Zequn Lin | Searcharxiv

arXiv2026

Dynamical Partition Functions of Stochastic Dynamics via Variational Flows

Nonequilibrium thermodynamics is governed by the dynamical partition function, and its computation in high-dimensional continuous-state dynamics is a longstanding challenge. The Feynman-Kac formalism provides a rigorous representation for generating functions of arbitrary path observables; however, practical evaluation beyond low dimensions or the weak-noise limit is hindered by the curse of dimensionality and the exponentially growing replica demands of trajectory-based methods. Here we develop a mesh-free neural variational framework that realizes the Feynman-Kac theorem with generative flow models, recasting tilted stochastic evolution as a time-dependent optimization problem. This approach enables the direct computation of both finite-time and asymptotic trajectory thermodynamics in a unified manner. The method applies to general observables, enabling the evaluation of work, entropy production, and current fluctuations. We demonstrate the accuracy and scalability of this method in various nonequilibrium systems including high-dimensional cases.

cond-mat.stat-mech↗

arXiv2023

Learning noise-induced transitions by multi-scaling reservoir computing

Noise is usually regarded as adversarial to extract the effective dynamics from time series, such that the conventional data-driven approaches usually aim at learning the dynamics by mitigating the noisy effect. However, noise can have a functional role of driving transitions between stable states underlying many natural and engineered stochastic dynamics. To capture such stochastic transitions from data, we find that leveraging a machine learning model, reservoir computing as a type of recurrent neural network, can learn noise-induced transitions. We develop a concise training protocol for tuning hyperparameters, with a focus on a pivotal hyperparameter controlling the time scale of the reservoir dynamics. The trained model generates accurate statistics of transition time and the number of transitions. The approach is applicable to a wide class of systems, including a bistable system under a double-well potential, with either white noise or colored noise. It is also aware of the asymmetry of the double-well potential, the rotational dynamics caused by non-detailed balance, and transitions in multi-stable systems. For the experimental data of protein folding, it learns the transition time between folded states, providing a possibility of predicting transition statistics from a small dataset. The results demonstrate the capability of machine-learning methods in capturing noise-induced phenomena.

nlin.AO↗