM aims to improve existing cubature methods by producing rules that are close to the optimal,…
In this paper, we propose a low rank approximation method for efficiently solving stochastic partial differential equations. Specifically, our method utilizes a novel low rank approximation of the stiffness matrices, which can significantly…
Walking motion planning based on Divergent Component of Motion (DCM) and Linear Inverted Pendulum Model (LIPM) is one of the alternatives that could be implemented to generate online humanoid robot gait trajectories. This algorithm requires…
Standard Bayesian retrievals for exoplanet atmospheric parameters from transmission spectroscopy, while well understood and widely used, are generally computationally expensive. In the era of the JWST and other upcoming observatories,…
State-of-the-art neural networks with early exit mechanisms often need considerable amount of training and fine tuning to achieve good performance with low computational cost. We propose a novel early exit technique, Early Exit Class Means…
In this paper, we introduce an accelerated distributed stochastic gradient method with momentum for solving the distributed optimization problem, where a group of $n$ agents collaboratively minimize the average of the local objective…
Event cameras unlock new frontiers that were previously unthinkable with standard frame-based cameras. One notable example is low-latency motion estimation (optical flow), which is critical for many real-time applications. In such…
We develop a non-empirical scheme to search for the minimum-energy escape paths from the minima of the potential surface to unknown saddle points nearby. A stochastic algorithm is constructed to move the walkers up the surface through the…
In multi-input-multi-output (MIMO) detection, semidefinite relaxation (SDR) has been shown to be an efficient high-performance approach. Developed initially for BPSK and QPSK, SDR has been found to be capable of providing near-optimal…
Continuous-time approximation of Stochastic Gradient Descent (SGD) is a crucial tool to study its escaping behaviors from stationary points. However, existing stochastic differential equation (SDE) models fail to fully capture these…