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In 2026, I will join the faculty in UT's Oden Institute and Department of ASE-EM. Prospective Ph.D. students are welcome to contact me by email.
NSF Mathematical Sciences Postdoctoral Research Fellow
Department of Mathematics
Massachusetts Institute of Technology
About Me
About Me
I am joining UT Austin as an Assistant Professor in Fall 2026
Welcome! I am an NSF Mathematical Sciences Postdoctoral Research Fellow in the Department of Mathematics at MIT, where I am hosted by Prof. Philippe Rigollet. I am also affiliated with LIDS, CCSE, IDSS/SDSC, and the UQ Group, where I collaborate with Prof. Youssef Marzouk. Broadly, my research interests lie at the intersection of computational mathematics and statistics. Using rigorous analysis and domain-specific insight, I develop novel data-driven machine learning methods for high- and infinite-dimensional problems, establish theoretical guarantees on the reliability and trustworthiness of these methods, and apply them in the physical and data sciences. My current work blends operator learning with ideas from inverse problems, generative modeling, and uncertainty quantification.
I received my Ph.D. from Caltech in 2024, where I was fortunate to be advised by Prof. Andrew M. Stuart and 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. (Mathematics), B.S.M.E., and B.S.A.E. degrees from Oklahoma State University in 2018.
nnelsen [at] mit [dot] edu
Recent News
Recent News
2025/05 (new): What distribution should training data be sampled from to best approximate a target function or operator? Based on theoretical insights, our preprint on Learning Where to Learn: Training Distribution Selection for Provable Out-of-Distribution Performance introduces two adaptive and target-dependent algorithms to answer this question. The optimal training distributions that result from our methods empirically outperform traditional nonadaptive or target-independent data distributions. This is joint work with Nicolas Guerra and Yunan Yang.
2025/05: I am a presenter and panelist at the NSF CompMath Meeting at the University of Utah.
2025/02: Our work on hyperparameter optimization for randomized algorithms is now published in Statistics and Computing.
2024/10 [In the media]: I was featured in an Okstate alumni highlight story about my research career and future plans. Thanks for the write-up!
2024/08: I am happy to announce that Andrew Stuart and I received a 2024 SIGEST Award from SIAM for our 2021 paper on operator learning using random features. This award recognizes an exceptional paper of general interest published in the SIAM Journal on Scientific Computing in the last few years. An expanded version of the article is now published online in the SIGEST section in SIAM Review.
2024/07: I am joining the Department of Mathematics at MIT as an NSF Mathematical Sciences Postdoctoral Research Fellow. The following year, I will join the Department of Mathematics at Cornell University as a Klarman Fellow.
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