projects | Roy T. Forestano

research

Invariant and Equivariant Classical and Quantum Graph Neural Networks

Deep geometric methods, such as graph neural networks (GNNs), can leverage the fundamental symmetries present in the data through the use of invariant inputs and equivariant layers. We test classical GNNs and equivariant GNNs (EGNNs) and their quantum counterparts, namely quantum GNNs (QGNNs) and equivariant quantum GNNs (EQGNN). Based on their AUC scores, the quantum networks were shown to outperform the classical networks. (2023 Google Summer of Code Project)

Deep Learning Symmetries

We design a deep-learning algorithm for the discovery and identification of the continuous group of symmetries present in a labeled dataset. We analyze the complete subgroup structure of the rotation groups SO(n), the Lorentz group SO(1,3), and the unitary groups U(n). Other examples include squeeze mapping, piecewise discontinuous labels, and non-linear latent space symmetries with the preservation of an oracle (function), demonstrating that our method is completely general, with many possible applications in physics and data science.

2022 NeurIPS Ariel Data Challenge 1st Place

In this ML challenge, we created a retrieval model using a Neural Network in PyTorch to obtain planet parameters from transit data and both star and planet parameters. We demonstrated data analysis, data cleaning, feature engineering and enhancement, dimensionality reduction, and interpretability. The challenge consisted of two tracks - the light track (LT) to predict three quantiles (16%,50%,84%) and the regular track (RT) to predict the full distribution of the planet parameters.

Quantum Computing

Here, you can find many Quantum Unconstrained Binary Optimization (QUBO) Problems used as a semi-classical introduction to quantum computing algorithms. Using CPLEX and DOCPLEX, two quantum computing API's, I solve many unique problems using QUBO models, which are Ising spin models intended to find novel ways to find solutions to NP-Hard problems. Problems include the knapsack, graph partitioning, clustering, and stable marriage problems, as well as, games such as Conway's The Game of Life.

Numerical Methods and Scientific Computing

This material was produced during a Spring 2021 Course at Boston College entitled Numerical Methods and Scientific Computing taught by Physics Professor Jan Engelbrecht. This was done with a Linux operating system in the XQuartz terminal using C++ and Gnuplot. Image - The evolution (top left) of the damped driven non linear pendulum for the chaotic case. The 3D limit cycle (top right) is also shown, as well as, two different poincare sections (bottom, 2D horizontal slices of the 3D limit cycle).