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My research team has several openings at the Ph.D. and postdoc levels. Prospective applicants are welcome to contact me by email.
Assistant Professor
The University of Texas at Austin
About Me
About Me
Welcome! I am an Assistant Professor at UT Austin, where I hold a joint appointment in the Oden Institute and the Department of ASE/EM. Broadly, my research interests lie at the intersection of computational mathematics and artificial intelligence. Using rigorous analysis and domain-specific insight, I develop novel AI methods for high- or infinite-dimensional problems, establish theoretical guarantees on the reliability and trustworthiness of these methods, and apply the methods in the physical and information sciences. My work blends operator learning with ideas from inverse problems, generative modeling, and uncertainty quantification. A current focus of my research centers on machine learning in the space of probability distributions.
Previously, I was a Klarman Fellow in the Department of Mathematics at Cornell University from 2025-2026. From 2024-2025, I was an NSF Postdoctoral Fellow in the Department of Mathematics at MIT. I received my Ph.D. from Caltech in 2024, where I was supported by the Amazon AI4Science Fellows Program and an NSF Graduate Research Fellowship. My doctoral dissertation was awarded two "best thesis" prizes, one in applied mathematics and another in engineering. I obtained my M.Sc. from Caltech in 2020 and my B.Sc. in Mathematics, B.S.M.E., and B.S.A.E. degrees from Oklahoma State University in 2018.
nnelsen [at] oden [dot] utexas [dot] edu
Recent News
Recent News
2026/08 (new): I am thrilled to have joined UT Austin as an Assistant Professor!
2026/05: In a new preprint on amortized probabilistic conditioning, we view the joint-to-conditional density map as an operator between function spaces and prove that neural operators can accurately approximate it. This is joint work with Panos Tsimpos, Edo Calvello, and Ayoub Belhadji.
2026/03: In a new preprint with Simone Brugiapaglia and Nicola Rares Franco, we give A short tour of operator learning theory by reviewing known sample complexity bounds for trained neural operators, contrasting them with minimax statistical limits, and highlighting key open problems.
2025/12: Our survey chapter on "Operator learning meets inverse problems" has been accepted in the Handbook of Numerical Analysis, Vol. 27: Machine Learning Solutions for Inverse Problems. I am excited to present this and recent work on approximating EIT in my plenary talk at the Inverse Days 2025 conference in Helsinki, Finland.
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