Axel Muñiz Tello

Online Parameter Estimation Methods for Dynamical Systems

August 2024 - Present

With the ever growing market interest in autonomous vehicles around the world, many car manufacturing car companies, have sought out to improve autonomous vehicles by improving overall safety while operating the vehicle. Other's have sought to explore methods to make these vehicles more algorithmic efficient and test algorithmic robustness. Many challenges up to this day exist with autonomous vehicles, mostly from the inherient trait of autonomous vehicles by considered to be "dyanmic" and never linear.

We seek to explore online methods for parameter estimation and explore and test robustness to noise, excitation condition analysis, the introduction of adaptive forgetting factors, and parameter convergence under finite excitation (FE).

Modeling Disease Spread Using SIR Agent Based Framework (ABM): Kinetic Monte Carlo Approach

May 2024 - August 2024

Using pre-existing computational methods such as Kinetic Monte Carlo (KMC) simulations, this research study intends to investigate the dynamics of disease transmission using the Susceptible-Infected-Recovered (SIR) with an agent-based modeling framework (ABM) on lattice-like structures for a controlled movement population vs an unrestricted movement population; through simulations to analyze the relationships between susceptible(S), infected(I), recovered(R) populations in an environment in these circumstances. Using these methods, we simulate the stochastic processes that govern disease transmission and recovery on the lattice grid, providing a comprehensive analysis of the evolution of the disease spread. We anticipate that the overall findings will uncover iterative patterns in disease transmission, highlighting the critical importance of spatial structure and stochastic effects on population dynamics. Furthermore, we expect these results to offer deeper insights into epidemic dynamics, thereby enhancing the effectiveness of disease control strategies for future outbreaks. However, future work is needed to address two unknown areas. First, the impact of different lattice configurations on disease dynamics should be investigated to comprehend how spatial structures influence disease spread. This should include exploring various spatial configurations. Second, further investigation is required into how different temperatures affect disease transmission within restricted populations in lattice-like structures compared to populations not restricted by these physical conditions.

Lawrence Livermore National Laboratory 2025 Data Science Challenge

July 2025

Computer vision problem relating to amodal and modal segmentation and object completion.

Modeling Ecological Time-Series Population with SINDy

April 2025

This project was created for the Applied Mathematics Challenge 2025 at the University of California, Merced. It tackles an ecological modeling problem posed by the Department of Wildlife: predicting the bobcat population over the next 90 days based on observed sightings of bobcats and their primary prey cottontail rabbits. The modeling is performed using a Lotka-Volterra predator-prey system, implemented as a system of ODEs. We use real data, interpolation, parameter estimation via optimization, and simulate future dynamics to determine whether wildlife control measures may be necessary.