Antonio Falcó Montesinos

Current Research        

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I am currently serving as Director of the ESI International Chair at UCH-CEU. My research is focused on the theoretical foundations of mathematical modeling, particularly for simulating complex physical and biological systems. A significant portion of my work revolves around the mathematical principles of the Proper Generalized Decomposition (PGD). Specifically, I investigate abstract topics related to PGD, such as Model Order Reduction (MOR) in a broad sense and the convergence of variational algorithms through the use of dictionaries. These efforts are carried out in collaboration with various industrial partners, aiming to develop formal frameworks that certify algorithms for regulated manufacturing processes, with applications in industrial settings and health sciences.

I lead two active research teams. The first team consists of nine members, including four senior and three junior researchers, along with two doctoral students, all affiliated with Universidad CEU Cardenal Herrera. This group focuses primarily on applying Topological Data Analysis (TDA) combined with Machine Learning and Artificial Intelligence techniques to (a) construct classification models for cancer therapies and (b) design drugs to combat antibiotic resistance.

The second research team, composed of five researchers (one senior and four junior), along with two doctoral students from institutions including Universidad CEU Cardenal Herrera, Universidad CEU San Pablo, CUNEF University, and Universidad Politécnica de Valencia, is dedicated to two primary areas: (a) developing the mathematical foundations of computational algorithms for simulating physical processes using both classical and quantum computers, and (b) creating a general framework to design algorithms capable of overcoming the curse of dimensionality.

In terms of collaboration, I have been fortunate to work with distinguished colleagues such as 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.

Among our most notable contributions are:

1. Establishing a general framework for the dictionaries used in PGD, known as minimal subspaces in tensor representations, to capture the intrinsic properties of this approach.
2. Developing a methodology, termed Progressive PGD, within approximation theory for addressing non-linear convex variational problems, which can be applied to a wide class of dictionaries, including Neural Networks.
3. Introducing a geometric approach to Model Order Reduction, enabling its application to a broader class of models, including those commonly used in Deep Learning.
4. Pioneering the use of Topological Data Analysis (TDA) in Material Science to classify material behaviors and describe the biological compatibility between 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.
• Four 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 access and download my research papers from my personal website: https://afalco.github.io