34 citations · 162 across the 24 of their papers we have counts for
6 papers · 1 filter
Generative AI for fast and accurate statistical computation of fluids
Roberto Molinaro, Samuel Lanthaler, Bogdan Raonić +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…
Operator Learning of Lipschitz Operators: An Information-Theoretic Perspective
Samuel Lanthaler
Operator learning based on neural operators has emerged as a promising paradigm for the data-driven approximation of operators, mapping between infinite-dimensional Banach spaces.…
Data Complexity Estimates for Operator Learning
Nikola B. Kovachki, Samuel Lanthaler, Hrushikesh Mhaskar
Operator learning has emerged as a new paradigm for the data-driven approximation of nonlinear operators. Despite its empirical success, the theoretical underpinnings governing the…
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…
Sharp conditions for energy balance in two-dimensional incompressible ideal flow with external force
Fabian Jin, Samuel Lanthaler, Milton C. Lopes Filho +1
Smooth solutions of the forced incompressible Euler equations satisfy an energy balance, where the rate-of-change in time of the kinetic energy equals the work done by the force pe…
Operator Learning: Algorithms and Analysis
Nikola B. Kovachki, Samuel Lanthaler, Andrew M. Stuart
Operator learning refers to the application of ideas from machine learning to approximate (typically nonlinear) operators mapping between Banach spaces of functions. Such operators…