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E(n) Equivariant Normalizing Flows [article]

Victor Garcia Satorras, Emiel Hoogeboom, Fabian B. Fuchs, Ingmar Posner, Max Welling
2022 arXiv   pre-print
This paper introduces a generative model equivariant to Euclidean symmetries: E(n) Equivariant Normalizing Flows (E-NFs).  ...  To the best of our knowledge, this is the first flow that jointly generates molecule features and positions in 3D.  ...  In this paper, we introduce E(n) Equivariant Normalizing Flows (E-NFs): A generative model for E(n) Equivariant data such as molecules in 3D.  ... 
arXiv:2105.09016v4 fatcat:55ud5nnie5ed7og3iy5rgtihcm

E(n) Equivariant Graph Neural Networks [article]

Victor Garcia Satorras, Emiel Hoogeboom, Max Welling
2022 arXiv   pre-print
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).  ...  In addition, whereas existing methods are limited to equivariance on 3 dimensional spaces, our model is easily scaled to higher-dimensional spaces.  ...  Acknowledgements We would like to thank Patrick Forré for his support to formalize the invariance features identification proof.  ... 
arXiv:2102.09844v3 fatcat:fmes7k4fdrhjlfci7bcnq2pjha

Top-N: Equivariant set and graph generation without exchangeability [article]

Clement Vignac, Pascal Frossard
2022 arXiv   pre-print
Top-n can replace i.i.d. generation in any Variational Autoencoder or Generative Adversarial Network.  ...  We then study equivariance in generative settings and show that non-exchangeable methods can still achieve permutation equivariance.  ...  ACKNOWLEDGMENTS Clément Vignac would like to thank the Swiss Data Science Center for supporting him through the PhD fellowship program (grant P18-11).  ... 
arXiv:2110.02096v4 fatcat:hstjghkhhnhwnpiv3xzf3zjjey

The Design Space of E(3)-Equivariant Atom-Centered Interatomic Potentials [article]

Ilyes Batatia, Simon Batzner, Dávid Péter Kovács, Albert Musaelian, Gregor N. C. Simm, Ralf Drautz, Christoph Ortner, Boris Kozinsky, Gábor Csányi
2022 arXiv   pre-print
Our framework also provides a practical tool for systematically probing different choices in the unified design space.  ...  design choices are critical for achieving high accuracy.  ...  The physical normalization can be written as: Ê = 1 α EN i=1 E 0,Zi (40) F = 1 α F, ( 41 ) where N is the number of atoms in the molecule, α is a scaling factor (can be interpreted as a change of units  ... 
arXiv:2205.06643v1 fatcat:n7rlbl4tqbgo7labr7dzsskj3m

Geometric and Physical Quantities Improve E(3) Equivariant Message Passing [article]

Johannes Brandstetter, Rob Hesselink, Elise van der Pol, Erik J Bekkers, Max Welling
2022 arXiv   pre-print
Through the definition of steerable node attributes, the MLPs provide a new class of activation functions for general use with steerable feature fields.  ...  We introduce Steerable E(3) Equivariant Graph Neural Networks (SEGNNs) that generalise equivariant graph networks, such that node and edge attributes are not restricted to invariant scalars, but can contain  ...  ACKNOWLEDGMENTS Johannes Brandstetter thanks the Institute of Advanced Research in Artificial Intelligence (IARAI) and the Federal State Upper Austria for the support.  ... 
arXiv:2110.02905v3 fatcat:hhnvua3cqbbyblpy4ams6mmz7i

Equivariant Diffusion for Molecule Generation in 3D [article]

Emiel Hoogeboom, Victor Garcia Satorras, Clément Vignac, Max Welling
2022 arXiv   pre-print
This work introduces a diffusion model for molecule generation in 3D that is equivariant to Euclidean transformations.  ...  In addition, we provide a probabilistic analysis which admits likelihood computation of molecules using our model.  ...  Although developed for discriminative tasks, E(n) equivariant layers can also be used for molecule generation in 3D.  ... 
arXiv:2203.17003v2 fatcat:npwvz4ru7nd3zp2fjeatfrpn2q

Equivariant Flows: sampling configurations for multi-body systems with symmetric energies [article]

Jonas Köhler, Leon Klein, Frank Noé
2019 arXiv   pre-print
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  ...  In order to scale and generalize these results, it is essential that the natural symmetries of the probability density - in physics defined by the invariances of the energy function - are built into the  ...  Equivariant Flows and Boltzmann Generators Equivariant normalizing flows yield symmetric densities Symmetries may be discussed in terms of a group G acting on a vector space V .  ... 
arXiv:1910.00753v1 fatcat:4tylnzbyl5dhbeshha5mxr7ade

Informing Geometric Deep Learning with Electronic Interactions to Accelerate Quantum Chemistry [article]

