DKU-SUFE Summer Research Program

Mentor: Dr. Dongmian Zou

Abstract: Generative models based on diffusion have emerged as crucial tools for generating high-quality data, driving advancements in AI-generated content (AIGC). These models refine noisy representations into meaningful outputs through iterative processes, making them highly effective in diverse applications such as image synthesis, molecular modeling, and other complex data domains. Despite their successes, existing approaches often fail to incorporate domain-specific geometric and structural knowledge into the modeling framework. This project aims to extend diffusion-based generative frameworks to specialized geometric domains, including graphs, spherical spaces, and hyperbolic spaces.

Students will start by reviewing foundational works, focusing on diffusion-based, scorebased, and flow-matching methodologies, as well as key advances in geometric deep learning that may be relevant. They will then work on generalizing existing diffusion models to various geometric domains, conducting numerical experiments to validate and refine their approaches. Based on these findings, they will explore theoretical frameworks, focusing on rigorous analysis. Finally, students will consolidate their work by implementing the results into a codebase and test on various datasets.

Mentor: Dr. Mustafa Misir

Abstract: This project explores the application of Large Language Models (LLMs) in Automated Algorithm Selection (AAS) for portfolio optimization. The research aims to develop an innovative system that leverages LLMs to select the most appropriate algorithm for each portfolio management task, enhancing both performance and robustness across varying market conditions.

The proposed system will utilize pretrained LLMs to extract key market features such as volatility patterns and sector trends, recommending the most suitable optimization strategy for each portfolio case. Real-world stock market indexes, including S&P 500 and CSI 300, will serve as target portfolio optimization instances.

The project will be executed in three phases:

1. Data collection from existing datasets and real-time stock market indexes via APIs.
2. Feature extraction from market data using LLMs.
3. Development of an AAS system that maps extracted features to performance data for automatically recommending algorithms.

The research will validate the system's generalization capabilities across different portfolio optimization scenarios, including rising/falling prices and shifts in market leadership.

Rationale and Research Aim: Portfolio optimization requires adapting algorithms to dynamic markets, but manual selection is expertise intensive. This project addresses this gap by accommodating LLMs for AAS, making advanced strategies accessible to nonexperts. The aim is to develop a robust AAS system that can outperform state-of-the-art algorithms in various market conditions.

Expected Outputs:

• A Python library integrating LLM prompting, feature extraction, and algorithm selection.
• Comprehensive analysis benchmarking LLM-driven vs. existing approaches.
• A research report suitable for publication in a peer-reviewed journal or conference.

Potential Academic/Research Impact: The novel application of AAS to portfolio optimization has the potential to significantly advance the field of financial mathematics and machine learning. The research outcomes may lead to improved portfolio management strategies and contribute to the broader understanding of LLM applications in finance.

Mentor: Dr. Changjuan Zhang

Abstract: This project investigates the dynamic behavior of Olympic rowing boats by employing Computational Fluid Dynamics (CFD)techniques to analyze the impact of hull geometry and dimensions on resistance characteristics. We will develop a multiphase coupled numerical model (water-air-boat) using the Volume of Fluid (VOF)method combined with the finite volume method to solve the incompressible Navier-Stokes equations, capturing dynamic interfacial changes during boat motion. Key research focuses include modeling the dynamic centroid of athletes during rowing, calculating motion trajectories based on a six-degree-of-freedom (6-DOF) model, and comparing resistance differences among various hull designs during acceleration and cruising phases. Simulation experiments will be conducted using open-source CFD tools like OpenFOAM. Through this project, students will gain hands-on experience in multiphase flow numerical simulation, learn algorithm implementation for moving body coupling simulations, and develop engineering modeling skills for scientific problems.

Mentor: Dr. Jing Yao

Abstract: This summer project is designed for undergraduate students interested in financial analysis, quantitative modeling, and portfolio optimization. The project will focus on analyzing historical stock return data using the mean-variance framework to develop efficient investment portfolios. Students will employ statistical techniques to estimate returns, variances, and covariances, construct efficient portfolios, and explore the Capital Assets Pricing Model (CAPM) and Efficient Market Hypothesis (EMH).

Objectives: The primary goals of this project are:

• To estimate expected returns, variances, and covariances of a given set of stocks.
• To construct an optimal portfolio using mean-variance optimization techniques.
• To examine the role of a risk-free asset in portfolio selection.
• To analyze the Capital Market Line and its implications for investment strategies.
• To evaluate the Efficient Market Hypothesis (EMH) based on the findings.

Project Tasks:

• Estimating Expected Returns and Risk Measures
  • Students will be learn how to collect historical data of stocks and the market index.
  • Using the unbiased estimator, they will calculate the expected returns, variances, and covariances.
  • A comparative analysis will be conducted to determine the best stock for a single-stock investment strategy.
• Constructing an Efficient Portfolio
  • Using the Lagrangian method and "solve" function in R, students will construct an efficient portfolio with an expected return of 0.5%.
  • The efficient portfolio will be compared with the single-stock recommendation to assess the benefits of diversification.
• Incorporating a Risk-Free Asset
  • Assuming a risk-free rate, students will optimize a new portfolio including this risk-free asset.
  • They will compare this new portfolio with the previous one to illustrate the improvement in risk-return trade-offs.
• Capital Market Line and Market Portfolio
  • Using the market index as the market portfolio, students will plot the Capital Market Line (CML) in R.
  • They will analyze whether the efficient portfolio can outperform the market portfolio and discuss the implications for EMH.

