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publications
Automatic Extraction of Ordinary Differential Equations from Data: Sparse Regression Tools for System Identification
Published in Durham University, 2023
PhD thesis developing three automated strategies for discovering ordinary differential equation models from data.
Recommended citation: Egan, K. (2023). "Automatic Extraction of Ordinary Differential Equations from Data: Sparse Regression Tools for System Identification." PhD thesis, Durham University.
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Automatically discovering ordinary differential equations from data with sparse regression
Published in Communications Physics, 2024
Developed ARGOS methodology combining denoising techniques, sparse regression, and bootstrap confidence intervals to automatically discover dynamical systems from noisy data.
Recommended citation: Egan, K., Li, W. & Carvalho, R. (2024). "Automatically discovering ordinary differential equations from data with sparse regression." Communications Physics. 7, 20.
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Physics-Informed Neural Networks as Differentiable Surrogates for 4D-Variational Data Assimilation
Accepted for publication in Journal of Advances in Modeling Earth Systems (JAMES), 2026
Developed a differentiable physics-informed neural surrogate for 4D-Variational Data Assimilation, using automatic differentiation to replace separately developed tangent-linear and adjoint models while maintaining comparable state-estimation accuracy.
Recommended citation: Egan, K. & Powell, B. (2026). "Physics-Informed Neural Networks as Differentiable Surrogates for 4D-Variational Data Assimilation." Journal of Advances in Modeling Earth Systems. Accepted for publication.
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talks
Discovering Governing Equations from Data using Sparse Regression
Published:
Presented work on sparse regression methods for system identification at the Society for Industrial and Applied Mathematics conferences.
Discovering Governing Equations from Data using Sparse Regression
Published:
Presented work on sparse regression methods for discovering ordinary differential equations from time-series data at the American Statistical Association conferences.
Building a Physics-Informed Neural Network for NPZ Modeling
Published:
Workshop presentation on developing physics-informed neural networks for NPZ ecosystem dynamics.
Leveraging Physics-Informed Neural Networks for 4D-Variational Data Assimilation
Published:
Presented research on physics-informed neural networks for 4D-Var data assimilation in marine ecosystem modeling.
Physics-Informed Neural Networks as Differentiable Surrogates for 4D-Variational Data Assimilation
Published:
Poster presentation on differentiable neural surrogates for 4D-Var data assimilation.
Physics-Informed Neural Networks as Differentiable Surrogates for 4D-Variational Data Assimilation
Published:
Poster presentation; received the Pacific Islands Impact Award.
teaching
Elementary Summer School Math Teacher
Instructor, Susan H. Hagen Center, 2014
Taught mathematics to elementary students in summer enrichment program.
Elementary School Teaching Assistant
Teaching Assistant, Wittenberg University, 2015
Assisted with elementary school mathematics instruction.
Math Workshop Tutor
Tutoring, Wittenberg University, 2016
Provided individual and group tutoring support for undergraduate mathematics courses.
Language and Culture Assistant
Teaching, IES Angel Correa, Madrid, Spain, 2016
Led classroom lessons in engineering subjects and developed instructional materials to present technical concepts more clearly.
Workshop Instructor and Lead Organizer
Workshop, CBIOMES Workshop on Machine Learning Methods for Time-Series Data, 2026
Taught a full day on neural networks and physics-informed neural networks at a Simons Foundation-funded workshop, pairing lectures with hands-on exercises for researchers from varied disciplinary backgrounds.
Undergraduate Research Mentor
Mentoring, University of Hawaiʻi at Mānoa, 2026
Mentored an undergraduate researcher developing machine learning methods to reconstruct particle tracks from detector measurements.