Talk Title: Covariant Neural Networks for Physics Applications

Watch Alexander’s Research Lightning Talk

Talk Abstract: Most traditional neural network architectures do not respect any intrinsic structure of the input data, and instead are expect to “learn” it. CNNs are the first widespread example of a symmetry, in this case the translational symmetry of images, being used to advise much more efficient and transparent network architectures. More recently, CNNs were generalized to other non-commutative symmetry groups such as SO(3). However, in physics application one is more likely to encounter input data that belong to linear representations of Lie Groups, as opposed to being functions (or “images”) on a symmetric space of the group.

To deal with such problems, I will present a general feed-forward architecture that takes vectors as inputs, works entirely in the Fourier space of the symmetry group, and is fully covariant. This approach allows one to achieve equal performance with drastically fewer learnable parameters, Moreover, the models become much more physically meaningful and more likely to be interpretable. My application of choice is in particle physics, where the main symmetry is the 6-dimensional Lorentz group. I will demonstrate the success of covariant architectures compared to more conventional approaches.

Bio: I am a PhD student at the University of Chicago working on theoretical hydrodynamics problems in relation to the quantum Hall effect. In addition, I am working on developing new group-covariant machine learning tools for physics applications, such as Lorentz-covariant neural networks for particle physics. My background is in mathematical physics, in which I hold a master’s degree from the Saint-Petersburg University in Russia. My interests lie on the intersection of theoretical and mathematical physics and new inter-disciplinary applications of such ideas.

Zhiyuan Han is a Postdoctoral Scholar at the Pritzker School of Molecular Engineering, University of Chicago, where he works under the supervision of Prof. Chibueze Amanchukwu. His research focuses on the intersection of data science, computation, and experiments to investigate molten salts and liquid electrolytes for next-generation batteries. Before his postdoctoral appointment, Zhiyuan earned his Ph.D. in Environmental Science and New Energy Technology at Tsinghua University, where he applied machine learning to uncover novel electrochemical mechanisms in high–energy-density battery systems.

Nils Strand is a Postdoctoral Scholar at the University of Chicago, working with Profs. Aaron Dinner (Chemistry) and Yuehaw Khoo (Statistics). He builds tensor-network algorithms to enable scalable density estimation and uncertainty quantification in biological modeling. His current focus is on tensor-train approaches that compress probability distributions and other high-dimensional functions, with the aim to boost the efficiency of commonly used strategies, such as inference and molecular simulation. Nils completed in 2023 a PhD in Chemistry at Northwestern University with Todd Gingrich, where he developed numerical methods for nonequilibrium stochastic systems to understand steady-state and reactive behavior in interacting classical processes. Across these projects, his goal is to bring ideas from modern AI and many-body physics to core problems in computational biology, reducing exponential bottlenecks that limit today’s simulations and parameter estimation.

Rodrigo Ferreira is a Molecular Engineering PhD candidate at the University of Chicago, advised by Prof. Junhong Chen. Ferreira received his Bachelor’s degree in Aerospace Engineering and Master’s degree in Physics from the Aeronautics Institute of Technology in Brazil. After completing research internships at Stanford University and University of California, Los Angeles, he joined the University of Chicago in 2023. His research interests revolve around the intelligent design of 2-dimensional synaptic transistors for enhanced sensing platforms. Ferreira is applying machine learning in two ways: 1.) using neuromorphic spiking graph neural networks (SGNNs) for better material screening to compose the sensors; and, 2.) developing novel time-series foundation models (TSFMs) for improved signal processing and drift correction. With work accepted in materials science journals and top AI conferences (e.g. NeurIPS), Ferreira seeks to improve sensing platforms across the full stack, from device design to signal processing.

Rachel is a Ph.D. student in Computer Science, advised by Kyle Chard and Ian Foster. Her research focuses on machine learning applications for medical imaging, including image reconstruction, segmentation, and synthesis. Before starting at the University of Chicago, she earned her MS in Data Science and BS in Statistics from Loyola University Chicago.

Qi-Nan Huang is a PhD student at the University of Chicago in Chibueze Amanchukwu’s Lab. His research focuses on the development of agentic artificial intelligence and machine learning frameworks for battery electrolyte discovery and design. He is particularly interested in integrating data-driven modeling with chemical intuition and experimental validation to accelerate materials innovation for energy storage applications.

Roxie is a Computer Science PhD student at the University of Chicago advised by Professor Rebecca Willett. Previously, she received her master’s degree in Operations Research at Columbia University and bachelor’s degree at Xi’an JiaoTong University.

Roxie’s research interests lie in machine learning for dynamical systems and its applications in scientific computing. In particular, she works on learning structural hidden representations of the high-dimensional data. Her work has been applied to addressing inverse problems with uncertainty quantification and designing practical algorithms to achieve data efficiency in decision-making problems (i.e., bandits). Currently, she is interested in predicting high-dimensional chaotic systems with deep learning.

Owen is a PhD student in computer science at the University of Chicago, advised by Rebecca Willett. For part of his PhD, he was supported by the NSF Research Traineeship in AI-enabled Molecular Engineering of Materials and Systems for Sustainablity. Before his PhD, he was a data scientist working with Haky Im.

Elena is a Compuer science PhD student at the University of Chicago, working with Professor Rebecca Willett. Her research focuses on machine learning and its scientific applications, with particular emphasis on generative models for quantum simulations, emulators for chaotic systems, and advanced techniques in weather forecasting. Elena has experience with tensor networks for neural network compression and generative adversarial networks (GANs).

Before her doctoral studies, she earned a Bachelor’s degree in Mathematics, and a Master’s degree in Mathematics and Computer Science.

Matt is a Computational Neuroscience student in Prof. Dave Freedman’s lab, where he works on the neurophysiology of visual cognition and working memory. Before this, he was an undergrad at Princeton, where he studied computer science.

Aidan Simpson is an Astronomy & Astrophysics PhD student at the University of Chicago working with Professor Alexander Ji. His research focuses on integrating both spatial and spectral dimensions of integral field spectroscopy into multimodal models of galaxies as well as utilizing the unified latent space for downstream tasks. He previously received his BS degree in physics and MS in astronomy from Rensselaer Polytechnic Institute.

Ruize (Richard) Xu is a Computer Science PhD student at the University of Chicago, advised by Professor Risi Kondor on artificial intelligence for science and working with Professors David McAllester and Professor Zhiyuan Li on artificial intelligence for mathematics. His research interests lie at the intersection of machine learning for science and mathematics, focusing on Graph Neural Networks based approaches for chemical property prediction and leveraging large language models for automated theorem proving. Before his doctoral studies, Ruize earned Bachelor’s degrees in Computer Science, Mathematics, and Economics from the University of Chicago.

I am a professor of mathematics in the Courant Institute of Mathematical Sciences at New York University. Previously I was an associate professor in the statistics department and in the James Franck Institute at the University of Chicago and, before that, an assistant professor in the mathematics department there. Before moving to Chicago, I was a Courant Instructor of mathematics at NYU and a PhD student in mathematics at the University of California at Berkeley.