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We consider adaptive finite element methods for second-order elliptic PDEs, where the arising discrete systems are not solved exactly. For contractive iterative solvers, we formulate an adaptive algorithm which monitors and steers the…

Enforcing safety while preventing overly conservative behaviors is essential for autonomous vehicles to achieve high task performance. In this paper, we propose a barrier-enhanced parallel homotopic trajectory optimization (BPHTO) approach…

Parallel trajectory optimization via the Alternating Direction Method of Multipliers (ADMM) has emerged as a scalable approach to long-horizon motion planning. However, existing frameworks typically decompose the problem into parallel…

We develop stochastic mixed finite element methods for spatially adaptive simulations of fluid-structure interactions when subject to thermal fluctuations. To account for thermal fluctuations, we introduce a discrete fluctuation-dissipation…

Smart mobility becomes paramount for meeting net-zero targets. However, autonomous, self-driving and electric vehicles require more than ever before an efficient, resilient and trustworthy computational offloading backbone that expands…

Multiphase flows are an important class of fluid flow and their study facilitates the development of diverse applications in industrial, natural, and biomedical systems. We consider a model that uses a continuum description of both phases…

Discrete ordinate ($S_N$) and filtered spherical harmonics ($FP_N$) based schemes have been proven to be robust and accurate in solving the Boltzmann transport equation but they have their own strengths and weaknesses in different physical…

In this paper we consider the convergence analysis of adaptive finite element method for elliptic optimal control problems with pointwise control constraints. We use variational discretization concept to discretize the control variable and…

Adaptive lattice Boltzmann methods (LBMs) are based on velocity discretizations that self-adjust to local macroscopic conditions such as velocity and temperature. While this feature improves the accuracy and the stability of LBMs for large…

Although federated learning has achieved many breakthroughs recently, the heterogeneous nature of the learning environment greatly limits its performance and hinders its real-world applications. The heterogeneous data, time-varying wireless…

The paper aims to establish a fully discrete finite element (FE) scheme and provide cost-effective solutions for one-dimensional time-space Caputo-Riesz fractional diffusion equations on a bounded domain $\Omega$. Firstly, we construct a…

With the growing importance of large network models and enormous training datasets, GPUs have become increasingly necessary to train neural networks. This is largely because conventional optimization algorithms rely on stochastic gradient…

Time-domain Boundary Element Methods (BEM) have been successfully used in acoustics, optics and elastodynamics to solve transient problems numerically. However, the storage requirements are immense, since the fully populated system matrices…

Edge computing is increasingly proposed as a solution for reducing resource consumption of mobile devices running simultaneous localization and mapping (SLAM) algorithms, with most edge-assisted SLAM systems assuming the communication…

We propose a federated version of adaptive gradient methods, particularly AdaGrad and Adam, within the framework of over-the-air model training. This approach capitalizes on the inherent superposition property of wireless channels,…

This paper develops an adaptive proximal alternating direction method of multipliers (ADMM) for solving linearly constrained, composite optimization problems under the assumption that the smooth component of the objective is weakly convex,…

Motivated by the drawbacks of cloud-based federated learning (FL), cooperative federated edge learning (CFEL) has been proposed to improve efficiency for FL over mobile edge networks, where multiple edge servers collaboratively coordinate…

Finding node correspondence across networks, namely multi-network alignment, is an essential prerequisite for joint learning on multiple networks. Despite great success in aligning networks in pairs, the literature on multi-network…

We consider a general nonsymmetric second-order linear elliptic PDE in the framework of the Lax-Milgram lemma. We formulate and analyze an adaptive finite element algorithm with arbitrary polynomial degree that steers the adaptive…

We introduce a novel network-adaptive algorithm that is suitable for alleviating network packet losses for low-latency interactive communications between a source and a destination. Our network-adaptive algorithm estimates in real-time the…