Rigid Body Flows for Sampling Molecular Crystal Structures

Jonas Köhler, Michele Invernizzi, Pim De Haan, Frank Noe
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:17301-17326, 2023.

Abstract

Normalizing flows (NF) are a class of powerful generative models that have gained popularity in recent years due to their ability to model complex distributions with high flexibility and expressiveness. In this work, we introduce a new type of normalizing flow that is tailored for modeling positions and orientations of multiple objects in three-dimensional space, such as molecules in a crystal. Our approach is based on two key ideas: first, we define smooth and expressive flows on the group of unit quaternions, which allows us to capture the continuous rotational motion of rigid bodies; second, we use the double cover property of unit quaternions to define a proper density on the rotation group. This ensures that our model can be trained using standard likelihood-based methods or variational inference with respect to a thermodynamic target density. We evaluate the method by training Boltzmann generators for two molecular examples, namely the multi-modal density of a tetrahedral system in an external field and the ice XI phase in the TIP4P water model. Our flows can be combined with flows operating on the internal degrees of freedom of molecules and constitute an important step towards the modeling of distributions of many interacting molecules.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-kohler23a, title = {Rigid Body Flows for Sampling Molecular Crystal Structures}, author = {K\"{o}hler, Jonas and Invernizzi, Michele and De Haan, Pim and Noe, Frank}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {17301--17326}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/kohler23a/kohler23a.pdf}, url = {https://proceedings.mlr.press/v202/kohler23a.html}, abstract = {Normalizing flows (NF) are a class of powerful generative models that have gained popularity in recent years due to their ability to model complex distributions with high flexibility and expressiveness. In this work, we introduce a new type of normalizing flow that is tailored for modeling positions and orientations of multiple objects in three-dimensional space, such as molecules in a crystal. Our approach is based on two key ideas: first, we define smooth and expressive flows on the group of unit quaternions, which allows us to capture the continuous rotational motion of rigid bodies; second, we use the double cover property of unit quaternions to define a proper density on the rotation group. This ensures that our model can be trained using standard likelihood-based methods or variational inference with respect to a thermodynamic target density. We evaluate the method by training Boltzmann generators for two molecular examples, namely the multi-modal density of a tetrahedral system in an external field and the ice XI phase in the TIP4P water model. Our flows can be combined with flows operating on the internal degrees of freedom of molecules and constitute an important step towards the modeling of distributions of many interacting molecules.} }
Endnote
%0 Conference Paper %T Rigid Body Flows for Sampling Molecular Crystal Structures %A Jonas Köhler %A Michele Invernizzi %A Pim De Haan %A Frank Noe %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-kohler23a %I PMLR %P 17301--17326 %U https://proceedings.mlr.press/v202/kohler23a.html %V 202 %X Normalizing flows (NF) are a class of powerful generative models that have gained popularity in recent years due to their ability to model complex distributions with high flexibility and expressiveness. In this work, we introduce a new type of normalizing flow that is tailored for modeling positions and orientations of multiple objects in three-dimensional space, such as molecules in a crystal. Our approach is based on two key ideas: first, we define smooth and expressive flows on the group of unit quaternions, which allows us to capture the continuous rotational motion of rigid bodies; second, we use the double cover property of unit quaternions to define a proper density on the rotation group. This ensures that our model can be trained using standard likelihood-based methods or variational inference with respect to a thermodynamic target density. We evaluate the method by training Boltzmann generators for two molecular examples, namely the multi-modal density of a tetrahedral system in an external field and the ice XI phase in the TIP4P water model. Our flows can be combined with flows operating on the internal degrees of freedom of molecules and constitute an important step towards the modeling of distributions of many interacting molecules.
APA
Köhler, J., Invernizzi, M., De Haan, P. & Noe, F.. (2023). Rigid Body Flows for Sampling Molecular Crystal Structures. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:17301-17326 Available from https://proceedings.mlr.press/v202/kohler23a.html.

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