Chicago Area SIAM Student Conference Day 2

Alongside connecting students and faculty from across the region, the conference, particularly Day 2, had a focus on fundamental science. The second day of the SPS Zone 9 Meeting & Chicago Area SIAM Student Conference advertised their mission to provide insights and perspectives on particular issues of math, physics, and machine learning. However, broader inquiries of the state and role of computational scientific approaches were the intended focus.

This was made clear through the discussion on the essentiality of rigorous algorithmic approaches in developing machine learning models, by the presentation on the development of Noether's theorem and its historical context, and from the demonstration of consequences of Maxwell's equations and electromagnetism.

Putting Math at the Foundations of Machine Learning

After an energizing continental breakfast to start the day, the talks began! Dr. Carlo Graziani opened up with a talk on the mathematical foundations needed – and lack of them present – in machine learning.

Dr. Graziani is a Computational Scientist at Argonne National Lab, previously having received a B.S. in Applied Physics from Columbia University School of Engineering and Applied Science and a Ph.D. in Physics from the University of Chicago, previously with a focus on astrophysics.

First beginning with an introduction of what is AI, we learned about the transition from a search for reasoning to one for learning – and the differences between the two – defined by the models ability to learn patterns through test data and validation. Dr. Graziani navigated us through the historical development of ML and gave some relevant modern examples to illustrate its mechanisms and outputs of learning. 

Two pathologies in ML were the defining issues presented: hallucinations and a lack of explainability, and how the former leads to some considerably highly-confident random results. Regarding explainability, the problem is clear: there is often nearly no possibility of locating the source of any problematic result to a point or feature of the learning model.

The latter portion of the talk discussed approaches to resolve these issues. If you are interested in learning more, follow along with Dr. Graziani's future publications!

A Lunch to Connect Students and Science

Lunch was introduced as a means for students to meet faculty from across the region, encouraging all faculty attendees to sit separately. This led to fun and interesting discussion at all of the tables, enabling connections between universities that are often prevented by geospatial distance and a proper forum to breed these connections. This also allowed for the continuation of some discussion from The Bog during Day 1, when the students were brainstorming further collaboration ideas. For the inquisitive students, it allowed many to follow up with Dr. Graziani about the dalk he had given and give preliminary questions to the upcoming speakers.

Reflecting Upon A Century of Noether’s Theorem

106 years ago, Emmy Noether published the theorems now infamous in the physics community, pervading all of physics and underlying many fundamental theories through conservation laws, or symmetries. 

Dr. Chriss Quigg, former Head of the Theoretical Physics Department at Fermilab, guided attendees through the theorems' consequential physical manifestations and abundant relevance of Noether's research and life as two eminent topics. Those interested in fundamental physics or learning more about Dr. Quigg are invited to read his new book, Grace in All Simplicity: Beauty, Truth, and Wonders on the Path to the Higgs Boson and New Laws of Nature, with co-author Robert Cahn.

The Present & Future of Math, Physics, and ML

Dr. Zack E. Sullivan, Dr. Robert S. Eisenberg, and Dr. Carlo J. Graziani were led in an hour-long discussion by Jacob H. Thomas on the defining problems that define and span the fields of math, physics, and ML. Of course, it was known while organizing this that there are very notable problems noticed by each panelist that correspond directly with those noticed by the others. As a result, a fruitful and engrossing conversation toured through the topic described by two words: uncertainty quantification.

This term had very visible effects in physics and machine learning, calling for an adequate advancement of mathematical and statistical methods in all fields. Meanwhile, there were other topics mentioned with solutions called for, but the topic of uncertainty quantification was unanimously reflected upon as the most pressing.

Universality & Exactness of the Maxwell Equations

Dr. Eisenberg is no stranger to issues and phenomena that characterize the fields of biology and physics, leading a talk on the fright induced upon the realization that the Maxwell Equations are universal and exact when written without a dielectric consta

Dr. Robert S. Eisenberg is a Chairman Emeritus and Professor of the Department of Physiology & Biophysics at Rush Medical College and Adjunct Research Professor of the Department of Applied Mathematics at the Illinois Institute of Technology.

The talk led students from one consequence to another of this scary feature, starting with the necessity for a redescription of the phenomenological stress strain relations for charge density and the lack of total current accumulation.

The Universe of Physics as the Symphony of an Orchestra

Concluding the day of physics and math deliberation, attendees reconvened in the Orchestra Hall of Symphony Center to experience the power of Mendelssohn's Elijah performed by one of the best musical ensembles in the world: The Chicago Symphony Orchestra. Like many modern physicists, Mendelssohn stood on the shoulders of giants, drawing musical inspiration from the likes of Bach and Handel, evident in the near-recomposition of Bach’s St John Passion in one the aria. It is known that throughout the process of writing Elijah, Mendelssohn often rewrote entire numbers, even writing to his english translator "little more trouble will be amply repaid by a little improvement." With respect to the actual significance of the story of Elijah, that will be left to the reader to manifest.