Preliminaries:

• Understanding the basic ideas in probability theory and statistics such as mean, variance and covariance.
• Understanding the optimization in calculus and matrix calculation in linear algebra.
• Capacity on simple coding in R/MATLAB/Python.

Learning Outcomes: By the end of this project, students will develop skills in quantitative finance, portfolio optimization, and statistical computing. They will gain insights into riskreturn trade-offs, efficient portfolio construction, and the practical application of financial theories in investment decision-making.

Mentor: Dr. Shixin Xu

Abstract: Indoor air quality is strongly influenced by the number of occupants in a space. Carbon dioxide (CO₂) concentration is a key indicator of occupancy levels since CO₂ is primarily produced by human respiration. Real-time estimation of occupancy based on CO₂ measurements has important applications in:

• Building Energy Management: Optimizing HVAC operation to improve energy efficiency.
• Indoor Air Quality Control: Ensuring adequate ventilation for health and comfort.
• Security and Emergency Management: Monitoring occupancy in public spaces for safety and evacuation planning.
• Smart Building Systems: Integrating sensor data for real-time decision-making in smart buildings.

While existing methods may rely on direct head counting or video analysis, using CO₂ concentration provides a non-intrusive, cost-effective alternative that can be deployed widely with modern sensor networks.

Project Objectives

• Model Development: Establish a mathematical model that relates CO₂ concentration dynamics to the number of occupants in a room.
• Data Analysis: Collect and preprocess data on CO₂ levels and actual occupancy to calibrate and validate the model.
• Prediction and Uncertainty Quantification: Use the model to predict occupancy, including estimates of uncertainty, and analyze model performance.
• Application Insights: Identify potential improvements in building energy management and indoor air quality control based on model predictions.

Expected Outcomes

• A validated mathematical model relating indoor CO₂ concentration dynamics to occupancy levels.
• Prediction algorithms that estimate the number of people in real time, with uncertainty quantification.
• Insights and recommendations for building managers on optimizing HVAC systems and indoor air quality based on occupancy predictions.
• A comprehensive report detailing model formulation, calibration, validation, simulation results, and potential applications.

Mentor: Dr. Naveen Vaidya

Abstract: About half of the world's population, about 4 billion people, live in areas with a risk of dengue infection. Recent evolutionary adaptation of dengue-transmitting mosquitoes (vectors) to colder places has raised severe public health concerns about global dengue outbreaks. This research project aims to develop several data-driven models to investigate dengue virus transmission. Specifically, students will have opportunities to get experience in creating data-driven probabilistic and deterministic models of (a) estimating reproduction numbers for dengue virus transmission, (b) spreading a single serotype of the virus, and (c) transmitting multiple serotypes of the virus. As a case study, we focus on the data from the dengue epidemic in Guangzhou, China. The students will also explore the developed models to evaluate potential public health policies for preventing and controlling dengue epidemics. The students' novel research in this project will contribute to modelingbased methodology to characterize the transmission of vector-borne diseases, ultimately providing effective strategies for preventing and controlling disease outbreaks.

Mentor: Dr. Xiangsheng Wang

Abstract: Srinivasa Ramanujan was an Indian mathematician who made profound contributions to pure mathematics despite having little formal training in the field. Throughout his short life, he discovered numerous remarkable formulas that astonished the mathematical community. Ramanujan claimed that he often dreamed of a Hindu goddess, Namagiri, who revealed complex mathematical formulas to him, which he would then test and verify upon waking.

Many of Ramanujan's formulas were presented without rigorous proofs, prompting renowned mathematicians to investigate and validate them. This research project aims to explore and analyze some of his extraordinary formulas. Students will engage in numerical approximations, asymptotic analysis, and various mathematical techniques to examine and verify Ramanujan's formulas.

Through this project, students will gain valuable research experience in formulating conjectures, identifying patterns, and developing rigorous proofs. A list of helpful references is provided below.

References:

• G. E. Andrews, B. C. Berndt, Ramanujan's lost notebook. Part I, Springer, New York, 2005
• G. E. Andrews, B. C. Berndt, Ramanujan's lost notebook. Part II, Springer, New York, 2009
• G. E. Andrews, B. C. Berndt, Ramanujan's lost notebook. Part III, Springer, New York, 2012
• G. E. Andrews, B. C. Berndt, Ramanujan's lost notebook. Part IV, Springer, New York, 2013
• G. E. Andrews, B. C. Berndt, Ramanujan's lost notebook. Part V, Springer, New York, 2018
• E. T. Copson, Asymptotic Expansions, Cambridge University Press, New York, 1965
• M. E. H. Ismail, Classical and quantum orthogonal polynomials in one variable, Cambridge University Press, Cambridge, 2005
• G. Szego, Orthogonal polynomials, American Mathematical Society, Providence, RI, 1975