Nicholas H. Nelsen
2024/02 (new): My new preprint provides "An operator learning perspective on parameter-to-observable maps" (with Daniel Z. Huang and Margaret Trautner). This work introduces and implements Fourier Neural Mappings, a principled extension of FNOs for learning maps with finite-dimensional inputs and/or outputs. For the task of predicting finite-dimensional quantities of interest (QoIs), a theoretical analysis explores the relative difficulty of full-field operator learning versus end-to-end learning of the QoIs. The accompanying code is publicly available here.
2024/02 (new): I am presenting my spotlight work on function-valued random features in MS146: Learning High-Dimensional Functions: Approximation, Sampling, and Algorithms at the SIAM Conference on Uncertainty Quantification (UQ24) in Trieste, Italy. There, I am also co-organizing a minisymposium on Recent Advances in Scalable Active Learning and Optimal Experimental Design.
2024/02: I presented my work on the "Foundations of Data-Efficient and Uncertainty-Aware Scientific Machine Learning" at the Joint ASE/Oden Institute Seminar at UT Austin and the MAE Colloquium at Cornell University.
2024/01: I gave a talk at the Cornell Scientific Computing and Numerics (SCAN) seminar.