相关论文: Active Learning for Saddle Point Calculation

The task of locating first order saddle points on high-dimensional surfaces describing the variation of energy as a function of atomic coordinates is an essential step for identifying the mechanism and estimating the rate of thermally…

Gaussian process (GP) regression provides a strategy for accelerating saddle point searches on high-dimensional energy surfaces by reducing the number of times the energy and its derivatives with respect to atomic coordinates need to be…

Saddle point search schemes are widely used to identify the transition state of different processes, like chemical reactions, surface and bulk diffusion, surface adsorption, and many more. In solid-state materials with relatively large…

Saddle points play important roles as the transition states of activated process in gradient system driven by energy functional. However, for the same energy functional, the saddle points, as well as other stationary points, are different…

Global sensitivity analysis of complex numerical simulators is often limited by the small number of model evaluations that can be afforded. In such settings, surrogate models built from a limited set of simulations can substantially reduce…

This paper introduces an active learning framework for manifold Gaussian Process (GP) regression, combining manifold learning with strategic data selection to improve accuracy in high-dimensional spaces. Our method jointly optimizes a…

Here we present a multiscale method to calculate the saddle point associated with the effective dynamics arising from a stochastic system which couples slow deterministic drift and fast stochastic dynamics. This problem is motivated by the…

Active learning methods for emulating complex computer models that rely on stationary Gaussian processes tend to produce design points that uniformly fill the entire experimental region, which can be wasteful for functions which vary only…

In many areas of science and engineering, discovering the governing differential equations from the noisy experimental data is an essential challenge. It is also a critical step in understanding the physical phenomena and prediction of the…

The high-index saddle dynamics (HiSD) method is a powerful approach for computing saddle points and solution landscape. However, its practical applicability is constrained by the need for the explicit energy function expression. To overcome…

Finding saddle points of dynamical systems is an important problem in practical applications such as the study of rare events of molecular systems. Gentlest ascent dynamics (GAD) is one of a number of algorithms in existence that attempt to…

Change-point detection (CPD) is crucial for identifying abrupt shifts in data, which influence decision-making and efficient resource allocation across various domains. To address the challenges posed by the costly and time-intensive data…

Gaussian process (GP) regression is a popular surrogate modeling tool for computer simulations in engineering and scientific domains. However, it often struggles with high computational costs and low prediction accuracy when the simulation…

Gaussian Process differential equations (GPODE) have recently gained momentum due to their ability to capture dynamics behavior of systems and also represent uncertainty in predictions. Prior work has described the process of training the…

Stochastic gradient descent (SGD) is a standard optimization method to minimize a training error with respect to network parameters in modern neural network learning. However, it typically suffers from proliferation of saddle points in the…

We consider stochastic strongly-convex-strongly-concave (SCSC) saddle point (SP) problems which frequently arise in applications ranging from distributionally robust learning to game theory and fairness in machine learning. We focus on the…

Despite the availability of ever more data enabled through modern sensor and computer technology, it still remains an open problem to learn dynamical systems in a sample-efficient way. We propose active learning strategies that leverage…

In this paper we introduce an active learning method for symbolic regression using StackGP. The approach begins with a small number of data points for StackGP to model. To improve the model the system incrementally adds a data point such…

Stochastically controlled stochastic gradient (SCSG) methods have been proved to converge efficiently to first-order stationary points which, however, can be saddle points in nonconvex optimization. It has been observed that a stochastic…

We present a class of simple algorithms that allows to find the reaction path in systems with a complex potential energy landscape. The approach does not need any knowledge on the product state and does not require the calculation of any…