Zobrazeno 1 - 10
of 249
pro vyhledávání: '"Owren, Brynjulf"'
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
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
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
Autor:
Sherry, Ferdia, Celledoni, Elena, Ehrhardt, Matthias J., Murari, Davide, Owren, Brynjulf, Schönlieb, Carola-Bibiane
Publikováno v:
In Physica D: Nonlinear Phenomena July 2024 463
Since their introduction, Lie group integrators have become a method of choice in many application areas. Various formulations of these integrators exist, and in this work we focus on Runge--Kutta--Munthe--Kaas methods. First, we briefly introduce th
Externí odkaz:
http://arxiv.org/abs/2109.12325
Since they were introduced in the 1990s, Lie group integrators have become a method of choice in many application areas. These include multibody dynamics, shape analysis, data science, image registration and biophysical simulations. Two important cla
Externí odkaz:
http://arxiv.org/abs/2102.12778