Multi-marginal Optimal Transport and Density Functional Theory:
a mathematical setting for physical ideas

CORDIS OTmeetsDFT | Quantum Matter in Chemistry and Physics| VU Press Release

This project has received funding from the European Research Council (ERC) under H2020/Marie Skłodowska-Curie Actions-Individual Fellowships (Grant agreement 795942 OTmeetsDFT)

Publications and Preprints

  2020 (Link)

Authors: A. Gerolin, A. Kausamo, T. Rajala


Title: Multi-marginal Entropy-Trasport with repulsive costs
Journal: Calculus of Variations and Partial Differential Equations 2020, 59, 90.
Year: 2020.

  2020  (Link)

Authors: A. Gerolin, J. Grossi and P. Gori-Giorgi


Title: Kinetic Correlation Functionals from the Entropic Regularization of the Strictly Correlated Electrons Problem
Journal: J. Chem. Theory Comput. 2020, 16, 1, 488-498
Year: 2020

  2019 (Link)

Authors: S. Di Marino, A. Gerolin


Title: An Optimal Transport approach for the Schrödinger bridge problem and convergence of Sinkhorn algorithm
Submitted to Journal of Scientific Computing (JOMP)
Year: 2019


Authors: A. Mallasto, A. Gerolin, H. Q. Mihn


Title: Entropy-Regularized 2-Wasserstein Distance between Gaussian Measures
Submitted to Springer Information Geometry and Optimal Transport
Year: 2019

  2019 (Link)

Authors: A. Mallasto, G. Montúfar, A. Gerolin


Title: How Well Do WGANs Estimate the Wasserstein Metric?
Submitted to ICRL 
Year: 2019

Organization of Workshops and Research Schools (planned)


January 18th-22th
Research School on Mathematics of Machine Learning
Centro De Giorgi, Pisa, Italy



January 25th-29th
Workshop on Mathematics of Machine Learning
Centro De Giorgi, Pisa, Italy
organized with Simone Di Marino (Genova) and Lorenzo Roscasco (Genova and MIT).



XI Young European Statisticians Workshop (YES XI)
Optimal Transport, Statistics, Machine Learning and moving in between
TU/e Eindhoen, The Netherlands.
organized with Rui Castro and Oliver Tse (TU/e)
(dates to be confirmed due to coronavirus restrictions)


Short research periods

Mar-May 2020

Thematic Program: High Dimensional Hamilton-Jacobi PDEs
Institute of Pure and Applied Mathematics (IPAM)
UCLA, Los Angeles, United States.


September 2019

Research in Teams with Mircea Petrache (PUC Chile)
Banff International Research Station (BIRS)
Banff, Canada.


May-June 2019

Thematic Program: Optimal Transport
Erwin Schrödinger Institute (ESI)
Vienna, Austria.



February 2020

Mircea Petrache
Pontificia Universidad Católica de Chile, Chile.

Carlo Mercuri
Swansea University, United Kingdom.


January 2020

Flavien Léger
École Normale Supérieure de Paris, France.


November 2019

Anton Mallasto
Probabilistic Machine Learning Group, Aalto University, Finland.


September 2019

Dario Feliciangeli and Lorenzo Portinale
Institute of Science and Technology, Austria.


Seminars and Conference Talks


CASA Colloquium TU/e. February, Eindhoven (The Netherlands)
Italian meeting of Calculus of Variations. Levico Terme (Italy)



Stochastic and Probability seminar at Aalto University.  Espoo (Finland)
Semester in Optimal Tranport at Erwin Schrodinger Institute.  Vienna (Austria)
Stochastic seminar at Radbound University. Nijmegen (The Netherlands)
People in Optimal Transport. Cortona (Italy).
Calculus of Variations on Schiermonnikoog (The Netherlands).
Math Colloquium at VU Amsterdam, Amsterdam  (The Netherlands)
Mathematical and Computational Aspects of Machine Learning. Pisa (Italy).
Math Colloquium Utrecht University. Utrecht (The Netherlands)


Student surpervision and projects with
Software for Chemistry & Materials (SCM)

Mar-Jun 2020

Yuman Hordijk, Vrije Universiteit Amsterdam (BS Chemistry)
Wasserstein distance to assign spectra
with P. Gori-Giorgi, L. Visscher, Arno Foerster (Chemistry)
and S. van Giesbergen (SCM)


Jan-Jul 2020

Finn Bohte, Vrije Universiteit Amsterdam (MSc Mathematics)
Computational Aspects of Discrete Optimal Transport
with P. Gori-Giorgi (Chemistry) and J. Hulshof (Mathematics)


Jan-Jul  2020

Lorian Coltof, University of Amsterdam (MSc Artificial Intelligence)
Wasserstein Generative Adversarial Networks
with Patrick Forré, University of Amsterdam (UvA), Computer Sciences


Jan-Jul 20

May Lee, University of Amsterdam (MSc Artificial Intelligence)
On Generative Modelling on graphs for Molecules
with Nick Austin (SCM)


Sep19-Jan 20

Annina Lieberherr, ETH Zurich (BS Chemistry)
Distances Between Electron Densities from Optimal Transport for Theoretical Chemistry
with P. Gori-Giorgi and Klaas Giesbertz (Chemistry)


Science Outreach

Signs of Mathematics, in collaboration with University of Jyväskylä.