Numerical Analysis and Scientific Computing Commons^™

Utilizing Computer Modeling To Optimize Electric Fields Within Xenon Time Projection Chambers, Miles Meloni

Honors Theses

XENONnT is a physics experiment designed with the goal of detecting dark matter particles. The detector is a time projection chamber; a series of charged electrodes creates an electric field, surrounding a central body filled with liquid and gaseous xenon. Photomultiplier tubes (PMTs), positioned on either end of the chamber, serve to detect light signals. We seek to minimize the root mean square of the electric field norms experienced by the PMTs. This quantity corresponds to the variance in the electric field observed by the PMTs. Establishing a consistent electric field is important to maintaining these sensitive components. The electric …

A 1d Symmetric Interior Penalty Discontinuous Galerkin Solver In Rust, William Aey

Williams Honors College, Honors Research Projects

This honors project will build a 1D Symmetric Interior Discontinuous Galerkin (SIPDG) solver in Rust for Stum-Liouville type problems such as the Poisson equation, with Robin, Dirichlet, and Neumann boundary conditions. The work will cover the full pipeline: starting from the strong form of the PDE, deriving the DG weak form, implementing element and interface operators, and assembling or apply the discrete operator. Rust's safety and concurrency (e.g, via Rayon) will be used to explore serial and parallel performance. A test-driven development approach will be used to maintain a strong suite of tests. The project will result in a documented …

Machine Learning For Recession Prediction, Ethan Reusser

Williams Honors College, Honors Research Projects

Macroeconomic predictions present challenges in machine learning due to the rarity of economic recessions, the constantly-changing matter of global markets, and severe class imbalance in historical data. This project focuses on predicting the onset of United States economic recessions within a 12-month window using Python and Jupyter Notebook. A machine learning pipeline was developed utilizing multiple models: Logistic Regression, Random Forest, XGBoost, and Long Short-Term Memory (LSTM) neural networks. For class imbalance, the Synthetic Minority Over-sampling Technique (SMOTE) was applied strictly to training data, paired with Platt scaling for calibration on thresholds. The resulting models were evaluated in the 2005 …

Data Defines Success: Algorithm For Dataset Quality Assessment In Deep Learning For Malware Detection, Matei Ionescu

Theses and Dissertations

The field of artificial intelligence is based upon the premise of constructing architectures through which to propagate training data. However, the majority of existing research literature is focused on architecture. While necessary, the attention devoted to the architecture should not so precipitously exceed that of the data. It should be noted that this disparity is not without reasonable cause. Data quality is often exceedingly difficult to verify due to particularities of the field or subfield; LLM repositories of text are distinct from image recognition pictures of dog breeds which are distinct from EEG waveforms of human brains which are distinct …

Performance Of Numerical Methods Applied To The Black–Scholes Model, Scott Cameron Williams

UNF Graduate Theses and Dissertations

We compare five numerical approaches for approximating solutions to the Black–Scholes partial differential equation for pricing European call options: FTCS, BTCS, Crank– Nicolson, Monte Carlo simulation, and a physics–informed neural network (PINN). These methods span finite difference techniques, probabilistic simulation, and machine learning. Performance is evaluated based on computational efficiency and accuracy relative to the analytical Black–Scholes solution.

Among the methods, Crank–Nicolson and the PINN demonstrated the strongest overall performance. Crank–Nicolson achieved the highest accuracy but exhibited increased runtime as the number of underlying stock price grid points grew. In contrast, the PINN produced slightly less accurate results but with …

Hybrid Learning And Optimization Methods For Solving Capacitated Vehicle Routing Problem, Monit Sharma, Hoong Chuin Lau

Research Collection School Of Computing and Information Systems

We propose a hybrid quantum–classical framework for the Capacitated Vehicle Routing Problem (CVRP) that integrates the Augmented Lagrangian Method (ALM) with deep reinforcement learning (RL). Directly solving CVRP via Variational Quantum Eigensolver (VQE) requires a slack-based QUBO formulation, where converting inequalities to equalities greatly increases the qubit count. To circumvent this, we employ an ALM-based reformulation that enforces constraints through Lagrange terms instead of slack variables, drastically reducing quantum resource demands. An RL agent, trained with Soft Actor–Critic, adaptively tunes the Lagrange penalties to improve convergence and feasibility. Experiments show that RL-Q-ALM outperforms static-penalty and plain VQE baselines in both …

Geovig And Purevig: Geometry-Aware Architectures For Efficient Computer Vision, Omar Ismail

Theses and Dissertations (Comprehensive)

Deploying deep learning models for medical image analysis on mobile devices requires a balance between inference latency, memory footprint, and delineating anatomical boundaries with high accuracy. While Convolutional Neural Networks (CNNs) and mobile Vision Transformers (ViTs) offer efficiency, they often struggle to model the irregular, non-local geometric structures inherent in biological tissues without incurring prohibitive computational costs. In this thesis, we introduce GeoViG (Geometric Vision Graph), an architecture that bridges the gap between efficient grid-based processing and explicit Geometric Deep Learning. GeoViG introduces a novel transition from high-resolution pixel grids to low-resolution dynamic graphs via a SpreadEdgePool operator, a geometry-aware …

