Results 21 to 30 of about 3,581,525 (255)
Derivative-Informed Neural Operator: An Efficient Framework for High-Dimensional Parametric Derivative Learning [PDF]
Journal of Computational Physics, 2022 We propose derivative-informed neural operators (DINOs), a general family of neural networks to approximate operators as infinite-dimensional mappings from input function spaces to output function spaces or quantities of interest.
Thomas O'Leary-Roseberry +3 more
semanticscholar +1 more source
Self-induced compactness in Banach spaces [PDF]
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1994 We consider the question: is every compact set in a Banach space X contained in the closed unit range of a compact (or even approximable) operator on X? We give large classes of spaces where the question has an affirmative answer, but observe that it has
P. Casazza, H. Jarchow
semanticscholar +1 more source
Variationally Mimetic Operator Networks [PDF]
Computer Methods in Applied Mechanics and Engineering, 2022 In recent years operator networks have emerged as promising deep learning tools for approximating the solution to partial differential equations (PDEs). These networks map input functions that describe material properties, forcing functions and boundary ...
Dhruv V. Patel +4 more
semanticscholar +1 more source
Very badly approximable matrix functions [PDF]
, 2003 .We study in this paper very badly approximable matrix functions on the unit circle $$ \mathbb{T}, $$ i.e., matrix functions Φ such that the zero function is a superoptimal approximation of Φ.
V. Peller, S. Treil
semanticscholar +1 more source
Nonlinear Reconstruction for Operator Learning of PDEs with Discontinuities [PDF]
International Conference on Learning Representations, 2022 A large class of hyperbolic and advection-dominated PDEs can have solutions with discontinuities. This paper investigates, both theoretically and empirically, the operator learning of PDEs with discontinuous solutions.
S. Lanthaler +3 more
semanticscholar +1 more source
Variable-Input Deep Operator Networks [PDF]
arXiv.org, 2022 Existing architectures for operator learning require that the number and locations of sensors (where the input functions are evaluated) remain the same across all training and test samples, significantly restricting the range of their applicability.
Michael Prasthofer +2 more
semanticscholar +1 more source
Single machine scheduling problems with uncertain parameters and the OWA criterion [PDF]
, 2014 In this paper a class of single machine scheduling problems is discussed. It is assumed that job parameters, such as processing times, due dates, or weights are uncertain and their values are specified in the form of a discrete scenario set.
Kasperski, Adam, Zielinski, Pawel
core +2 more sources
On the abominable properties of the almost Mathieu operator with well-approximated frequencies [PDF]
Duke mathematical journal, 2021 We show that some spectral properties of the almost Mathieu operator with frequency well approximated by rationals can be as poor as at all possible in the class of all one-dimensional discrete Schroedinger operators.
A. Avila, Y. Last, M. Shamis, Qi Zhou
semanticscholar +1 more source
Data-driven reduced-order models via regularised Operator Inference for a single-injector combustion process [PDF]
Journal of the Royal Society of New Zealand, 2020 This paper derives predictive reduced-order models for rocket engine combustion dynamics via Operator Inference, a scientific machine learning approach that blends data-driven learning with physics-based modelling.
Shane A. Mcquarrie +2 more
semanticscholar +1 more source
WKB approximation with conformable operator
Modern Physics Letters A, 2022 In this paper, the Wentzel–Kramers–Brillouin (WKB) method is extended to be applicable for conformable Hamiltonian systems, where the concept of conformable operator with fractional order [Formula: see text] is involved. The WKB approximation for the [Formula: see text]-wave function is derived for potentials which slowly vary in space.
Mohamed Al-Masaeed +2 more
openaire +2 more sources