Below is a list of potential projects for the 2026 UCLA Computational and Applied Mathematics REU (subject to funding approval)
To apply: https://www.mathprograms.org/db/programs/1877
Title: Neural Scaling Laws
Project Lead: Professor Hayden Schaeffer
Overview: This project explores how the performance of neural networks changes as models and computational resources are scaled. Students will conduct computational experiments with a set of learning algorithms (in ML or SciML) over a range of problem settings to investigate patterns in training and testing behavior. The project emphasizes empirical analysis and interpretation, with the goal of gaining insight into general trends that inform the design and deployment of large-scale AI systems.
Title: Learning Models from Biological Data
Project Lead: Professor Hayden Schaeffer
Overview: This project investigates learning and simulating interacting dynamics and waves for modeling pattern formation in biological systems. Students will use AI tools to analyze experimental data and study the dynamics of boundaries in complex systems. The project focuses on computational and data-driven techniques, with an emphasis on developing tools that connect experimental observations with interpretable mathematical models of emergent biological behavior. This project is in collaboration with Montana State University.
Title: AI for Healthcare
Project Lead: Professor Deanna Needell
Overview: This REU project focuses on harnessing the power of artificial intelligence (AI) and machine learning (ML) to unravel the complexities of persistent (chronic) Lyme disease. In collaboration with a nonprofit partner, this cutting-edge initiative seeks to analyze an extensive dataset to gain deeper insights into the epidemiology, diagnosis, and treatment of Lyme disease. Under the mentorship of leading experts in ML and medical research, participants will explore innovative techniques for analyzing patient data. By leveraging advanced algorithms, as well as novel adaptations of these methods, the team aims to identify patterns, correlations, and predictive biomarkers that can enhance our understanding of chronic Lyme disease and support the development of more effective prevention and intervention strategies. This REU project provides a unique opportunity for aspiring researchers to work at the intersection of technology and healthcare, making meaningful contributions toward combating one of the most prevalent vector-borne illnesses. Participants will gain hands-on experience in ML applications while playing a vital role in advancing Lyme disease research with real-world impact. This project is a joint effort between UCLA and The College of New Jersey, with co-PI Jana Gevertz. Experience in linear algebra, machine learning, and programming is a plus but not required.
Title: AI for Justice
Project Lead: Professor Deanna Needell
Overview: This project is at the forefront of justice, where the fusion of Artificial Intelligence (AI) and large language models (LLMs) is harnessed to empower innocence centers in their mission to rectify wrongful convictions. Collaborating with several innocence projects across the country and internationally, this initiative aims to develop predictive and analytical tools that transform the processing of case files and wrongly convictions. As a participant, you will explore the use of AI in case processing and flagging, working alongside leading experts in AI and legal advocacy. Your role will involve crafting sophisticated algorithms capable of parsing vast amounts of legal data, identifying patterns, anomalies, and potential avenues for exoneration, while also examining inconsistencies, trade-offs, and explanations of AI behavior. This REU opportunity offers a unique chance to blend technological innovation with social justice, as you contribute to the development of tools with the potential to make a tangible impact on the lives of those unjustly imprisoned. Experience in linear algebra, machine learning, and programming is a plus but not required.
Title: Ensemble Monte Carlo samplers and generative models for uncertainty quantificationÂ
Project Lead: Professor Yifan Chen
Overview: This project focuses on advanced ensemble Monte Carlo methods and probabilistic generative modeling techniques for scientific applications, with particular emphasis on uncertainty quantification in inverse problems. We will design novel stochastic algorithms for sampling from probability distributions with rigorous mathematical guarantees. Practical applications include forecasting dynamical systems and integrating observational data with computational simulations, such as those arising in fluid dynamics and astrophysics. Students should have a solid foundation in numerical analysis and probability and be comfortable working with stochastic differential equations.
Title: Financial Transaction Data Project
Project Lead: Professor Andrea Bertozzi
Overview: Students will assist with the development of algorithms to sift through financial transaction graphs for suspicious patterns, learn new patterns to anticipate future activities, and develop techniques to represent patterns of illicit financial behavior in a concise, machine-readable format that is also easily understood by human analysts. This is an important task for the detection of fraud and money laundering. Students will work with synthetic datasets provided for the project. The ideal student will have some background in network modeling and graph theory and will be proficient in Python.
Title: DNA folding and selection algorithms
Project Lead: Professor Andrea Bertozzi
Overview: Students will study algorithms for the design of DNA aptamers, which are single strands of DNA that can bind to specific target molecules of interest. The algorithms will consider how the DNA folds on itself and whether it binds to targets. Some expertise in machine learning and AI, including Python coding, is relevant.
Title: Particle Laden Flow
Project Lead: Professor Andrea Bertozzi
Overview: Students will work in the applied mathematics lab to conduct experiments and develop computational models for particle-laden flow. Students should have a background in physical experiments, mathematical modeling, and partial differential equations. Both mathematics students and students from physics and engineering are encouraged to apply.