相关论文: An efficient saddle search method for ordered phas…

Monte Carlo methods are widely used in particle physics to integrate and sample probability distributions (differential cross sections or decay rates) on multi-dimensional phase spaces. We present a Neural Network (NN) algorithm optimized…

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…

Training deep neural network is a high dimensional and a highly non-convex optimization problem. Stochastic gradient descent (SGD) algorithm and it's variations are the current state-of-the-art solvers for this task. However, due to…

Nudging is a popular algorithmic strategy in numerical filtering to deal with the problem of inference in high-dimensional dynamical systems. We demonstrate in this paper that general nudging techniques can also tackle another crucial…

Zeolites are important for industrial catalytic processes involving organic molecules. Understanding molecular reaction mechanisms within the confined nanoporous environment can guide the selection of pore topologies, material compositions,…

Convergence detection of iterative stochastic optimization methods is of great practical interest. This paper considers stochastic gradient descent (SGD) with a constant learning rate and momentum. We show that there exists a transient…

Several reduced order models have been developed for nonlinear dynamical systems. To achieve a considerable speed-up, a hyper-reduction step is needed to reduce the computational complexity due to nonlinear terms. Many hyper-reduction…

In comparison to numerous enhanced sampling methods for equilbrium thermodynamics, accelerating simulations for kinetics and nonequilibrium statistics are relatively rare and less effective. Here we derive a time-reversal path sampling…

The Potts model is a generalization of the Ising model with $Q>2$ components. In the fully connected ferromagnetic Potts model, a first-order phase transition is induced by varying thermal fluctuations. Therefore, the computational time…

Algorithms for computing local minima of smooth objective functions enjoy a mature theory as well as robust and efficient implementations. By comparison, the theory and practice of saddle search is destitute. In this paper we present…

We study phase transitions and the nature of order in a class of classical generalized $O(N)$ nonlinear $\sigma$-models (NLS) constructed by minimally coupling pure NLS with additional degrees of freedom in the form of (i) Ising…

Within the Projected Entangled Pair State (PEPS) tensor network formalism, a simple update (SU) method has been used to investigate the time evolution of a two-dimensional U(1) critical spin-1/2 spin liquid under Hamiltonian quench [Phys.…

A strategy for finding transition paths connecting two stable basins is presented. The starting point is the Hamilton principle of stationary action; we show how it can be transformed into a minimum principle through the addition of…

Policy gradient (PG) is widely used in reinforcement learning due to its scalability and good performance. In recent years, several variance-reduced PG methods have been proposed with a theoretical guarantee of converging to an approximate…

The wide application of machine learning (ML) techniques in statistics physics has presented new avenues for research in this field. In this paper, we introduce a semi-supervised learning method based on Siamese Neural Networks (SNN),…

In this paper I will describe some results that have been recently obtained in the study of random Euclidean matrices, i.e. matrices that are functions of random points in Euclidean space. In the case of {\sl translation invariant} matrices…

Multi-way data analysis has become an essential tool for capturing underlying structures in higher-order datasets stored in tensor $\mathcal{X} \in \mathbb{R} ^{I_1 \times \dots \times I_N} $. $CANDECOMP/PARAFAC$ (CP) decomposition has been…

In the Lagrange-Newton method, where Newton's method is applied to a Lagrangian function that includes equality constraints, all stationary points are saddle points. It is therefore not possible to use a line-search method based on the…

In this paper, we investigate a class of constrained saddle point (SP) problems where the objective function is nonconvex-concave and smooth. This class of problems has wide applicability in machine learning, including robust multi-class…

Stochastic Gradient Descent (SGD) is one of the many iterative optimization methods that are widely used in solving machine learning problems. These methods display valuable properties and attract researchers and industrial machine learning…