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pro vyhledávání: '"Lanthaler"'
We propose a scalable encoding of combinatorial optimization problems with arbitrary connectivity, including higher-order terms, on arrays of trapped neutral atoms requiring only a global laser drive. Our approach relies on modular arrangements of a
Externí odkaz:
http://arxiv.org/abs/2410.03902
Autor:
Molinaro, Roberto, Lanthaler, Samuel, Raonić, Bogdan, Rohner, Tobias, Armegioiu, Victor, Wan, Zhong Yi, Sha, Fei, Mishra, Siddhartha, Zepeda-Núñez, Leonardo
We present a generative AI algorithm for addressing the challenging task of fast, accurate and robust statistical computation of three-dimensional turbulent fluid flows. Our algorithm, termed as GenCFD, is based on a conditional score-based diffusion
Externí odkaz:
http://arxiv.org/abs/2409.18359
Autor:
Lanthaler, Samuel
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. Despite significant empirical progress, our theoretical understanding
Externí odkaz:
http://arxiv.org/abs/2406.18794
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 conditions for efficient operator learning remain incomplete. The pre
Externí odkaz:
http://arxiv.org/abs/2405.15992
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 a common model architecture used for operator learning. The FNO combines pointwise linear
Externí odkaz:
http://arxiv.org/abs/2405.02221
Sharp conditions for energy balance in two-dimensional incompressible ideal flow with external force
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 per unit time. Interesting phenomena such as turbulence are closely link
Externí odkaz:
http://arxiv.org/abs/2404.12572
Operator learning refers to the application of ideas from machine learning to approximate (typically nonlinear) operators mapping between Banach spaces of functions. Such operators often arise from physical models expressed in terms of partial differ
Externí odkaz:
http://arxiv.org/abs/2402.15715
Autor:
Lanthaler, Samuel, Stuart, Andrew M.
Neural operator architectures employ neural networks to approximate operators mapping between Banach spaces of functions; they may be used to accelerate model evaluations via emulation, or to discover models from data. Consequently, the methodology h
Externí odkaz:
http://arxiv.org/abs/2306.15924
Autor:
Lanthaler, Samuel, Nelsen, Nicholas H.
Publikováno v:
Advances in Neural Information Processing Systems Vol. 36 (2023) pp. 71834-71861
This paper provides a comprehensive error analysis of learning with vector-valued random features (RF). The theory is developed for RF ridge regression in a fully general infinite-dimensional input-output setting, but nonetheless applies to and impro
Externí odkaz:
http://arxiv.org/abs/2305.17170