arXiv subjects

Sergei V. Krivov

Publications and source records attributed to Sergei V. Krivov.

7 recordsLinked to original sources

arXiv2026

Nonparametric Reaction Coordinate Optimization with Histories: A Framework for Rare Event Dynamics

Rare but critical events in complex systems, such as protein folding, chemical reactions, disease progression, and extreme weather or climate phenomena, are governed by complex, high-dimensional, stochastic dynamics. Identifying an optimal reaction coordinate (RC) that accurately captures the progress of these dynamics is crucial for understanding and simulating such processes. However, determining an optimal RC for realistic systems is notoriously difficult, due to methodological challenges that limit the success of standard machine learning techniques. These challenges include the absence of ground truth, the lack of a loss function for general nonequilibrium dynamics, the difficulty of selecting expressive neural network architectures that avoid overfitting, the irregular and incomplete nature of many real world trajectories, limited sampling and the extreme data imbalance inherent in rare event problems. Here, we introduce a nonparametric RC optimization framework that incorporates trajectory histories and circumvents these challenges, enabling robust analysis of irregular or incomplete data without requiring extensive sampling. The power of the method is demonstrated through increasingly challenging analyses of protein folding dynamics, where it yields accurate committor estimates that pass stringent validation tests and produce high resolution free energy profiles. Its generality is further illustrated through applications to phase space dynamics, a conceptual ocean circulation model, and a longitudinal clinical dataset. These results demonstrate that rare event dynamics can be accurately characterized without extensive sampling of the configuration space, establishing a general, flexible, and robust framework for analyzing complex dynamical systems and longitudinal datasets.

physics.chem-ph↗

arXiv2023

Nonequilibrium Optimal Reaction Coordinates for Diffusion

Complex multidimensional stochastic dynamics can be approximately described as diffusion along reaction coordinates (RCs). If the RCs are optimally selected, the diffusive model allows one to compute important properties of the dynamics exactly. The committor is a primary example of an optimal RC. Recently, additive eigenvectors (addevs) have been introduced in order to extend the formalism to non-equilibrium dynamics. An addev describes a sub-ensemble of trajectories of a stochastic process together with an optimal RC. The sub-ensemble is conditioned to have a single RC optimal for both the forward and time-reversed non-equilibrium dynamics of the sub-ensemble. Here we consider stationary addevs and obtain the following results. We show that the forward and time-reversed committors are functions of the addev, meaning a diffusive model along an addev RC can be used to compute important properties of non-equilibrium dynamics exactly. The rates of the conditioned stochastic process, describing an addev sub-ensemble, can be computed ``on the fly'', thus allowing efficient sampling schemes. We obtain two families of addev solutions for diffusion. The first is described by equations of classical mechanics, while the second can be approximated by quantum mechanical equations. We show how the potential can be introduced into the formalism self-consistently. The developments are illustrated on simple examples. The two addev families provide stochastic models together with optimal RCs and new sampling schemes for classical and quantum mechanical systems. It suggests that the conditioned stochastic processes defined by addevs are suitable for description of dynamics of physical origin.

physics.chem-ph↗

arXiv2021

Non-Parametric Analysis of Non-Equilibrium Simulations

We extend the non-parametric framework of reaction coordinate optimization to non-equilibrium ensembles of (short) trajectories. For example, we show how, starting from such an ensemble, one can obtain an equilibrium free energy profile along the committor, which can be used to determine important properties of the dynamics exactly. New adaptive sampling approach, the transition state ensemble enrichment, is suggested, which samples the configuration space by "growing" committor segments towards each other starting from the boundary states. This framework is suggested as a general tool, alternative to the Markov state models, for a rigorous and accurate analysis of simulations of large biomolecular systems, as it has the following attractive properties. It is immune to the curse of dimensionality, it does not require system specific information, it can approximate arbitrary reaction coordinates with high accuracy and it has sensitive and rigorous criteria to test optimality and convergence. The approaches are illustrated on a 50-dimensional model system and a realistic protein folding trajectory.

physics.chem-ph↗

arXiv2018

Towards a Theory of Additive Eigenvectors

The standard approach in solving stochastic equations is eigenvector decomposition. Using separation ansatz $P(i,t)=u(i)e^{μt}$ one obtains standard equation for eigenvectors $Ku=μu$, where $K$ is the rate matrix of the master equation. While universally accepted, the standard approach is not the only possibility. Using additive separation ansatz $S(i,t)=W(i)-νt$ one arrives at additive eigenvectors. Here we suggest a theory of such eigenvectors. We argue that additive eigenvectors describe conditioned Markov processes and derive corresponding equations. The formalism is applied to one-dimensional stochastic process corresponding to the telegraph equation. We derive differential equations for additive eigenvectors and explore their properties. The proposed theory of additive eigenvectors provides a new description of stochastic processes with peculiar properties.

cond-mat.stat-mech↗

arXiv2013

Optimal Coordinate as a General Method in Stochastic Dynamics

A general method to describe stochastic dynamics of Markov processes is suggested. The method aims to solve three related problems. The determination of an optimal coordinate for the description of stochastic dynamics. The reconstruction of time from an ensemble of stochastic trajectories. The decomposition of stationary stochastic dynamics on eigen-modes which do not decay exponentially with time. The problems are solved by introducing additive eigenvectors which are transformed by a stochastic matrix in a simple way - every component is translated on a constant distance. Such solutions have peculiar properties. For example, an optimal coordinate for stochastic dynamics with detailed balance is a multi-valued function. An optimal coordinate for a random walk on the line corresponds to the conventional eigenvector of the one dimensional Dirac equation. The equation for the optimal coordinate in a slow varying potential reduces to the Hamilton-Jacobi equation for the action function.

physics.chem-ph↗

arXiv2011

Optimal Dimensionality Reduction of Complex Dynamics: The Chess Game as Diffusion on a Free Energy Landscape

Dimensionality reduction is ubiquitous in analysis of complex dynamics. The conventional dimensionality reduction techniques, however, focus on reproducing the underlying configuration space, rather than the dynamics itself. The constructed low-dimensional space does not provide complete and accurate description of the dynamics. Here I describe how to perform dimensionality reduction while preserving the essential properties of the dynamics. The approach is illustrated by analyzing the chess game - the archetype of complex dynamics. A variable that provides complete and accurate description of chess dynamics is constructed. Winning probability is predicted by describing the game as a random walk on the free energy landscape associated with the variable. The approach suggests a possible way of obtaining a simple yet accurate description of many important complex phenomena. The analysis of the chess game shows that the approach can quantitatively describe the dynamics of processes where human decision-making plays a central role, e.g., financial and social dynamics.

physics.data-an↗

arXiv2007

Importance of Metastable States in the Free Energy Landscapes of Polypeptide Chains

We show that the interplay between excluded volume effects, hydrophobicity, and hydrogen bonding of a tube-like representation of a polypeptide chain gives rise to free energy landscapes that exhibit a small number of metastable minima corresponding to common structural motifs observed in proteins. The complexity of the landscape increases only moderately with the length of the chain. Analysis of the temperature dependence of these landscapes reveals that the stability of specific metastable states is maximal at a temperature close to the mid-point of folding. These mestastable states are therefore likely to be of particular significance in determining the generic tendency of proteins to aggregate into potentially pathogenic agents.

cond-mat.soft↗