PINNs

Leveraging Physics Informed Neural Networks (PINNs) to solve a system of coupled equations and generate initial data for boson stars.

  • Exploring different neural network architectures and training them on CPU and GPU (using CUDA).
  • Experimenting with different loss functions and sampling methods for Monte Carlo integration.
  • Comparing results agaist traditional shooting methods for numerical integration.
Keywords: Machine Learning, Neural Networks, PyTorch
Repository:
PINNS_Boson_stars
Date: 3 April 2025 (work in progress)

Time series

Exploring different machine learning algorithms to predict stock prices in an interval 1-10 days, on historical data.

  • Linear Regression models with different features using scikit-learn.
  • Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU) models using TensorFlow.
  • Experimenting with different lag features and comparing results.
Keywords: Machine Learning, Scikit-learn, TensorFlow
Repository:
timeseries_forecasting_ml
Date: 3 April 2025 (work in progress)

SpheriCo.jl

A Julia package for the Spherical Collapse of a scalar field in classical and semiclassical gravity.

  • Combined the method of lines and summation-by-parts finite difference operators to solve stiff equations and resolve instabilities.
  • Reduced runtime and resource requirements, enabling longer and more extensive simulations compared to what was possible before.
  • Achieved clear second-order convergence in numerical solutions, improving reliability and accuracy.
Keywords: Julia, Numerical Simulations, Black Holes
Repository:
SpheriCo.jl
Date: 24 March 2025

Hyperbolicity

Investigated the hyperbolicity of the characteristic setup in general relativity and its impact in applications.

  • Found that common characteristic formulations are only weakly hyperbolic, contrary to expectations.
  • Analysed the effect of weak hyperbolicity in numerical simulations through suitable convergence test.
  • Discussed the implications in applications such as gravitational waveform modelling, and specifically the well-posedness of the CCE and CCM methods.
Keywords: Differential Equations, Numerical Convergence, General Relativity
Repository:
model_CCE_CCM
,
PhD_thesis
,
Bondi_Toy
Date: 3 January 2024