Antonio Falcó Montesinos

Current Research        

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I am currently Director of the ESI International Chair @UCH-CEU. My work focuses on the theoretical foundations of the mathematical modelling for the simulation of physical and biological systems. A significant part of my work is devoted to the mathematical foundations of the Proper Generalized Decomposition (PGD). The abstract subjects investigated, related with the PGD, are Model Order Reduction (MOR) in a wide sense and the convergence of variational algorithms by using dictionaries. These approaches are constructed with the valuate collaboration of various industrial partners. The general challenge is to provide a formal framework to certify algorithms, related to regulated manufacturing processes, to be used in industrial applications and health sciences.

I led two research teams, the first one composed by 9 researchers (4 seniors and 3 juniors) together two doctoral students, all from the Universidad CEU Cardenal Herrera. The research is mainly dedicated to the use of the TDA combined with Machine Learning and I.A techniques (a) to construct classification models for cancer therapies and (b) to design drugs against antibiotic resistance. The second research team is composed by 5 researchers (1 senior and 4 juniors) together two doctoral students, from the Universidad CEU Cardenal Herrera, Universidad CEU San Pablo, CUNEF University and Universidad Politécnica de Valencia. The research is mainly dedicated (a) to the mathematical foundations of computational algorithms used in the simulation of physical process by using either classical or quantum computers and (b) to develop a general framework to design algorithms in order to break the curse of dimensionality.

We collaborate with Professor Francisco Chinesta from ENSAM Paris (since 2005), Professor Anthony Nouy from Centrale Nantes (since 2007), Professor Wolfgang Hackbusch from Max Planck Institute (since 2009), Professor Elias Cueto from Universidad de Zaragoza (since 2010), Professor Tomás Chacón from Universidad de Sevilla (since 2015) and Professor Alberto Conejero from Universidad Politécnica de Valencia (since 2017).

Our four most relevant results are.

1 We provide a general framework for the dictionaries used in the PGD (called the minimal subspaces in tensor representations) to describe the intrinsic properties of this approach.
2 We provide a general methodology (Progressive PGD), in the framework of approximation theory, for non-linear convex variational problems that can be extended to a wide class of dictionaries, like Neural Networks.
3. We introduce a geometric approach to Model Order Reduction that allows to be extended to a wide class of models, including some of that are used in Deep Learning.
4. We introduce the use of Topological Data Analysis (TDA) in Material Science to be used in the classification of material behavior and to describe the biological compatibility of drugs and proteins.

We recently start to work in the extension of some of the above results and techniques in a Quantum Computing framework. In short, the research numbers are the following:
• Journal articles with peer review (Wos): 68 (14/03/23).
o Papers in WoS: 59 (14/03/23).
o Citations (WoS): 372 (14/03/23).
o h index (WoS): 8 (14/03/2023).
• Chapters in monographs and conference proceedings: 10
• Participation in research projects: 14
• Around more than 70 contributions in scientific meetings.
• Three periods (sexenios) of research evaluated positively, last 2016.
• Positive evaluation ANECA for the figure of Associate Professor.
• Positive evaluation AQU for the figure of Full Professor.
• Habilitation à diriger des Recherches by the University of Nantes.
• Ángel Herrera Award from the San Pablo CEU University Foundation in the Polytechnic Area (1998).
• Research Prize Risk Management Club of Spain 2000-2001.
• Thesis supervised in the last 10 years: 6.

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You can download my papers from my personal web page: https://afalco.github.io