Swimming In Uncertainty: Filling Data Gaps And Providing An Educational Platform For Beach Water Quality At Tybee Island, Georgia, Lukas Roberson

College of Graduate Studies: Theses & Dissertations

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Swimming in beaches water contaminated with high levels of bacteria can make you sick. Current monitoring at the public beaches on Tybee Island consists of weekly monitoring and enumeration of fecal indicator bacteria that takes 24 hours for results. If the number of bacteria exceed regulatory limits, a public health advisory is issued, and affected waters are retested until …

A General Algorithm For Assortment Optimization Under Random Utility Choice Models, Tien Mai, Andrea Lodi

Research Collection School Of Computing and Information Systems

This work concerns the assortment optimization problem that refers to selecting a subset of items that maximizes the expected revenue in the presence of the substitution behavior of consumers specified by a random utility choice model. The key challenge lies in the computational difficulty of finding the best subset solution, which often requires exhaustive search. The literature on constrained assortment optimization lacks a practically efficient method that is general to deal with different types of customer choice models (e.g., the multinomial logit, mixed logit or general multivariate extreme value models). In this work, we propose a new approach that allows …

Decentralized Linear Solvers: Communication Cost And Privacy, Nelson G. Brasil, Vinay A. Vaishampayan

Publications and Research

We consider the problem of multiple parties iteratively solving a system of linear equations in a decentralized manner. Specifically, we solve for $\negr{x} \in \R^n$, the $n \times n$ system of linear equations $M\negr{x} = \negr{b}$ when each party only knows their row of the matrix $M$ and a single component of $\negr{b} \in \R^n$. Our objective is to determine the tradeoff between the accuracy of the solution and the total communication cost measured in bits. A fully connected, reliable mesh network is assumed to connect the different parties. We develop a general formulation that applies to a large class …

Learning-Based Graph Shrinking For Quantum Optimization Of Constrained Combinatorial Problems, Monit Sharma, Hoong Chuin Lau

Research Collection School Of Computing and Information Systems

Graph shrinking has recently emerged as a powerful preprocessing technique for hybrid classical–quantum optimization, enabling variable and constraint reduction before quantum solving. Conventional approaches rely on Semi-Definite Programming (SDP) relaxations to compute vertex correlations, but these methods suffer from high computational overhead, instance-specific tuning, and limited generalizability. In this work, we replace the handcrafted SDP correlation stage with a reinforcement learning (RL) based correlation estimator, trained to predict merge quality directly from graph structure. We reformulate the graph shrinking process as a Markov Decision Process (MDP), design a Graph Neural Network (GNN) policy to guide vertex merging, and integrate the …

Multi-Timescale Monitoring And Modeling For Resilient Smart Grids: Pmu Anomaly Detection And Battery Digital Twins, Muhammad Imran Hossain

Graduate Theses, Dissertations, and Problem Reports (ETD)

Modern power systems face failures at very different timescales. Cyber-physical disturbances may emerge within seconds, while battery degradation develops over hundreds of operating cycles. Both monitoring problems share the same underlying difficulty: power systems produce measurement data in abundance, but reliably labeled examples of abnormal or degraded operation are scarce. Rare grid events are difficult to label, and battery degradation data are heterogeneous across cells, cycling protocols, and chemistries. This thesis addresses these challenges through two complementary domain-informed learning frameworks that constrain representation learning using information specific to each physical problem.

First, at the system level, T-BiGAN, a Transformer-augmented bidirectional …

Improved Pid Search Algorithm For Uav Path Planning In Mountainous Environments, Yi Peng, Yunkui Lei, Qingqing Yang, Hui Li, Jianming Wang

Journal of System Simulation

Abstract: To address the challenges of UAV path planning in mountainous environments, including high computational complexity and suboptimal optimization performance, and the disadvantages of the PIDbased search algorithm, such as low optimization accuracy and slow convergence rate, this paper proposed an improved PID search algorithm (IPSA). The method introduced a good point set to ensure a more uniform population distribution, thereby enhancing population diversity and global search capability. The Q-learning algorithm was employed to adapt PID parameter adjustments, incorporating an exploration rate factor to further improve the algorithm's exploration and computational capabilities. A lens imaging opposition-based learning mechanism was also …

Dynamic Characteristic Simulation And Optimization Of Ground Test System For Airborne Launch Rack, Yuguang Bai, Sheng Zhang, Yushun Cao, Xiaoshi Zhang, Hu Huang

