Practicum Experience(s)
Lawrence Berkeley National Laboratory (2024)
Summary of Research
I'm developing symmetry equivariant neural networks (ENNs) for applications in the natural sciences. If our data originates from or describes a physical system, we know it's subject to physical laws which have known symmetries. We can achieve superior data-efficiency, generalization, and robustness to physical laws when using ENNs as opposed to standard neural networks through incorporating physical symmetries. Currently, I'm working on using the mathematics of symmetry-breaking and properties of ENNs to uncover symmetry-implied missing information from diverse physical data. These methods will be broadly applicable to anomaly detection-identifying when our observations of physical systems imply we do not have a complete description and determining how the unobserved information must transform by symmetry (e.g. resolve galactic dynamics caused by unobservable black holes or dark matter). I aim to build generalized algorithms that aid in the understanding and engineering of physical systems.
Annual Program Review Abstracts
Publications
Lawrence, H.*, Hofgard, E.*, Chen, Y., Smidt, T., and Walters, R. (2025). Detecting Symmetry-Breaking in Molecular Data Distributions. To appear at the AI for Accelerated Materials Design Workshop at the 2025 International Conference on Learning Representations (ICLR), April 2025. https://openreview.net/forum?id=yEvdOXW5iY
Hofgard, E., Wang, R., Walters, R., and Smidt, T. (2024). Relaxed Equivariant Graph Neural Networks. Geometry-grounded Representation Learning and Generative Modeling Workshop (GRaM) at the 41st International Conference on Machine Learning (ICML), July 2024. https://arxiv.org/abs/2407.20471
Wang, R., Hofgard, E., Gao, H., Walters, R., and Smidt, T. (2024). Discovering Symmetry Breaking in Physical Systems with Relaxed Group Convolution. 41st International Conference on Machine Learning (ICML), July 2024. https://arxiv.org/abs/2310.02299
(2023). Artificial Intelligence for Science in Quantum, Atomistic, and Continuum Systems: Materials Characterization. November 2023. https://arxiv.org/abs/2307.08423
Cotter, D., Hofgard, E., Szpiech, A., and Rosenberg, N. (2023). A rarefaction approach for measuring population differences in rare and common variation. Genetics, 224(2), 2023.
ATLAS Collaboration. (2023). Search for Dark Photons from Higgs Boson Decays via ZH Production with a Photon plus Missing Transverse Momentum Signature from pp Collisions at sqrt(s) = 13 TeV with the ATLAS Detector. Journal of High Energy Physics, 133, 2023. https://doi.org/10.1007/JHEP07%282023%29133
Garg, R. B., Hofgard, E., Tompkins, L., and Gray, H. (2022). Exploration of Different Parameter Optimization Algorithms within the Context of ACTS Software Framework. November 1, 2022. https://doi.org/10.48550/arXiv.2211.00764
Hofgard, E., Chinn, G., and Levin, C. (2020). Simultaneous Multi-Isotope PET: A Computational Framework for Line of Response (LOR) Identification. In 2020 IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS/MIC). https://doi.org/10.1109/NSS/MIC42677.2020.9507891
(Oral presentation also given at 2020 IEEE NSS/MIC.)
LIGO Scientific Collaboration and Virgo Collaboration. (2021). GWTC-2: Compact Binary Coalescences Observed by LIGO and Virgo during the First Half of the Third Observing Run. Physical Review X, 11(2), 021053. https://doi.org/10.1103/PhysRevX.11.021053
(See my Google Scholar page for inclusion on other LIGO publications as a member of the collaboration.)
Awards
Listed as a laureate for the 2025 Breakthrough Prize in Fundamental Physics as a member of the ATLAS collaboration, see https://breakthroughprize.org/Laureates/1/L3993.
QuARC (MIT Center for Quantum Science and Engineering Annual Conference), Jan 2024, Best Poster in Quantum Algorithms and Machine Learning Session.
Recipient, Department of Defense National Defense Science and Engineering Graduate Fellowship (NDSEG), April 2023. Declined for DOE CSGF.
Recipient, MIT Advanced Television and Signal Processing Fellowship, 2022-2023 academic year.
NSF GRFP Honorable Mention, April 2022.
Firestone Medal for Excellence in Undergraduate Research, August 2021. Award given to the top ten percent of all honors theses in the social sciences, natural sciences, and engineering and applied sciences.
American Physical Society Far West Section Meeting, Nov 2019, Honorable Mention for Best Undergraduate Poster.