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A DEEP LEARNING METHOD FOR COMPUTING COMMITTOR FUNCTIONS WITH ADAPTIVE SAMPLING.

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Titel: A DEEP LEARNING METHOD FOR COMPUTING COMMITTOR FUNCTIONS WITH ADAPTIVE SAMPLING.
Autoren: LIN, BO1 matrw@nus.edu.sg, REN, WEIQING1
Quelle: SIAM Journal on Scientific Computing. 2025, Vol. 47 Issue 5, pC1091-C1114. 24p.
Schlagwörter: *DEEP learning, *ADAPTIVE sampling (Statistics), *DYNAMICAL systems, *ASYMPTOTIC distribution, *METASTABLE states
Abstract: The committor function is a central object for quantifying transitions between metastable states in randomly perturbed dynamical systems. Recently, effective methods based on deep learning have been proposed to compute the committor function in high-dimensional systems. However, sampling training data in these methods remains a challenging task, particularly for systems with small noise. In this work, we propose a deep learning method in which the data are sampled from the equilibrium distribution of a modified potential. We introduce two such modified potentials: the first (scheme I) incorporates a bias formed by localized Gaussian functions along a one-dimensional variable constructed from the learned committor function; the second (scheme II) uses a bias involving the free energy associated with the learned committor function. We analyze the distribution of the sampled data and show that, in both schemes, the data are well spread out and effectively cover the transition tube. Both schemes enable adaptive learning of the committor function without requiring prior knowledge of the transition pathways. The efficiency of the method is demonstrated using high-dimensional examples, including the alanine dipeptide and a solvated dimer system. [ABSTRACT FROM AUTHOR]
Datenbank: Academic Search Index
Beschreibung
Abstract:The committor function is a central object for quantifying transitions between metastable states in randomly perturbed dynamical systems. Recently, effective methods based on deep learning have been proposed to compute the committor function in high-dimensional systems. However, sampling training data in these methods remains a challenging task, particularly for systems with small noise. In this work, we propose a deep learning method in which the data are sampled from the equilibrium distribution of a modified potential. We introduce two such modified potentials: the first (scheme I) incorporates a bias formed by localized Gaussian functions along a one-dimensional variable constructed from the learned committor function; the second (scheme II) uses a bias involving the free energy associated with the learned committor function. We analyze the distribution of the sampled data and show that, in both schemes, the data are well spread out and effectively cover the transition tube. Both schemes enable adaptive learning of the committor function without requiring prior knowledge of the transition pathways. The efficiency of the method is demonstrated using high-dimensional examples, including the alanine dipeptide and a solvated dimer system. [ABSTRACT FROM AUTHOR]
ISSN:10648275
DOI:10.1137/24M1654750