Zobrazeno 1 - 10
of 254
pro vyhledávání: '"Celledoni, Elena"'
Autor:
Celledoni, Elena, Çokaj, Ergys, Leone, Andrea, Leyendecker, Sigrid, Murari, Davide, Owren, Brynjulf, de Almagro, Rodrigo T. Sato Martín, Stavole, Martina
Euler's elastica is a classical model of flexible slender structures, relevant in many industrial applications. Static equilibrium equations can be derived via a variational principle. The accurate approximation of solutions of this problem can be ch
Externí odkaz:
http://arxiv.org/abs/2312.00644
Publikováno v:
Journal of Computational Dynamics Vol. 11, No. 1, January 2024, pp. 92-107
We propose a generalization of nonlinear stability of numerical one-step integrators to Riemannian manifolds in the spirit of Butcher's notion of B-stability. Taking inspiration from Simpson-Porco and Bullo, we introduce non-expansive systems on such
Externí odkaz:
http://arxiv.org/abs/2308.08261
Autor:
Sherry, Ferdia, Celledoni, Elena, Ehrhardt, Matthias J., Murari, Davide, Owren, Brynjulf, Schönlieb, Carola-Bibiane
Motivated by classical work on the numerical integration of ordinary differential equations we present a ResNet-styled neural network architecture that encodes non-expansive (1-Lipschitz) operators, as long as the spectral norms of the weights are ap
Externí odkaz:
http://arxiv.org/abs/2306.17332
We introduce the mean inverse integrator (MII), a novel approach to increase the accuracy when training neural networks to approximate vector fields of dynamical systems from noisy data. This method can be used to average multiple trajectories obtain
Externí odkaz:
http://arxiv.org/abs/2306.03548
As supported by abundant experimental evidence, neural networks are state-of-the-art for many approximation tasks in high-dimensional spaces. Still, there is a lack of a rigorous theoretical understanding of what they can approximate, at which cost,
Externí odkaz:
http://arxiv.org/abs/2305.00723
Neural networks have gained much interest because of their effectiveness in many applications. However, their mathematical properties are generally not well understood. If there is some underlying geometric structure inherent to the data or to the fu
Externí odkaz:
http://arxiv.org/abs/2210.02373
The numerical method of Kahan applied to quadratic differential equations is known to often generate integrable maps in low dimensions and can in more general situations exhibit preserved measures and integrals. Computerized methods based on discrete
Externí odkaz:
http://arxiv.org/abs/2209.01094
Publikováno v:
Bit Numer Math 63, 50 (2023)
One of the fundamental problems in shape analysis is to align curves or surfaces before computing geodesic distances between their shapes. Finding the optimal reparametrization realizing this alignment is a computationally demanding task, typically d
Externí odkaz:
http://arxiv.org/abs/2207.11141
Recently, there has been an increasing interest in modelling and computation of physical systems with neural networks. Hamiltonian systems are an elegant and compact formalism in classical mechanics, where the dynamics is fully determined by one scal
Externí odkaz:
http://arxiv.org/abs/2201.13254