A semigroup method for high dimensional committor functions based on neural network

Li, Haoya; Khoo, Yuehaw; Ren, Yinuo; Ying, Lexing

doi:10.48550/arxiv.2012.06727

Cited by 2 publications

References 13 publications

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Computing committors via Mahalanobis diffusion maps with enhanced sampling data

Evans

Cameron

Tiwary

2022

The Journal of Chemical Physics

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The study of phenomena, such as protein folding and conformational changes in molecules, is a central theme in chemical physics. Molecular dynamics (MD) simulation is the primary tool for the study of transition processes in biomolecules, but it is hampered by a huge timescale gap between the processes of interest and atomic vibrations that dictate the time step size. Therefore, it is imperative to combine MD simulations with other techniques in order to quantify the transition processes taking place on large timescales. In this work, the diffusion map with Mahalanobis kernel, a meshless approach for approximating the Backward Kolmogorov Operator (BKO) in collective variables, is upgraded to incorporate standard enhanced sampling techniques, such as metadynamics. The resulting algorithm, which we call the target measure Mahalanobis diffusion map (tm-mmap), is suitable for a moderate number of collective variables in which one can approximate the diffusion tensor and free energy. Imposing appropriate boundary conditions allows use of the approximated BKO to solve for the committor function and utilization of transition path theory to find the reactive current delineating the transition channels and the transition rate. The proposed algorithm, tm-mmap, is tested on the two-dimensional Moro–Cardin two-well system with position-dependent diffusion coefficient and on alanine dipeptide in two collective variables where the committor, the reactive current, and the transition rate are compared to those computed by the finite element method (FEM). Finally, tm-mmap is applied to alanine dipeptide in four collective variables where the use of finite elements is infeasible.

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Computing committors via Mahalanobis diffusion maps with enhanced sampling data

Evans

Cameron

Tiwary

2022

The Journal of Chemical Physics

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Committor functions via tensor networks

Chen¹,

Hoskins²,

Khoo³

et al. 2021

Preprint

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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 settings of interest, it is intractable to compute and store the solution with traditional numerical methods. By parametrizing the committor function in a matrix product state/tensor train format and using a similar representation for the equilibrium probability density, we solve the variational formulation of the backward Kolmogorov equation with linear time and memory complexity in the number of dimensions. This approach bypasses the need for sampling the equilibrium distribution, which can be difficult when the distribution has multiple modes. Numerical results demonstrate the effectiveness of the proposed method for high-dimensional problems.

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A semigroup method for high dimensional committor functions based on neural network

Cited by 2 publications

References 13 publications

Computing committors via Mahalanobis diffusion maps with enhanced sampling data

Computing committors via Mahalanobis diffusion maps with enhanced sampling data

Committor functions via tensor networks

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