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We present an efficient algorithm for calculating the minimum energy path (MEP) and energy barriers between local minima on a multidimensional potential energy surface (PES). Such paths play a central role in the understanding of transition…

Computational Physics · Physics 2012-04-19 Amit Samanta , Weinan E

We present a new and efficient method for computing the transition pathways, free energy barriers, and transition rates in complex systems with relatively smooth energy landscapes. The method proceeds by evolving strings, i.e. smooth curves…

Condensed Matter · Physics 2009-11-07 Weinan E , Weiqing Ren , Eric Vanden-Eijnden

A novel and powerful method is presented for the study of rare switching events in complex systems with multiscale energy landscapes. The method performs an umbrella sampling of the equilibrium distribution of the system in hyperplanes…

Condensed Matter · Physics 2007-05-23 Weinan E , Weiqing Ren , Eric Vanden-Eijnden

Popular methods for identifying transition paths between energy minima, such as the nudged elastic band and string methods, typically do not incorporate potential energy curvature information, leading to slow relaxation to the minimum…

Computational Physics · Physics 2019-03-11 Stela Makri , Christoph Ortner , James R. Kermode

Understanding the transition events between metastable states in complex systems is an important subject in the fields of computational physics, chemistry and biology. The transition pathway plays an important role in characterizing the…

Computational Physics · Physics 2024-04-10 Bo Lin , Yangzheng Zhong , Weiqing Ren

Characterizing conformational transitions in physical systems remains a fundamental challenge, as traditional sampling methods struggle with the high-dimensional nature of molecular systems and high-energy barriers between stable states.…

Chemical Physics · Physics 2025-09-22 Magnus Petersen , Gemma Roig , Roberto Covino

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…

Numerical Analysis · Mathematics 2023-09-15 Wei Wei , Jianyu Hu

A method combining denoising diffusion probabilistic models (DDPMs) with the string method is presented to generate minimum free energy paths between metastable states in molecular systems. It has been demonstrated in recent work that DDPMs…

Chemical Physics · Physics 2024-12-17 Vladimir Grigorev

The minimum energy path (MEP) is the most probable transition path that connects two equilibrium states of a potential energy landscape. It has been widely used to study transition mechanisms as well as transition rates in the fields of…

Numerical Analysis · Mathematics 2022-07-01 Xuanyu Liu , Huajie Chen , Christoph Ortner

We show that neural networks can be optimized to represent minimum energy paths as continuous functions, offering a flexible alternative to discrete path-search methods such as Nudged Elastic Band (NEB). Our approach parameterizes reaction…

Machine Learning · Computer Science 2025-07-10 Kalyan Ramakrishnan , Lars L. Schaaf , Chen Lin , Guangrun Wang , Philip Torr

Transition states and minimum energy paths are essential to understand and predict chemical reactivity. Double-ended methods represent a standard approach for their determination. We introduce a new double-ended method that optimizes…

Chemical Physics · Physics 2020-02-18 Alain C. Vaucher , Markus Reiher

Understanding the geometry of learned distributions is fundamental to improving and interpreting diffusion models, yet systematic tools for exploring their landscape remain limited. Standard latent-space interpolations fail to respect the…

Machine Learning · Statistics 2026-02-26 Elio Moreau , Florentin Coeurdoux , Grégoire Ferre , Eric Vanden-Eijnden

Phase equilibrium calculation, also known as flash calculation, plays significant roles in various aspects of petroleum and chemical industries. Since Michelsen proposed his milestone studies in 1982, through several decades of development,…

Computational Physics · Physics 2020-08-11 Yuze Zhang , Yiteng Li , Lei Zhang , Shuyu Sun

An analysis of the network defined by the potential energy minima of multi-atomic systems and their connectivity via reaction pathways that go through transition states allows to understand important characteristics like thermodynamic,…

Materials Science · Physics 2016-08-03 Bastian Schaefer , Stefan Goedecker

Chemical Species Tomography (CST) has been widely used for in situ imaging of critical parameters, e.g. species concentration and temperature, in reactive flows. However, even with state-of-the-art computational algorithms the method is…

Image and Video Processing · Electrical Eng. & Systems 2021-04-06 Yunfan Jiang , Jingjing Si , Rui Zhang , Godwin Enemali , Bin Zhou , Hugh McCann , Chang Liu

Transition state (TS) searches are a critical bottleneck in computational studies of chemical reactivity, as accurately capturing complex phenomena like bond breaking and formation events requires repeated evaluations of expensive ab-initio…

Chemical Physics · Physics 2025-09-23 Jonah Marks , Joseph Gomes

Optimization of atomic structures presents a challenging problem, due to their highly rough and non-convex energy landscape, with wide applications in the fields of drug design, materials discovery, and mechanics. Here, we present a graph…

Machine Learning · Computer Science 2023-06-21 Vaibhav Bihani , Sahil Manchanda , Srikanth Sastry , Sayan Ranu , N. M. Anoop Krishnan

Stable states in complex systems correspond to local minima on the associated potential energy surface. Transitions between these local minima govern the dynamics of such systems. Precisely determining the transition pathways in complex and…

Machine Learning · Computer Science 2024-10-25 Adittya Pal

We introduce an extension to the Weighted Ensemble (WE) path sampling method to restrict sampling to a one dimensional path through a high dimensional phase space. Our method, which is based on the finite-temperature string method, permits…

Statistical Mechanics · Physics 2013-01-25 Joshua L. Adelman , Michael Grabe

Using a model heat engine, we show that neural network-based reinforcement learning can identify thermodynamic trajectories of maximal efficiency. We consider both gradient and gradient-free reinforcement learning. We use an evolutionary…

Neural and Evolutionary Computing · Computer Science 2021-12-21 Chris Beeler , Uladzimir Yahorau , Rory Coles , Kyle Mills , Stephen Whitelam , Isaac Tamblyn
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