Related papers: Computing Slow Manifolds of Saddle Type
We investigate the convergence properties of a stochastic primal-dual splitting algorithm for solving structured monotone inclusions involving the sum of a cocoercive operator and a composite monotone operator. The proposed method is the…
Gradient-related first-order methods have become the workhorse of large-scale numerical optimization problems. Many of these problems involve nonconvex objective functions with multiple saddle points, which necessitates an understanding of…
Synthetic molecular dynamics (synMD) trajectories from learned generative models have been proposed as a useful addition to the biomolecular simulation toolbox. The computational expense of explicitly integrating the equations of motion in…
Clustering algorithms fundamentally group data points by characteristics to identify patterns. Over the past two decades, researchers have extended these methods to analyze trajectories of humans, animals, and vehicles, studying their…
In this paper, we address a manifold constrained nonsmooth optimization problem involving the composition of a weakly convex function and a smooth mapping under the availability of a parametrization of the manifold. To find a stationary…
We investigate the persistence and regularity of spectral submanifolds (SSMs) in high-dimensional parametric dynamical systems undergoing a Hopf bifurcation. By analyzing how resonances in the linearized spectrum near bifurcation points…
The folded node is a singularity associated with loss of normal hyperbolicity in systems where mixtures of slow and fast timescales arise due to singular perturbations. Canards are special solutions that reveal a counteractive feature of…
A stochastic mode reduction strategy is applied to multiscale models with a deterministic energy-conserving fast sub-system. Specifically, we consider situations where the slow variables are driven stochastically and interact with the fast…
We propose a new Monte Carlo method for efficiently sampling trajectories with fixed initial and final conditions in a system with discrete degrees of freedom. The method can be applied to any stochastic process with local interactions,…
A version of the Dynamical Systems Method (DSM) for solving ill-posed nonlinear equations with monotone operators in a Hilbert space is studied in this paper. An a posteriori stopping rule, based on a discrepancy-type principle is proposed…
This paper presents an optimised algorithm implementing the method of slices for analysing the stability of slopes. The algorithm adopts an improved physically based parameterisation of slip lines according to their geometrical…
Learning a stable Linear Dynamical System (LDS) from data involves creating models that both minimize reconstruction error and enforce stability of the learned representation. We propose a novel algorithm for learning stable LDSs. Using a…
Recently, a flexible and stable algorithm was introduced for the computation of 2D unstable manifolds of periodic solutions to systems of ordinary differential equations. The main idea of this approach is to represent orbits in this…
Symmetry reduction by the method of slices quotients the continuous symmetries of chaotic flows by replacing the original state space by a set of charts, each covering a neighborhood of a dynamically important class of solutions,…
Stochastic gradient descent (SGD) holds as a classical method to build large scale machine learning models over big data. A stochastic gradient is typically calculated from a limited number of samples (known as mini-batch), so it…
When solitary waves are characterized as homoclinic orbits of a finite-dimensional Hamiltonian system, they have an integer-valued topological invariant, the Maslov index. We are interested in developing a robust numerical algorithm to…
We model incompressible flows with an adaptive stabilized finite element method Stokes flows, which solves a discretely stable saddle-point problem to approximate the velocity-pressure pair. Additionally, this saddle-point problem delivers…
When analyzing parametric statistical models, a useful approach consists in modeling geometrically the parameter space. However, even for very simple and commonly used hierarchical models like statistical mixtures or stochastic deep neural…
We present a black-box method to numerically investigate the linear stability of arbitrary multi-physics problems. While the user just has to enter the system's residual in weak formulation, i.e. by a finite element method, all required…
Saddle point problems arise in many important practical applications. In this paper we propose and analyze some algorithms for solving symmetric saddle point problems which are based upon the block Gram-Schmidt method. In particular, we…