7 papers
Towards a Certificate of Trust: Task-Aware OOD Detection for Scientific AI
Bogdan RaoniÄ, Siddhartha Mishra, Samuel Lanthaler
Data-driven models are increasingly adopted in critical scientific fields like weather forecasting and fluid dynamics. These methods can fail on out-of-distribution (OOD) data, but…
Discretization Error of Fourier Neural Operators
Samuel Lanthaler, Andrew M. Stuart, Margaret Trautner
Operator learning is a variant of machine learning that is designed to approximate maps between function spaces from data. The Fourier Neural Operator (FNO) is one of the main mode…
Universality of physical neural networks with multivariate nonlinearity
Benjamin Savinson, David J. Norris, Siddhartha Mishra +1
The enormous energy demand of artificial intelligence is driving the development of alternative hardware for deep learning. Physical neural networks try to exploit physical systems…
Theory-to-Practice Gap for Neural Networks and Neural Operators
Philipp Grohs, Samuel Lanthaler, Margaret Trautner
This work studies the sampling complexity of learning with ReLU neural networks and neural operators. For mappings belonging to relevant approximation spaces, we derive upper bound…
The Parametric Complexity of Operator Learning
Samuel Lanthaler, Andrew M. Stuart
Neural operator architectures employ neural networks to approximate operators mapping between Banach spaces of functions; they may be used to accelerate model evaluations via emula…
Generative AI for fast and accurate statistical computation of fluids
Roberto Molinaro, Samuel Lanthaler, Bogdan RaoniÄ +9
We present a generative AI algorithm for addressing the pressing task of fast, accurate, and robust statistical computation of three-dimensional turbulent fluid flows. Our algorith…