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Equivariant vector field network for many-body system modeling [article]

Weitao Du, He Zhang, Yuanqi Du, Qi Meng, Wei Chen, Bin Shao, Tie-Yan Liu
<span title="2021-10-26">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this paper, we leverage insights from the scalarization technique in differential geometry to model many-body systems by learning the gradient vector fields, which are SE(3) and permutation equivariant  ...  Equivariance is a critical physical symmetry for many-body dynamic systems, which enables robust and accurate prediction under arbitrary reference transformations.  ...  To mitigate this issue, we propose a new model called Equivariant Vector Field Network (EVFN) to fit the gradient vector fields (Song & Ermon, 2019; Shi et al., 2021) of many-body systems.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2110.14811v1">arXiv:2110.14811v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jns74rrddndohdg3v7o5r24ia4">fatcat:jns74rrddndohdg3v7o5r24ia4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20211101140600/https://arxiv.org/pdf/2110.14811v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/8e/3c/8e3ca5951f705406d5a89bf4cbd4d4c436cdd8f0.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2110.14811v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Equivariant Point Cloud Analysis via Learning Orientations for Message Passing [article]

Shitong Luo, Jiahan Li, Jiaqi Guan, Yufeng Su, Chaoran Cheng, Jian Peng, Jianzhu Ma
<span title="2022-03-28">2022</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Equivariance has been a long-standing concern in various fields ranging from computer vision to physical modeling.  ...  In this work, we propose a novel and simple framework to achieve equivariance for point cloud analysis based on the message passing (graph neural network) scheme.  ...  N-Body System Modeling Modeling a dynamic particle system is a fundamental yet challenging task in many other research areas.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2203.14486v1">arXiv:2203.14486v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/i64audysvvchfkkjjdjdmjum7e">fatcat:i64audysvvchfkkjjdjdmjum7e</a> </span>
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Geometrically Equivariant Graph Neural Networks: A Survey [article]

Jiaqi Han, Yu Rong, Tingyang Xu, Wenbing Huang
<span title="2022-02-22">2022</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Researchers have leveraged such inductive bias and developed geometrically equivariant Graph Neural Networks (GNNs) to better characterize the geometry and topology of geometric graphs.  ...  The prospect for future potential directions is also provided.  ...  Acknowledgments This work was jointly supported by the following projects: the Scientific Innovation 2030 Major Project for New Generation of AI under Grant NO. 2020AAA0107300, Ministry of Science and  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2202.07230v3">arXiv:2202.07230v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qb3kjk3ysvcapbas7kccm7u4qu">fatcat:qb3kjk3ysvcapbas7kccm7u4qu</a> </span>
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Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densities [article]

Jonas Köhler, Leon Klein, Frank Noé
<span title="2020-10-26">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Furthermore, we propose building blocks for flows which preserve symmetries which are usually found in physical/chemical many-body particle systems.  ...  Recent work showed that such generative models can be utilized in statistical mechanics to sample equilibrium states of many-body systems in physics and chemistry.  ...  We further thank Moritz Hoffmann (FU Berlin), Pim de Haan (UvA Amsterdam / Qualcomm) and Onur Caylak (TU Eindhoven) for helpful remarks and discussions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2006.02425v2">arXiv:2006.02425v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/swcl2juh2vaj5opcahwxnkuxeq">fatcat:swcl2juh2vaj5opcahwxnkuxeq</a> </span>
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A Data and Compute Efficient Design for Limited-Resources Deep Learning [article]

Mirgahney Mohamed, Gabriele Cesa, Taco S. Cohen, Max Welling
<span title="2020-07-08">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
To be able to reach a much larger body of patients, mobile, on-device implementations of deep learning solutions have been developed for medical applications.  ...  Thanks to their improved data efficiency, equivariant neural networks have gained increased interest in the deep learning community.  ...  ACKNOWLEDGMENTS We would like to thank Markus Nagel and Andrii Skliar for helping with quantization.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2004.09691v2">arXiv:2004.09691v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vxshbh2g25hupjbl4qgp6nvdkm">fatcat:vxshbh2g25hupjbl4qgp6nvdkm</a> </span>
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3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data [article]

