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pro vyhledávání: '"P, Cavoretto"'
Background: Deep learning techniques, particularly neural networks, have revolutionized computational physics, offering powerful tools for solving complex partial differential equations (PDEs). However, ensuring stability and efficiency remains a cha
Externí odkaz:
http://arxiv.org/abs/2407.07375
Unisolvence of unsymmetric Kansa collocation is still a substantially open problem. We prove that Kansa matrices with MultiQuadrics and Inverse MultiQuadrics for the Dirichlet problem of the Poisson equation are almost surely nonsingular, when the co
Externí odkaz:
http://arxiv.org/abs/2403.18017
In this paper we present a new fast and accurate method for Radial Basis Function (RBF) approximation, including interpolation as a special case, which enables us to effectively find the optimal value of the RBF shape parameter. In particular, we pro
Externí odkaz:
http://arxiv.org/abs/2311.04311
Partition of unity methods (PUMs) on graphs represent straightforward and remarkably adaptable auxiliary techniques for graph signal processing. By relying solely on the intrinsic graph structure, we propose the generation of a partition of unity thr
Externí odkaz:
http://arxiv.org/abs/2311.04299
In this paper, we employ Bayesian optimization to concurrently explore the optimal values for both the shape parameter and the radius in the partition of unity interpolation using radial basis functions. Bayesian optimization is a probabilistic, iter
Externí odkaz:
http://arxiv.org/abs/2311.04289
In this paper, Bayesian optimisation is used to simultaneously search the optimal values of the shape parameter and the radius in radial basis function partition of unity interpolation problem. It is a probabilistic iterative approach that models the
Externí odkaz:
http://arxiv.org/abs/2311.04210
Graph signal processing benefits significantly from the direct and highly adaptable supplementary techniques offered by partition of unity methods (PUMs) on graphs. In our approach, we demonstrate the generation of a partition of unity solely based o
Externí odkaz:
http://arxiv.org/abs/2311.04935
Autor:
Cavoretto, R., Dell'Accio, F., De Rossi, A., Di Tommaso, F., Siar, N., Sommariva, A., Vianello, M.
We construct cubature methods on scattered data via resampling on the support of known algebraic cubature formulas, by different kinds of adaptive interpolation (polynomial, RBF, PUM). This approach gives a promising alternative to other recent metho
Externí odkaz:
http://arxiv.org/abs/2307.07203
Autor:
Paolo I. Cavoretto, Antonio Farina
Publikováno v:
The Lancet Regional Health. Europe, Vol 45, Iss , Pp 101069- (2024)
Externí odkaz:
https://doaj.org/article/088724feefa347ca8f546f213896645f
Autor:
Cavoretto, Roberto
In this paper we propose an adaptive scheme for the solution of time-dependent boundary value problems (BVPs). To solve numerically these problems, we consider the kernel-based method of lines that allows us to split the spatial and time derivatives,
Externí odkaz:
http://arxiv.org/abs/2203.14091