Zobrazeno 1 - 10
of 41
pro vyhledávání: '"Duruisseaux, Valentin"'
Autor:
White, Alistair, Büttner, Anna, Gelbrecht, Maximilian, Duruisseaux, Valentin, Kilbertus, Niki, Hellmann, Frank, Boers, Niklas
Neural differential equations offer a powerful approach for learning dynamics from data. However, they do not impose known constraints that should be obeyed by the learned model. It is well-known that enforcing constraints in surrogate models can enh
Externí odkaz:
http://arxiv.org/abs/2410.23667
In numerous contexts, high-resolution solutions to partial differential equations are required to capture faithfully essential dynamics which occur at small spatiotemporal scales, but these solutions can be very difficult and slow to obtain using tra
Externí odkaz:
http://arxiv.org/abs/2311.02328
Autor:
Lin, Wu, Duruisseaux, Valentin, Leok, Melvin, Nielsen, Frank, Khan, Mohammad Emtiyaz, Schmidt, Mark
Riemannian submanifold optimization with momentum is computationally challenging because, to ensure that the iterates remain on the submanifold, we often need to solve difficult differential equations. Here, we simplify such difficulties for a class
Externí odkaz:
http://arxiv.org/abs/2302.09738
Incorporating prior knowledge of physics laws and structural properties of dynamical systems into the design of deep learning architectures has proven to be a powerful technique for improving their computational efficiency and generalization capacity
Externí odkaz:
http://arxiv.org/abs/2211.16006
A continuous-time dynamical system with parameter $\varepsilon$ is nearly-periodic if all its trajectories are periodic with nowhere-vanishing angular frequency as $\varepsilon$ approaches 0. Nearly-periodic maps are discrete-time analogues of nearly
Externí odkaz:
http://arxiv.org/abs/2210.05087
Autor:
Duruisseaux, Valentin, Leok, Melvin
Geometric numerical integration has recently been exploited to design symplectic accelerated optimization algorithms by simulating the Lagrangian and Hamiltonian systems from the variational framework introduced in Wibisono et al. In this paper, we d
Externí odkaz:
http://arxiv.org/abs/2207.11460
Publikováno v:
Journal of Computational Dynamics, 9 (2022), 421-450
Numerical bifurcation analysis, and in particular two-parameter continuation, is used in consort with numerical simulation to reveal complicated dynamics in the Mackey-Glass equation for moderate values of the delay close to the onset of chaos. In pa
Externí odkaz:
http://arxiv.org/abs/2203.00181
Autor:
Duruisseaux, Valentin, Leok, Melvin
A variational framework for accelerated optimization was recently introduced on normed vector spaces and Riemannian manifolds in Wibisono et al. (2016) and Duruisseaux and Leok (2021). It was observed that a careful combination of timeadaptivity and
Externí odkaz:
http://arxiv.org/abs/2201.03774
Autor:
Duruisseaux, Valentin, Leok, Melvin
A variational formulation of accelerated optimization on normed spaces was recently introduced by considering a specific family of time-dependent Bregman Lagrangian and Hamiltonian systems whose corresponding trajectories converge to the minimizer of
Externí odkaz:
http://arxiv.org/abs/2201.02904
Autor:
Duruisseaux, Valentin, Leok, Melvin
A variational formulation for accelerated optimization on normed vector spaces was recently introduced in Wibisono et al., and later generalized to the Riemannian manifold setting in Duruisseaux and Leok. This variational framework was exploited on n
Externí odkaz:
http://arxiv.org/abs/2104.07176