arXiv subjects

Tri P. Nguyen

Publications and source records attributed to Tri P. Nguyen.

5 recordsLinked to original sources

arXiv2025

Exploring exponential time integration for strongly magnetized charged particle motion

A fundamental task in particle-in-cell (PIC) simulations of plasma physics is solving for charged particle motion in electromagnetic fields. This problem is especially challenging when the plasma is strongly magnetized due to numerical stiffness arising from the wide separation in time scales between highly oscillatory gyromotion and overall macroscopic behavior of the system. In contrast to conventional finite difference schemes, we investigated exponential integration techniques to numerically simulate strongly magnetized charged particle motion. Numerical experiments with a uniform magnetic field show that exponential integrators yield superior performance for linear problems (i.e. configurations with an electric field given by a quadratic electric scalar potential) and are competitive with conventional methods for nonlinear problems with cubic and quartic electric scalar potentials.

physics.comp-ph↗

arXiv2025

Nystr\"om Type Exponential Integrators for Strongly Magnetized Charged Particle Dynamics

Solving for charged particle motion in electromagnetic fields (i.e. the particle pushing problem) is a computationally intensive component of particle-in-cell (PIC) methods for plasma physics simulations. This task is especially challenging when the plasma is strongly magnetized due numerical stiffness arising from the wide range of time scales between highly oscillatory gyromotion and long term macroscopic behavior. A promising approach to solve these problems is by a class of methods known as exponential integrators that can solve linear problems exactly and are A-stable. This work extends the standard exponential integration framework to derive Nystr\"om-type exponential integrators that integrates the Newtonian equations of motion as a second-order differential equation directly. In particular, we derive second-order and third-order Nystr\"om-type exponential integrators for strongly magnetized particle pushing problems. Numerical experiments show that the Nystr\"om-type exponential integators exhibit significant improvement in computation speed over the standard exponential integrators.

physics.comp-ph↗

arXiv2017

Importance Sketching of Influence Dynamics in Billion-scale Networks

The blooming availability of traces for social, biological, and communication networks opens up unprecedented opportunities in analyzing diffusion processes in networks. However, the sheer sizes of the nowadays networks raise serious challenges in computational efficiency and scalability. In this paper, we propose a new hyper-graph sketching framework for inflence dynamics in networks. The central of our sketching framework, called SKIS, is an efficient importance sampling algorithm that returns only non-singular reverse cascades in the network. Comparing to previously developed sketches like RIS and SKIM, our sketch significantly enhances estimation quality while substantially reducing processing time and memory-footprint. Further, we present general strategies of using SKIS to enhance existing algorithms for influence estimation and influence maximization which are motivated by practical applications like viral marketing. Using SKIS, we design high-quality influence oracle for seed sets with average estimation error up to 10x times smaller than those using RIS and 6x times smaller than SKIM. In addition, our influence maximization using SKIS substantially improves the quality of solutions for greedy algorithms. It achieves up to 10x times speed-up and 4x memory reduction for the fastest RIS-based DSSA algorithm, while maintaining the same theoretical guarantees.

cs.DS↗

arXiv2017

Outward Influence and Cascade Size Estimation in Billion-scale Networks

Estimating cascade size and nodes' influence is a fundamental task in social, technological, and biological networks. Yet this task is extremely challenging due to the sheer size and the structural heterogeneity of networks. We investigate a new influence measure, termed outward influence (OI), defined as the (expected) number of nodes that a subset of nodes $S$ will activate, excluding the nodes in S. Thus, OI equals, the de facto standard measure, influence spread of S minus |S|. OI is not only more informative for nodes with small influence, but also, critical in designing new effective sampling and statistical estimation methods. Based on OI, we propose SIEA/SOIEA, novel methods to estimate influence spread/outward influence at scale and with rigorous theoretical guarantees. The proposed methods are built on two novel components 1) IICP an important sampling method for outward influence, and 2) RSA, a robust mean estimation method that minimize the number of samples through analyzing variance and range of random variables. Compared to the state-of-the art for influence estimation, SIEA is $Ω(\log^4 n)$ times faster in theory and up to several orders of magnitude faster in practice. For the first time, influence of nodes in the networks of billions of edges can be estimated with high accuracy within a few minutes. Our comprehensive experiments on real-world networks also give evidence against the popular practice of using a fixed number, e.g. 10K or 20K, of samples to compute the "ground truth" for influence spread.

cs.DS↗

arXiv2017

Towards Optimal Strategy for Adaptive Probing in Incomplete Networks

We investigate a graph probing problem in which an agent has only an incomplete view $G' \subsetneq G$ of the network and wishes to explore the network with least effort. In each step, the agent selects a node $u$ in $G'$ to probe. After probing $u$, the agent gains the information about $u$ and its neighbors. All the neighbors of $u$ become \emph{observed} and are \emph{probable} in the subsequent steps (if they have not been probed). What is the best probing strategy to maximize the number of nodes explored in $k$ probes? This problem serves as a fundamental component for other decision-making problems in incomplete networks such as information harvesting in social networks, network crawling, network security, and viral marketing with incomplete information. While there are a few methods proposed for the problem, none can perform consistently well across different network types. In this paper, we establish a strong (in)approximability for the problem, proving that no algorithm can guarantees finite approximation ratio unless P=NP. On the bright side, we design learning frameworks to capture the best probing strategies for individual network. Our extensive experiments suggest that our framework can learn efficient probing strategies that \emph{consistently} outperform previous heuristics and metric-based approaches.

cs.SI↗