Journal of System Simulation

Abstract: To solve the ground equivalent test problem of the airborne launch system, an optimization method for the dynamic characteristics of the ground launch rack test system based on a multi-variable optimization approach was proposed. Through the discussion on the boundary conditions of the foundation, an effective dynamic simulation model of the ground launch test system was established. By comparing the dynamic characteristics of the launch rack structure in the airborne state and the ground test state, the objectives and constraints of the optimization design were determined. The dynamic characteristics of the ground test system were optimized and designed. …

Optimization Of Dynamic Weapon Target Assignment Considering Random Disturbances, Zhenzu Bai, Yizhi Hou, Zhangming He, Juhui Wei, Haiyin Zhou, Jiongqi Wang

Journal of System Simulation

Abstract: The impact of various random disturbances in the actual command and control environment of unmanned systems on problem modeling and solving of weapon target assignment was considered, and three types of uncertainty disturbance constraints were investigated. A multi-objective dynamic sensor weapon target assignment model was established. By considering the issues of model property changes caused by disturbances and insufficient robustness of the traditional single-operator solving algorithm, a multi-operator constrained multi-objective evolutionary framework based on the deep Q-network was proposed. The algorithm described the convergence, diversity, and feasibility of the population in both the objective and decision spaces. It established …

Survey Of Cooperative Multi-Agent Path Finding, Jun Xiong, Wenbo Zhang, Zhi Xiong, Feng Zhou, Bo Yang

Journal of System Simulation

Abstract: Cooperative multi-agent path finding (Co-MAPF) has been widely applied in fields such as UAV formation and multi-agent systems, which enhances the overall system efficiency through task collaboration, path planning, and task execution among multiple agents. This paper introduced three main system architectures, namely centralized, distributed, and hybrid, along with their advantages and disadvantages based on the definition of the Co-MAPF problem, categorized, and reviewed mainstream Co-MAPF algorithms, including those based on sampling, search, intelligent optimization, and learning. Furthermore, this paper analyzed the main current challenges faced by Co-MAPF algorithms on the basis of summarizing existing research and outlined the …

Optimization Of Order Picking And Sorting Coordintion In “Goods-To-Person” System, Liang Ren, Zerong Zhou, Yunfeng Ma

Journal of System Simulation

Abstract: To improve the order picking and sorting collaboration with time windows in the "goods-to-person" system, a mathematical model aiming to minimize the number of sorting batches was established. With the characteristics of this issue considered, a hybrid variable neighborhood search (HVNS) algorithm based on the "classified loading" strategy was proposed for solutions. The numerical experimental results show that the HVNS algorithm can obtain high-quality solutions while shortening the solution time; different order structures have varying effects on the utilization of the loading capacity of sorting automated guided vehicles (AGVs); under the tested experimental conditions, the collaborative operation mode …

Interoperability Model And Application Of Military Training System For Combination Of Virtuality And Reality, Jianxing Gong, Hai Hu, Haihui Ren, Ruixiang Wu

Journal of System Simulation

Abstract: With the development of AI technology, VR technology, and combat simulation technology, in order to achieve the practical training effect of "how to fight and how to train soldiers", virtual and real training has become a widely popular military training mode. It has become a trend to integrate digital systems, virtual equipment, semi-physical models, physical models, and other heterogeneous systems to carry out training in the same training environment. Therefore, it is necessary to study the interoperability model and application of training systems for the combination of virtuality and reality. This paper proposed the definition of interoperability between virtuality …

Research On Infrared And Visible Light Fusion Method Based On Resnet-50 And Laplacian Filtering, Xiao Wang, Xiangyang Li, Feng Liang, Zhili Zhang

Journal of System Simulation

Abstract: In order to solve the problem that existing infrared and visible light image fusion techniques often suffer from artifacts caused by insufficient contrast, spectral distortion, and high computational complexity, a fusion framework based on ResNet-50 and Laplacian filtering was proposed. ResNet-50 was used to extract shallow and deep features, followed by multi-scale feature fusion. Laplacian filtering was applied to optimize feature information, and an automatic discriminator was introduced to further improve the fusion effect. Simulation results show that, compared with comparison algorithms, the proposed method achieves an average increase of 2.71% and 2.16% in information entropy, 5.98% and …

Analysis Of Optimal Spectral Bands For Thermal Infrared Hyperspectral Image Reconstruction Driven By Physical Simulation Model, Yonghao Yang, Xiaoyu He

Journal of System Simulation

Abstract: To achieve accurate reconstruction of thermal infrared hyperspectral images under limited spectral bands, this paper proposed a reconstruction method based on physical modeling and simulation. Semi-global decomposition algorithm was adopted to invert the thermophysical properties of the scenario based on the physical model of thermal radiation, simulating and generating full-band hyperspectral data. An optimal spectral band selection strategy driven by a physical model was proposed, which integrated the sensitivity of temperature inversion and the separability of material spectra. Experiments were conducted on both simulated and measured datasets to evaluate the performance of material identification, temperature inversion, and spectral …