Welcome

to the GSSI Numerical Analysis and Data Science Group website! We work on mathematical and computational methods to solve complex problems in physics, data science, machine learning and other real-world applications, combining numerical analysis, machine learning, optimization, quantum computing and applied mathematics.

Our Research Areas

• Numerical Analysis & Dynamical Systems
  We design and analyze numerical methods for dynamical systems, including ordinary, delay, and stochastic differential equations, with a focus on stability in high-dimensional systems. Our work extends to matrix theory, with contributions to eigenvalue optimization, matrix perturbation theory, matrix nearness problems, control, and graph theory.
• Machine Learning & Data Science
  We are interested in understanding different ways to train deep learning models: using implicit layers by studying their stability and possible effective application and also using low-parametric training for neural networks. These modelistic choices are often justified by empirically observed implicit biases of optimization, which is our interest to characterize. Our interest also extends to developing surrogate deep-learning models for complex physical phenomena that are usually impossible to simulate using standard numerical methods.
• Computational Fluid & Plasma Dynamics
  We study high-performance numerical methods for hyperbolic partial differential equations and kinetic models, with applications in gas dynamics, fluid dynamics, and plasma physics. Our purposed technique enhance the accuracy, efficiency and physical consistency of simulations used in scientific and industrial applications.
• Quantum Computing
  We develop quantum algorithms for solving computationally hard combinatorial optimization problems. Our focus is on leveraging Quantum Annealers and Neutral Atom quantum hardware to tackle real-world optimization challenges. By evaluating different quantum processing units (QPUs), we seek alternatives to classical methods for problems where quantum computing can offer significant speedups.
• Optimization & Optimal Transport
  We address the challenges posed by nonlinear least squares problems by developing novel algorithms that accelerate convergence and reduce computational time. Our work also extends to optimal transport problems with concave cost functions.

For news, data and code, please also refer to our GitHub Repository.

About GSSI

The Gran Sasso Science Institute (GSSI) is an international PhD school and a center for research and higher education in the areas of Physics, Mathematics, Computer Science and Social Sciences. Professors, researchers and students from all scientific backgrounds are selected internationally, following the standards set by the best research centers and PhD schools worldwide.