Calculus of Variations,
Optimal Transport,
Gradient Flows in the space of probability measures,
Numerical methods and approximation,
Computational Chemistry,
  - Density Functional Theory
  - One-body Reduced Density Matrix Theory
Mathematical Aspects of Machine learning theory
  - Likelihood-free Variational Inference and Generative Modelling
  - Normalizing flows
  - Generative Adversarial Networks
  - Statistical Learning Theory

Brief Research Description



  • Calculus of Variations

    I am mainly interested in Fundamental theory of multi-marginal optimal transport (transport plans, densities, potentials, existence and regularity of transport maps); Gamma-convergence. Computational realizations of Multi-marginal Optimal Transport (MOT), Convex/Entropic regularization of MOT.

     

  • Computational Chemistry

    The focus of my current research is to extend the accuracy of electronic Density Functional Theory (DFT) to systems in which electronic correlation plays a prominent role. In particular using the SCE formalism in the study of ground state properties of many-electrons system (existence and next-order corrections of SCE DFT) and time-dependent DFT (1d). I am also developing Non-commutative Optimal Transport methods to One-body Reduced Density Matrix (1RDM) functional theory.

  • Mathematical and Computational Aspects of Machine Learning

    I am developing tools to improve the understanding of density estimation and generation in GANs, VAES and Normalizing Flows; and developing novel deep learning methods for Computational Chemistry.


Collaborators and Mentors


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Giuseppe Buttazzo (Pisa, Ph.D. advisor)
Simone Di Marino (SNS Pisa)
Chris Finlay (McGill, Montréal)
Klaas Giesbertz (Chemistry, Amsterdam)
Juri Grossi (Chemistry, UC Merced)
Paola Gori-Giorgi (Chemistry, Amsterdam)
Juri Grossi (Chemistry, Amsterdam)
Anna Kausamo (Firenze)
Anton Mallasto (AI, Aalto)
Ha Quang Minh (AI, RIKEN-AIP)

Guido Montúfar (UCLA & MPI)
Luca Nenna (Paris-Orsay)
Mircea Petrache (PUC Chile)
Aram Pooladian (Data Sciences, NYU)
Tapio Rajala (Jyväskylä)
Berardo Ruffini (Bologna)
Michael Seidl (Physics, Regensburg)
Robert van Leeuwen (Physics, Jyväskylä)
Bozhidar Velichkov (Pisa)
Johannes Zimmer (Bath).