Leon Escobar-Diaz

Welcome! I am a mathematical physicist driven by a deep curiosity for complex problems that bridge rigorous analytical theory with high-performance numerical computing. My research sits at the intersection of mathematical physics, computational methods, and modern machine learning.

Currently, my primary focus lies in uncovering the mathematical foundations and numerical mechanics of both classical and quantum neural networks. I am particularly interested in how concepts from physics—such as dynamical systems, statistical mechanics, and quantum information theory—can be leveraged to better understand, optimize, and scale learning algorithms. While this is my main research vector, I remain open to any compelling problem in mathematical physics that poses nontrivial analytical or computational challenges.

Below, you will find more details about my academic background, ongoing projects, and specific research interests. Feel free to explore or reach out if you would like to collaborate!

Open projects 

Currently, I am primarily interested in projects related to the mathematical and numerical aspects of neural networks. Below are some of the projects I am currently working on:

• Classification algorithms for DNA sequences (with my master student Jorge Leandro Rodríguezt and Dr. Andres Castillo).
  
  

• Implementing PINNs for solving partial differencial equations (With my master student Geiler Galindo)
  
  

• Spectral analysis of the quantum neural tangent kernel for small variational quantum circuits( With my master in collaboration with Yuhad).
  
  

• Implementacion of inhomogeneopus initial data sets for evolulution of cosmological models ( with Dr. Alexander Gallego, Alejandro Estrada)

If you would like to learn more about my research, please visit my google scholar

Last update 20/05/2025