相关论文: Multiscale Gentlest Ascent Dynamics for Saddle Poi…

In this paper, we propose a new way to obtain optimal convergence rates for smooth stochastic (strong) convex optimization tasks. Our approach is based on results for optimization tasks where gradients have nonrandom noise. In contrast to…

This paper explores numerical methods for solving a convex differentiable semi-infinite program. We introduce a primal-dual gradient method which performs three updates iteratively: a momentum gradient ascend step to update the constraint…

In order to understand the impact of random influences at physical boundary on the evolution of multiscale systems, a stochastic partial differential equation model under a fast random dynamical boundary condition is investigated. The…

Characterizing and understanding the dynamics of stochastic gradient descent (SGD) around saddle points remains an open problem. We first show that saddle points in neural networks can be divided into two types, among which the Type-II…

This study develops a fixed-time convergent saddle point dynamical system for solving min-max problems under a relaxation of standard convexity-concavity assumption. In particular, it is shown that by leveraging the dynamical systems…

We present an algorithm for the simulation of the exact real-time dynamics of classical many-body systems with discrete energy levels. In the same spirit of kinetic Monte Carlo methods, a stochastic solution of the master equation is found,…

We demonstrate the possibility to systematically steer the most probable escape paths (MPEPs) by adjusting relative noise intensities in dynamical systems that exhibit noise-induced escape from a metastable point via a saddle point. Using a…

The training of modern machine learning models often consists in solving high-dimensional non-convex optimisation problems that are subject to large-scale data. In this context, momentum-based stochastic optimisation algorithms have become…

We present a numerical method for computing optimal transition pathways and transition rates in systems of stochastic differential equations (SDEs). In particular, we compute the most probable transition path of stochastic equations by…

Stochastic nonconvex-concave min-max saddle point problems appear in many machine learning and control problems including distributionally robust optimization, generative adversarial networks, and adversarial learning. In this paper, we…

The stochastic gradient descent method with momentum (SGDM) is a common approach for solving large-scale and stochastic optimization problems. Despite its popularity, the convergence behavior of SGDM remains less understood in nonconvex…

We address the problem of safely learning controlled stochastic dynamics from discrete-time trajectory observations, ensuring system trajectories remain within predefined safe regions during both training and deployment. Safety-critical…

Increasing effort is put into the development of methods for learning mechanistic models from data. This task entails not only the accurate estimation of parameters but also a suitable model structure. Recent work on the discovery of…

We analyze stochastic algorithms for optimizing nonconvex, nonsmooth finite-sum problems, where the nonconvex part is smooth and the nonsmooth part is convex. Surprisingly, unlike the smooth case, our knowledge of this fundamental problem…

We introduce a nonlinear stochastic model reduction technique for high-dimensional stochastic dynamical systems that have a low-dimensional invariant effective manifold with slow dynamics, and high-dimensional, large fast modes. Given only…

Being able to effectively locate saddle (and other fixed) points in dynamical systems holds tremendous implications in a number of applications in engineering and science, among which the study of rare events in molecular simulations stands…

We study the convergence to equilibrium of an underdamped Langevin equation that is controlled by a linear feedback force. Specifically, we are interested in sampling the possibly multimodal invariant probability distribution of a Langevin…

Robots are still poor at traversing cluttered large obstacles required for important applications like search and rescue. By contrast, animals are excellent at doing so, often using direct physical interaction with obstacles rather than…

Distribution-dependent stochastic dynamical systems arise widely in engineering and science. We consider a class of such systems which model the limit behaviors of interacting particles moving in a vector field with random fluctuations. We…

The power system, a fundamental public utility, is increasingly important due to growing global electricity demand. Recent large-scale blackouts (e.g., Iberian Peninsula, UK) have raised concerns about transient stability under impact…