Related papers: A reduced variational approach for searching cycle…

This survey concerns subspace recycling methods, a popular class of iterative methods that enable effective reuse of subspace information in order to speed up convergence and find good initial guesses over a sequence of linear systems with…

While existing mathematical descriptions can accurately account for phenomena at microscopic scales (e.g. molecular dynamics), these are often high-dimensional, stochastic and their applicability over macroscopic time scales of physical…

This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…

Most complex systems are intrinsically dynamic in nature. The evolution of a dynamic complex system is typically represented as a sequence of snapshots, where each snapshot describes the configuration of the system at a particular instant…

Determining low-energy eigenstates in electronic many-body quantum systems is a key challenge in computational chemistry and condensed-matter physics. Hybrid quantum-classical approaches, such as the Variational Quantum Eigensolver and…

First order optimization algorithms play a major role in large scale machine learning. A new class of methods, called adaptive algorithms, were recently introduced to adjust iteratively the learning rate for each coordinate. Despite great…

The problem of packing equal circles in a circle is a classic and famous packing problem, which is well-studied in academia and has a variety of applications in industry. This problem is computationally challenging, and researchers mainly…

Convolutional dictionary learning (CDL) estimates shift invariant basis adapted to multidimensional data. CDL has proven useful for image denoising or inpainting, as well as for pattern discovery on multivariate signals. As estimated…

One of the challenging scientific computing problems is topology optimization, where searching through the combinatorially complex configurations and solving the constraints of partial differential equations need to be done simultaneously.…

This paper proposes novel algorithm for non-convex multimodal constrained optimisation problems. It is based on sequential solving restrictions of problem to sections of feasible set by random subspaces (in general, manifolds) of low…

We propose a novel multiple-scale spatial marching method for flows with slow streamwise variation. The key idea is to couple the boundary region equations, which govern large-scale flow evolution, with local exact coherent structures that…

We investigate the evolution of families of periodic orbits in a bisymmetrical potential made up of a two-dimensional harmonic oscillator with only one quartic perturbing term, in a number of resonant cases. Our main objective is to compute…

We propose to compute approximations to general invariant sets in dynamical systems by minimizing the distance between an appropriately selected finite set of points and its image under the dynamics. We demonstrate, through computational…

Exploration requires that robots reason about numerous ways to cover a space in response to dynamically changing conditions. However, in continuous domains there are potentially infinitely many options for robots to explore which can prove…

We present high-order variational Lagrangian finite element methods for compressible fluids using a discrete energetic variational approach. Our spatial discretization is mass/momentum/energy conserving and entropy stable. Fully implicit…

Common trends in model order reduction of large nonlinear finite-element-discretized systems involve the introduction of a linear mapping into a reduced set of unknowns, followed by Galerkin projection of the governing equations onto a…

In the dynamical systems approach to describing turbulent or otherwise chaotic flows, an important quantity is the Lyapunov exponents and vectors that characterize the strange attractor of the flow. In particular, knowledge of the Lyapunov…

A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It…

In this paper, we propose a variationally consistent technique for decreasing the maximum eigenfrequencies of structural dynamics related finite element formulations. Our approach is based on adding a symmetric positive-definite term to the…

The aim of this work is to establish the existence of invariant manifolds in complex systems. Considering trajectory curves integral of multiple time scales dynamical systems of dimension two and three (predator-prey models, neuronal…