An adaptive time-step variational integrator for simulating flexible multibody system
dynamics is proposed. The integrator can adapt the time-step based on the variation of the …

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 …

It was shown recently by W. Su, S. Boyd, and E. Candes, J. Mach. Learn. Res., 17 (2016),
pp. 1--43 that Nesterov's accelerated gradient method for minimizing a smooth convex …

As numerous modern challenges in scientific questions, industrial needs, and societal
requirements emerge, the demand for designing numerical methods to solve tremendously …

A variational formulation for accelerated optimization on normed vector spaces was recently
introduced in Wibisono et al.(PNAS 113: E7351–E7358, 2016), and later generalized to the …

We first derive the Hamilton-Jacobi theory underlying continuous-time Markov processes,
and then we use the construction to develop a variational algorithm for estimating escape …

A bstract We study the dynamics of the solar basin—the accumulated population of weakly-
interacting particles on bound orbits in the Solar System. We focus on particles starting off on …

A variational formulation of accelerated optimization on normed spaces was recently
introduced by considering a specific family of time-dependent Bregman Lagrangian and …

Many of the new developments in machine learning are connected with gradient-based
optimization methods. Recently, these methods have been studied using a variational …

Geometric numerical integration has recently been exploited to design symplectic
accelerated optimization algorithms by simulating the Bregman Lagrangian and Hamiltonian …