Summary of Research
Broadly, I conduct research in computational and mathematical science; more specifically on complex large-scale optimization problems. I am motivated to work on both strong fundamental mathematical theory along with useful practical implementations.
I am particularly interested in developing efficient second-order methods and tools for randomized numerical linear algebra. Active projects I am involved with include novel Newton-type algorithms for non-convex optimization, sketch-based online training of neural compressors, and entropy regularization for piece-wise linear quadratic convex programs.
Publications
- Simpson, C., Becker, S., & Doostan, A. (2025). Sketch Based Online Training of Implicit Neural Compressors for Scientific Simulations. In-progress
- Simpson, C. & Becker, S. (2025). Regularized Saddle-Free Newton: A Globally Convergent and Efficient Non-Convex Newton Method. In-progress
- Doherty, K., Simpson, C., Becker, S., & Doostan, A. (2024). QuadConv: Quadrature-based convolutions with applications to non-uniform PDE data compression. Journal of Computational Physics, 498, 112636.
- Balin, R., Simini, F., Simpson, C., Shao, A., Rigazzi, A., Ellis, M., ... & Jansen, K. E. (2023). In Situ Framework for Coupling Simulation and Machine Learning with Application to CFD. arXiv preprint arXiv:2306.12900.
- Simpson, C. R. (2022). Regularized Saddle-Free Newton: Saddle Avoidance and Efficient Implementation (Doctoral dissertation, University of Colorado).
- Manzano, S. A., Hughes, D. T., Simpson, C. R., Patel, R., Heckman, C., & Correll, N. (2019, October). Embedded neural networks for robot autonomy. In The International Symposium of Robotics Research (pp. 242-257). Cham: Springer International Publishing.
Awards
Department of Energy Computational Science Graduate Fellowship (DOE CSGF), 2025, Prestigious four-year fellowship for research in Ph.D research in computational science
Wan Fellowship, 2024, Prestigious two-year University of Washington Applied Math departmental Ph.D fellowship
CRA Honorable Mention, 2020 Computing Research Association Outstanding Undergraduate Researcher