The NSF-Simons National Institute for Theory and Mathematics in Biology is bringing together mathematicians and biologists each week for the NITMB Seminar Series. NITMB Seminar Series talks cover diverse topics and are given by either visiting researchers or NITMB members. These talks take place in-person at the NITMB Collaboration Hub in downtown Chicago, with a webinar available for remote attendees. We are proud to invite a wide variety of scientists and mathematicians to mingle and explore topics of interest for the convergence of mathematics and biology. One speaker presenting as part of the NITMB Seminar Series is Jorge Nocedal.
Jorge Nocedal, Walter P. Murphy Professor, Industrial Engineering and Management Sciences, Northwestern University
Jorge Nocedal is the Walter P. Murphy Professor of Industrial Engineering and Management Sciences in the McCormick School of Engineering at Northwestern University. He has a courtesy appointment in the Department of Engineering Sciences and Applied Mathematics at Northwestern University. Nocedal’s research focuses on the creation of new algorithms for solving complex optimization problems.
We spoke with Professor Nocedal to learn more about his work with optimization and how engaging with the NITMB community could benefit his work.
What is a big open question you’ve been asking throughout your research?
“One of the big open questions today is how to train deep neural networks efficiently. This is equivalent to asking if there is an optimization algorithm that is much more efficient than the ones used today for finding the parameters of a neural network, which can number in the hundreds of millions.”
What disciplines does your research integrate?
“My work lies at the intersection of computer science and applied mathematics.”
Where do you find inspiration?
“I have found inspiration by reading classic papers and trying to understand how other researchers came up with innovative ideas. I don’t look only at my discipline. I try to read more broadly about fundamental breakthroughs in other areas of science. I like to debate and discuss far-out ideas with some of my colleagues. Brainstorming has been one of my modes of operating. I find it liberating.”
What aspects of your research could be interesting to mathematicians or applied to biology?
“There are many things we do not understand about the optimization of deep neural networks. We do not know what the landscape of the objective function is and what the nature of the minimizers is. It is also unknown how stochastic optimization methods are able to navigate this optimization landscape. The optimization research done in the main tech companies is heuristic, and the training process consumes enormous amounts of energy. We need to understand the mathematical properties of such highly nonlinear, high-dimensional functions and how to handle noise and uncertainty.”
What about the NITMB do you find exciting?
“I feel that the intersection of machine learning and biology will give rise to important advances. What I find particularly exciting is that there are no experts in this incipient field. A young researcher is as likely to make a discovery as an established math or biology researcher. In fact, since we need a new mindset to develop the intersection of these two fields, young people have the advantage since they do not have an established approach to their research.”
What career achievement are you most proud of?
“I find it rewarding that some of the algorithms I have created are used in dozens of disciplines, some of them outside science and engineering. Their usefulness appears to be increasing with time.”
Outside of your research, what other interests do you have?
“I like reading all kinds of books and I like classical music. I am addicted to swimming, whether in lakes, oceans, or pools. I have also always loved creating stories for children, inventing toys, and learning simple things.”
What are you hoping to work on in the future?
“I would like to continue investigating the solution of very large and very nonlinear optimization problems, this time with applications in biology. I would like to start collaborations of this kind.”
More information on Nocedal's work is available on Jorge Nocedal’s website, as well as in YouTube lectures that provide an overview of Nocedal’s research inquiries and methodology. Links to a few of Nocedal’s lectures can be found below: