133 citations · 198 across the 12 of their papers we have counts for
5 papers · 1 filter
Universal Approximation of Measure-to-Measure Operators by Pushforwards
Takashi Furuya, Nicholas H. Nelsen, Frank Cole
Many learning tasks map an input distribution to an output distribution. A natural way to model such an operator is to transform each input sample using a continuous function that…
Learning where to learn: Training data distribution optimization for scientific machine learning
Nicolas Guerra, Nicholas H. Nelsen, Yunan Yang
In scientific machine learning, models are routinely deployed with parameter values or boundary conditions far from those used in training. This paper studies the learning-where-to…
Operator Learning Using Random Features: A Tool for Scientific Computing
Nicholas H. Nelsen, Andrew M. Stuart
Supervised operator learning centers on the use of training data, in the form of input-output pairs, to estimate maps between infinite-dimensional spaces. It is emerging as a power…
Hyperparameter Optimization for Randomized Algorithms: A Case Study on Random Features
Oliver R. A. Dunbar, Nicholas H. Nelsen, Maya Mutic
Randomized algorithms exploit stochasticity to reduce computational complexity. One important example is random feature regression (RFR) that accelerates Gaussian process regressio…
An operator learning perspective on parameter-to-observable maps
Daniel Zhengyu Huang, Nicholas H. Nelsen, Margaret Trautner
Computationally efficient surrogates for parametrized physical models play a crucial role in science and engineering. Operator learning provides data-driven surrogates that map bet…