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pro vyhledávání: '"Moraga, Sebastian"'
Operator learning problems arise in many key areas of scientific computing where Partial Differential Equations (PDEs) are used to model physical systems. In such scenarios, the operators map between Banach or Hilbert spaces. In this work, we tackle
Externí odkaz:
http://arxiv.org/abs/2406.13928
Learning approximations to smooth target functions of many variables from finite sets of pointwise samples is an important task in scientific computing and its many applications in computational science and engineering. Despite well over half a centu
Externí odkaz:
http://arxiv.org/abs/2404.03761
Infinite-dimensional, holomorphic functions have been studied in detail over the last several decades, due to their relevance to parametric differential equations and computational uncertainty quantification. The approximation of such functions from
Externí odkaz:
http://arxiv.org/abs/2310.16940
Over the last decade, approximating functions in infinite dimensions from samples has gained increasing attention in computational science and engineering, especially in computational uncertainty quantification. This is primarily due to the relevance
Externí odkaz:
http://arxiv.org/abs/2305.18642
The past decade has seen increasing interest in applying Deep Learning (DL) to Computational Science and Engineering (CSE). Driven by impressive results in applications such as computer vision, Uncertainty Quantification (UQ), genetics, simulations a
Externí odkaz:
http://arxiv.org/abs/2211.12633
Sparse polynomial approximation has become indispensable for approximating smooth, high- or infinite-dimensional functions from limited samples. This is a key task in computational science and engineering, e.g., surrogate modelling in uncertainty qua
Externí odkaz:
http://arxiv.org/abs/2203.13908
In this chapter, we discuss recent work on learning sparse approximations to high-dimensional functions on data, where the target functions may be scalar-, vector- or even Hilbert space-valued. Our main objective is to study how the sampling strategy
Externí odkaz:
http://arxiv.org/abs/2202.02360
Spurred in part by the ever-growing number of sensors and web-based methods of collecting data, the use of Intensive Longitudinal Data (ILD) is becoming more common in the social and behavioural sciences. The ILD collected in this field are often hyp
Externí odkaz:
http://arxiv.org/abs/2201.09033
Accurate approximation of scalar-valued functions from sample points is a key task in computational science. Recently, machine learning with Deep Neural Networks (DNNs) has emerged as a promising tool for scientific computing, with impressive results
Externí odkaz:
http://arxiv.org/abs/2012.06081
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