PathFlow: A normalizing flow generator that finds transition paths

Tianyi Liu, Weihao Gao, Zhirui Wang, Chong Wang
Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence, PMLR 180:1232-1242, 2022.

Abstract

Sampling from a Boltzmann distribution to calculate important macro statistics is one of the central tasks in the study of large atomic and molecular systems. Recently, a one-shot configuration sampler, the Boltzmann generator [Noé et al., 2019], is introduced. Though a Boltzmann generator can directly generate independent metastable states, it lacks the ability to find transition pathways and describe the whole transition process. In this paper, we propose PathFlow that can function as a one-shot generator as well as a transition pathfinder. More specifically, a normalizing flow model is constructed to map the base distribution and linear interpolated path in the latent space to the Boltzmann distribution and a minimum (free) energy path in the configuration space simultaneously. PathFlow can be trained by standard gradient-based optimizers using the proposed gradient estimator with a theoretical guarantee. PathFlow, validated with the extensively studied examples including a synthetic Müller potential and Alanine dipeptide, shows a remarkable performance.

Cite this Paper

BibTeX
@InProceedings{pmlr-v180-liu22b, title = {PathFlow: A normalizing flow generator that finds transition paths}, author = {Liu, Tianyi and Gao, Weihao and Wang, Zhirui and Wang, Chong}, booktitle = {Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence}, pages = {1232--1242}, year = {2022}, editor = {Cussens, James and Zhang, Kun}, volume = {180}, series = {Proceedings of Machine Learning Research}, month = {01--05 Aug}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v180/liu22b/liu22b.pdf}, url = {https://proceedings.mlr.press/v180/liu22b.html}, abstract = {Sampling from a Boltzmann distribution to calculate important macro statistics is one of the central tasks in the study of large atomic and molecular systems. Recently, a one-shot configuration sampler, the Boltzmann generator [Noé et al., 2019], is introduced. Though a Boltzmann generator can directly generate independent metastable states, it lacks the ability to find transition pathways and describe the whole transition process. In this paper, we propose PathFlow that can function as a one-shot generator as well as a transition pathfinder. More specifically, a normalizing flow model is constructed to map the base distribution and linear interpolated path in the latent space to the Boltzmann distribution and a minimum (free) energy path in the configuration space simultaneously. PathFlow can be trained by standard gradient-based optimizers using the proposed gradient estimator with a theoretical guarantee. PathFlow, validated with the extensively studied examples including a synthetic Müller potential and Alanine dipeptide, shows a remarkable performance. } }
Endnote
%0 Conference Paper %T PathFlow: A normalizing flow generator that finds transition paths %A Tianyi Liu %A Weihao Gao %A Zhirui Wang %A Chong Wang %B Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2022 %E James Cussens %E Kun Zhang %F pmlr-v180-liu22b %I PMLR %P 1232--1242 %U https://proceedings.mlr.press/v180/liu22b.html %V 180 %X Sampling from a Boltzmann distribution to calculate important macro statistics is one of the central tasks in the study of large atomic and molecular systems. Recently, a one-shot configuration sampler, the Boltzmann generator [Noé et al., 2019], is introduced. Though a Boltzmann generator can directly generate independent metastable states, it lacks the ability to find transition pathways and describe the whole transition process. In this paper, we propose PathFlow that can function as a one-shot generator as well as a transition pathfinder. More specifically, a normalizing flow model is constructed to map the base distribution and linear interpolated path in the latent space to the Boltzmann distribution and a minimum (free) energy path in the configuration space simultaneously. PathFlow can be trained by standard gradient-based optimizers using the proposed gradient estimator with a theoretical guarantee. PathFlow, validated with the extensively studied examples including a synthetic Müller potential and Alanine dipeptide, shows a remarkable performance.
APA
Liu, T., Gao, W., Wang, Z. & Wang, C.. (2022). PathFlow: A normalizing flow generator that finds transition paths. Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 180:1232-1242 Available from https://proceedings.mlr.press/v180/liu22b.html.

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