Maurice Weiler, Mario Geiger, Max Welling, Wouter Boomsma, Taco Cohen
<span title="2018-10-27">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We present a convolutional network that is equivariant to rigid body motions.  ...  The model uses scalar-, vector-, and tensor fields over 3D Euclidean space to represent data, and equivariant convolutions to map between such representations.  ...  most closely related works achieving full SE(3) equivariance are the Tensor Field Network (TFN) [41] and the N-Body networks (NBNs) [27] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1807.02547v2">arXiv:1807.02547v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6spgxt5sjveadif5sw4oxlj4iu">fatcat:6spgxt5sjveadif5sw4oxlj4iu</a> </span>
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Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data [article]

Marc Finzi, Samuel Stanton, Pavel Izmailov, Andrew Gordon Wilson
<span title="2020-09-24">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
For Hamiltonian systems, the equivariance of our models is especially impactful, leading to exact conservation of linear and angular momentum.  ...  The translation equivariance of convolutional layers enables convolutional neural networks to generalize well on image problems.  ...  for modeling dynamical systems.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2002.12880v3">arXiv:2002.12880v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hjtrai2btreu7inxyiixbrrj74">fatcat:hjtrai2btreu7inxyiixbrrj74</a> </span>
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Equivariant Flows: sampling configurations for multi-body systems with symmetric energies [article]

Jonas Köhler, Leon Klein, Frank Noé
<span title="2019-10-02">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Boltzmann Generators (BG) combine flows and statistical mechanics to sample equilibrium states of strongly interacting many-body systems such as proteins with 1000 atoms.  ...  Here we develop theoretical tools for constructing such equivariant flows and demonstrate that a BG that is equivariant with respect to rotations and particle permutations can generalize to sampling nontrivially  ...  It is simple to see that this vector field is equivariant with respect to symmetries 1.-3..  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1910.00753v1">arXiv:1910.00753v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4tylnzbyl5dhbeshha5mxr7ade">fatcat:4tylnzbyl5dhbeshha5mxr7ade</a> </span>
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E(n) Equivariant Graph Neural Networks [article]

Victor Garcia Satorras, Emiel Hoogeboom, Max Welling
<span title="2022-02-16">2022</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
This paper introduces a new model to learn graph neural networks equivariant to rotations, translations, reflections and permutations called E(n)-Equivariant Graph Neural Networks (EGNNs).  ...  We demonstrate the effectiveness of our method on dynamical systems modelling, representation learning in graph autoencoders and predicting molecular properties.  ...  Acknowledgements We would like to thank Patrick Forré for his support to formalize the invariance features identification proof.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2102.09844v3">arXiv:2102.09844v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/fmes7k4fdrhjlfci7bcnq2pjha">fatcat:fmes7k4fdrhjlfci7bcnq2pjha</a> </span>
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SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks [article]

Fabian B. Fuchs, Daniel E. Worrall, Volker Fischer, Max Welling
<span title="2020-11-24">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In all cases, our model outperforms a strong, non-equivariant attention baseline and an equivariant model without attention.  ...  We evaluate our model on a toy N-body particle simulation dataset, showcasing the robustness of the predictions under rotations of the input.  ...  Acknowledgements We would like to express our gratitude to the Bosch Center for Artificial Intelligence and Konincklijke Philips N.V. for their support and contribution to open research in publishing our  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2006.10503v3">arXiv:2006.10503v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2xpxlc5shrhi3mlqll5ldafkry">fatcat:2xpxlc5shrhi3mlqll5ldafkry</a> </span>
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Ab-initio study of interacting fermions at finite temperature with neural canonical transformation [article]

