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Transformers have exhibited exceptional capabilities in sequence modeling tasks, leveraging self-attention and in-context learning. Critical to this success are induction heads, attention circuits that enable copying tokens based on their…

Machine Learning · Computer Science 2025-09-11 Francesco D'Angelo , Francesco Croce , Nicolas Flammarion

Transformer based language models exhibit intelligent behaviors such as understanding natural language, recognizing patterns, acquiring knowledge, reasoning, planning, reflecting and using tools. This paper explores how their underlying…

Machine Learning · Computer Science 2023-11-15 Sumeet S. Singh

Transition path sampling is a method for estimating the rates of rare events in molecular systems based on the gradual transformation of a path distribution containing a small fraction of reactive trajectories into a biased distribution in…

Statistical Mechanics · Physics 2015-10-28 Pierre Terrier , Mihai-Cosmin Marinica , Manuel Athènes

The thermal cis-trans isomerization around the C$_{13}$=C$_{14}$ double bond of retinal is a prototypical high-barrier reaction whose mechanism hinges on subtle out-of-plane bending motions. We apply Artificial Intelligence for Molecular…

Path sampling approaches have become invaluable tools to explore the mechanisms and dynamics of so-called rare events that are characterized by transitions between metastable states separated by sizeable free energy barriers. Their…

Statistical Mechanics · Physics 2022-06-08 Steven W. Hall , Grisell Díaz Leines , Sapna Sarupria , Jutta Rogal

In addition to translational and rotational symmetries, clusters of identical interacting particles possess permutational symmetry. Coarse-grained models for such systems are instrumental in identifying metastable states, providing an…

Chemical Physics · Physics 2025-07-02 Jiaxin Yuan , Shashank Sule , Yeuk Yin Lam , Maria Cameron

Disentangling the mechanistic details of a chemical reaction pathway is a hard problem that often requires a considerable amount of chemical intuition and a component of luck. Experiments struggle in observing short-life metastable…

Chemical Physics · Physics 2019-08-01 Valerio Rizzi , Dan Mendels , Emilia Sicilia , Michele Parrinello

Transition path theory computes statistics from ensembles of reactive trajectories. A common strategy for sampling reactive trajectories is to control the branching and pruning of trajectories so as to enhance the sampling of low…

Statistical Mechanics · Physics 2022-08-10 Bodhi P. Vani , Jonathan Weare , Aaron R. Dinner

Mean-field molecular dynamics based on path integrals is used to approximate canonical quantum observables for particle systems consisting of nuclei and electrons. A computational bottleneck is the sampling from the Gibbs density of the…

Numerical Analysis · Mathematics 2023-11-30 Xin Huang , Petr Plechac , Mattias Sandberg , Anders Szepessy

Stochastic systems often exhibit multiple viable metastable states that are long-lived. Over very long timescales, fluctuations may push the system to transition between them, drastically changing its macroscopic configuration. In realistic…

Statistical Mechanics · Physics 2023-04-14 Tobias Grafke , Alessandro Laio

Using random walk sampling methods for feature learning on networks, we develop a method for generating low-dimensional node embeddings for directed graphs and identifying transition states of stochastic chemical reacting systems. We…

Numerical Analysis · Mathematics 2020-10-30 Paula Mercurio , Di Liu

Reaction paths and probabilities are inferred, in a usual Monte Carlo or Molecular Dynamic simulation, directly from the evolution of the positions of the particles. The process becomes time-consuming in many interesting cases in which the…

Statistical Mechanics · Physics 2011-10-11 Massimiliano Picciani , Manuel Athenes , Jorge Kurchan , Julien Tailleur

The identification of environmental changes is crucial in many fields. The present research is aimed at investigating the optimal performance for detecting change points in a quantum system when its Hamiltonian suddenly changes at a…

Quantum Physics · Physics 2024-04-18 Kenji Nakahira

While Kramers' rates have been studied for almost a century, the transition path time between states has only recently received attention. Transition paths between different energy levels are expected to be indistinguishable in shape and…

Statistical Mechanics · Physics 2020-06-02 Jannes Gladrow , Marco Ribezzi-Crivellari , Felix Ritort , Ulrich F. Keyser

Despite the remarkable empirical performance of Transformers, their theoretical understanding remains elusive. Here, we consider a deep multi-head self-attention network, that is closely related to Transformers yet analytically tractable.…

Machine Learning · Computer Science 2024-12-10 Lorenzo Tiberi , Francesca Mignacco , Kazuki Irie , Haim Sompolinsky

We propose a novel approach for computing committor functions, which describe transitions of a stochastic process between metastable states. The committor function satisfies a backward Kolmogorov equation, and in typical high-dimensional…

Numerical Analysis · Mathematics 2021-08-04 Yian Chen , Jeremy Hoskins , Yuehaw Khoo , Michael Lindsey

We consider the problem of sampling transition paths between two given metastable states of a molecular system, e.g. a folded and unfolded protein or products and reactants of a chemical reaction. Due to the existence of high energy…

Biomolecules · Quantitative Biology 2023-07-19 Lars Holdijk , Yuanqi Du , Ferry Hooft , Priyank Jaini , Bernd Ensing , Max Welling

Rare events in molecular dynamics are often related to noise-induced transitions between different macroscopic states (e.g., in protein folding). A common feature of these rare transitions is that they happen on timescales that are on…

Probability · Mathematics 2026-01-06 Carsten Hartmann , Annika Jöster , Christof Schütte , Alexander Sikorski , Marcus Weber

Spontaneous structural rearrangements play a central role in the organization and function of complex biomolecular systems. In principle, physics-based computer simulations like Molecular Dynamics (MD) enable us to investigate these…

Quantum Physics · Physics 2026-03-19 Danial Ghamari , Philipp Hauke , Roberto Covino , Pietro Faccioli

The essence of a chemical reaction lies in the redistribution and reorganization of electrons, which is often manifested through electron transfer or the migration of electron pairs. These changes are inherently discrete and abrupt in the…

Machine Learning · Computer Science 2025-07-14 Haitao Lin , Junjie Wang , Zhifeng Gao , Xiaohong Ji , Rong Zhu , Linfeng Zhang , Guolin Ke , Weinan E