73 citations · 398 across the 44 of their papers we have counts for
4 papers · 1 filter
Elliptic PDE learning is provably data-efficient
Nicolas Boullé, Diana Halikias, Alex Townsend
PDE learning is an emerging field that combines physics and machine learning to recover unknown physical systems from experimental data. While deep learning models traditionally re…
Arbitrary-Depth Universal Approximation Theorems for Operator Neural Networks
Annan Yu, Chloé Becquey, Diana Halikias +2
The standard Universal Approximation Theorem for operator neural networks (NNs) holds for arbitrary width and bounded depth. Here, we prove that operator NNs of bounded width and a…
Data-driven discovery of Green's functions with human-understandable deep learning
Nicolas Boullé, Christopher J. Earls, Alex Townsend
There is an opportunity for deep learning to revolutionize science and technology by revealing its findings in a human interpretable manner. To do this, we develop a novel data-dri…
Why are Big Data Matrices Approximately Low Rank?
Madeleine Udell, Alex Townsend
Matrices of (approximate) low rank are pervasive in data science, appearing in recommender systems, movie preferences, topic models, medical records, and genomics. While there is a…