Hao Xie, Linfeng Zhang, Lei Wang
<span title="2021-05-18">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The variational density matrix is parametrized by a permutation equivariant many-body unitary transformation together with a discrete probabilistic model.  ...  The approach is general and flexible for further extensions, thus holds the promise to deliver new physical results on strongly correlated fermions in the context of ultracold quantum gases, condensed  ...  ACKNOWLEDGMENTS We thank Yuan Wan, Zi-Long Li, Hao Wu, Zi Cai, Jun Wang, Xiang Chen, and Vincent Moens for useful discussions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2105.08644v1">arXiv:2105.08644v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bjyliulyovaijiiqfsxm34fqve">fatcat:bjyliulyovaijiiqfsxm34fqve</a> </span>
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NewtonNet: A Newtonian message passing network for deep learning of interatomic potentials and forces [article]

Mojtaba Haghighatlari, Jie Li, Xingyi Guan, Oufan Zhang, Akshaya Das, Christopher J. Stein, Farnaz Heidar-Zadeh, Meili Liu, Martin Head-Gordon, Luke Bertels, Hongxia Hao, Itai Leven (+1 others)
<span title="2021-08-06">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
, and many-body interactions are inferred by more interpretable physical features.  ...  With the advantage of directional information from trainable latent force vectors, and physics-infused operators that are inspired by the Newtonian physics, the entire model remains rotationally equivariant  ...  Consequently, we avoid any many-to-one mapping of rotationally equivariant features to invariant energies.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2108.02913v1">arXiv:2108.02913v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/f7ytkudfvvaibotaqljioezp7u">fatcat:f7ytkudfvvaibotaqljioezp7u</a> </span>
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Learning Dipole Moments and Polarizabilities [article]

Yaolong Zhang, Jun Jiang, Bin Jiang
<span title="2021-11-09">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this chapter, we review machine learning models for these tensorial properties, with special focus on how to encode the rotational equivariance into these models by taking a similar form as the physical  ...  You will then learn how to use an embedded atom neural network model to train dipole moments and polarizabilities of a representative molecule.  ...  neural network (EANN) model [45, 63] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2111.04306v2">arXiv:2111.04306v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hs2zmk2tu5gbjglakz3clsdpfa">fatcat:hs2zmk2tu5gbjglakz3clsdpfa</a> </span>
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Equivariant Graph Hierarchy-Based Neural Networks [article]

Jiaqi Han, Yu Rong, Tingyang Xu, Fuchun Sun, Wenbing Huang
<span title="2022-02-22">2022</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Equivariant Graph neural Networks (EGNs) are powerful in characterizing the dynamics of multi-body physical systems.  ...  Existing EGNs conduct flat message passing, which, yet, is unable to capture the spatial/dynamical hierarchy for complex systems particularly, limiting substructure discovery and global information fusion  ...  Conclusion In this paper, we have proposed a novel framework dubbed Equivariant Graph Hierarchy-based Network (EGHN) to model and represent the dynamics of multi-body systems.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2202.10643v1">arXiv:2202.10643v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3vjknvxftvbxdeqmn3ysq6z3sy">fatcat:3vjknvxftvbxdeqmn3ysq6z3sy</a> </span>
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Physics-Guided Deep Learning for Dynamical Systems: A Survey [article]

Rui Wang, Rose Yu
<span title="2022-03-03">2022</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
systems, nor do they generalize well across different systems.  ...  In this paper, we provide a structured overview of existing methodologies of integrating prior physical knowledge or physics-based modeling into DL, with a special emphasis on learning dynamical systems  ...  , a rotationally covariant neural network architecture for learning the behavior and properties of complex many-body physical systems.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2107.01272v5">arXiv:2107.01272v5</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/k6hhdt6csnfebgkzrpuoeqkwzi">fatcat:k6hhdt6csnfebgkzrpuoeqkwzi</a> </span>
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