28/02/2025

'We managed to do cutting-edge science,' says Arthur Bizzi.

In the second half of 2020, IMPA doctoral student Arthur Bizzi left the European cold of his time in Paris, France, to face the high temperatures of Rio de Janeiro. The engineer from Brasília embraced mathematics, IMPA, and the city of Rio to pursue a long-held dream: to enter a doctoral program in applied mathematics at the institute.

On Thursday (6), at 10 am, he concludes this stage with the defense of the thesis “Neural Networks with Flow Structure for Physics-Informed Machine Learning”, supervised by the institute's then researcher João Pereira. The defense can be followed on IMPA's YouTube channel.

However, before the big day, Arthur is in the United States to present the paper “Neural Conjugate Flows: A Physics-Informed architecture with flow structure” at the “Association for the Advancement of Artificial Intelligence (AAAI) Conference” in Pennsylvania this Saturday (March 1st). The work is the result of his doctoral thesis.

The young man's busy week concludes or pauses his journey at IMPA. Despite having a good relationship with mathematics since childhood, it was during his undergraduate studies in mechatronics engineering at the University of Brasília (UNB) that Arthur realized that working with numbers could effectively become a career. "I spent most of my undergraduate studies thinking about becoming a mathematician, which was what I really liked about engineering."

A deeper interest in the field was accompanied by other possibilities, such as becoming a researcher, solving real-world problems through mathematics, and working directly with industry. The decision to change fields came during the "Summer Course" that the student took at IMPA in 2017, when he was still an undergraduate. "I finally mustered the courage to pursue my dream. It was love at first sight. It ruined my career as an engineer," he joked.

At the Institute, Arthur is one of the collaborators at the PI Center (IMPA Center for Projects and Innovation) and actively participated in the Petrobras Project – which uses neural networks to model wave propagation on the seabed, an important part of locating oil reservoirs. This work was a starting point for his doctoral research. In it, the young man sought to solve an old problem in the application of neural networks: in general, these computing systems are excellent with associations, but not so much with causality, which hinders their functionality in physical contexts.

“There is a very big difference between observing two things happening and establishing a causal relationship between them. They are very different things. Especially in my case, I want to apply artificial intelligence, machine learning, to the study of real-world physical systems, of nature — where, obviously, this causal relationship is very important.”

Thus, one of the main objectives of the thesis was to create a neural network specialized in thinking about physical systems. To achieve this, the main research strategy was to use the "notion of mathematical flow" to manage causal relationships.

“This process is linked to the notion that time passes; the present affects the future; the future depends on the past, and so on. When we talk about causality, abstractly, it is very difficult to define what that means. In the research, we were able to realize that we can reach a possible definition of causality, which is precisely the structure of this mathematical flow; that was the key,” explained Arthur.

Presentation in the United States

Alongside his defense, Arthur will fulfill another academic commitment next week: the presentation of the paper “Neural Conjugate Flows: A Physics-Informed architecture with flow structure” at the AAAI in the United States. Derived from his doctoral thesis, the paper blends concepts of dynamical systems with machine learning applications – allowing for an innovative theoretical approach to the field.

“We brought concepts from pure mathematics into machine learning. And, using that, we were able to make neural networks grasp the idea of flow. Our neural networks have many special properties that relate to the special properties of dynamic systems,” explained the doctoral student.

Among the 13,000 articles submitted to the conference, Arthur's work—in partnership with researcher João Pereira—was among the just under 5% of research accepted for the main session of the meeting. The session discussed the application of machine learning to real-world problems. In 2023, the article "Amniotic Fluid Segmentation and Volume Prediction with Uncertainty Quantification," developed by master's and doctoral students from the Pi Center, won an award at the conference in one of the most competitive categories of the AAAI, the "Deployed Application Award."

After presenting and defending his thesis, the student's next career step will be the start of a postdoctoral fellowship in applied mathematics at the Swiss Federal Institute of Technology in Lausanne (EPFL), in Switzerland. “This postdoc is an opportunity to strengthen myself and learn many things, to solidify my research. But I don't see myself doing anything else but being at IMPA, at least not for most of my life,” he said.

Arthur is leaving Brazil in March, hoping to return to Rio de Janeiro in the future. Meanwhile, he holds onto the expectation that national scientific production is advancing in an increasingly promising way. “I have a very strong feeling that what we are doing at IMPA is perhaps more important than we imagine. My hope is that we, as a nation, as a society, can increasingly participate in the technological revolution; that we can find our own niche, be involved in research and science. I think that now, more than ever, we are managing to do cutting-edge science that can change the course of our society,” he concluded.