Zhuoran Qiao, Anders S. Christensen, Matthew Welborn, Frederick R. Manby, Anima Anandkumar, Thomas F. Miller III
2022 arXiv   pre-print
We anticipate that the strategy presented here will help to expand opportunities for studies in chemistry and materials science, where the acquisition of experimental or reference training data is costly  ...  Our method also describes interactions in challenging charge-transfer complexes and open-shell systems.  ...  Z.Q. acknowledges Bo Li, Vignesh Bhethanabotla, Dani Kiyasseh, Hongkai Zheng, Sahin Lale, and Rafal Kocielnik for proofreading and helpful comments on the manuscript.  ... 
arXiv:2105.14655v4 fatcat:5hnrmhtwerh7nn53f2zolaypvu

Learning Equivariant Energy Based Models with Equivariant Stein Variational Gradient Descent [article]

Priyank Jaini, Lars Holdijk, Max Welling
2021 arXiv   pre-print
We apply these equivariant energy models for modelling joint densities in regression and classification tasks for image datasets, many-body particle systems and molecular structure generation.  ...  generated samples.  ...  A Sampling using Equivariant Flows Neural transport augmented sampling, first introduced by Parno and Marzouk (2018) , is a general method for using normalizing flows to sample from a given density π.  ... 
arXiv:2106.07832v2 fatcat:bkbaudbsg5dhxc2oariw43wkly

Equivariant geometric learning for digital rock physics: estimating formation factor and effective permeability tensors from Morse graph [article]

Chen Cai, Nikolaos Vlassis, Lucas Magee, Ran Ma, Zeyu Xiong, Bahador Bahmani, Teng-Fong Wong, Yusu Wang, WaiChing Sun
2021 arXiv   pre-print
SE(3) equivariant neural network is found to generate more accurate predictions, especially when the training data is limited.  ...  While the graph and Euclidean convolutional approaches both employ neural networks to generate low-dimensional latent space to represent the features of the micro-structures for forward predictions, the  ...  that generates predictions equivariant with respect to 3D rotation, and (3) the graph convolutional neural network that generates low-dimensional features to aid predictions for the formation factor and  ... 
arXiv:2104.05608v3 fatcat:nuolmvukjjdqlfrxzxm7k7n3sy

Score-Based Generative Models for Molecule Generation [article]

Dwaraknath Gnaneshwar, Bharath Ramsundar, Dhairya Gandhi, Rachel Kurchin, Venkatasubramanian Viswanathan
2022 arXiv   pre-print
Recent advances in generative models have made exploring design spaces easier for de novo molecule generation.  ...  In this work, we lay the foundations by testing the efficacy of score-based models for molecule generation.  ...  Reference [4] explores a NF model that is equivariant under Euclidean symmetries to generate 3D molecules.  ... 
arXiv:2203.04698v1 fatcat:pabnlgdimzca7ijehkolcizzmu

GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation [article]

Minkai Xu, Lantao Yu, Yang Song, Chence Shi, Stefano Ermon, Jian Tang
2022 arXiv   pre-print
Inspired by the diffusion process in classical non-equilibrium thermodynamics where heated particles will diffuse from original states to a noise distribution, in this paper, we propose a novel generative  ...  the desirable equivariance property.  ...  ACKNOWLEDGEMENT Minkai thanks Huiyu Cai, David Wipf, Zuobai Zhang, and Zhaocheng Zhu for their helpful discussions and comments.  ... 
arXiv:2203.02923v1 fatcat:z6xc7gjty5gdbavmqvh37qfy5u

Galaxy Merger Reconstruction with Equivariant Graph Normalizing Flows [article]

Kwok Sun Tang, Yuan-Sen Ting
2022 arXiv   pre-print
In this work, we employ a generative graph network, E(n) Equivariant Graph Normalizing Flows Model.  ...  A key yet unresolved question in modern-day astronomy is how galaxies formed and evolved under the paradigm of the ΛCDM model.  ...  generating molecule features and their 3D positions as a graph.  ... 
arXiv:2207.02786v1 fatcat:nrr5tqeg5jcnxft7hbolhoz6my

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
2022 arXiv   pre-print
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.  ...  Equivariance has been a long-standing concern in various fields ranging from computer vision to physical modeling.  ...  Introduction 3D point cloud has become a prevalent data structure for representing a wide range of 3D objects such as 3D scenes [1, 4, 8, 36] , molecules [12, 15, 28] , and physical particles [7, 31  ... 
arXiv:2203.14486v1 fatcat:i64audysvvchfkkjjdjdmjum7e

Torsional Diffusion for Molecular Conformer Generation [article]

Bowen Jing, Gabriele Corso, Jeffrey Chang, Regina Barzilay, Tommi Jaakkola
2022 arXiv   pre-print
Molecular conformer generation is a fundamental task in computational chemistry.  ...  On a standard benchmark of drug-like molecules, torsional diffusion generates superior conformer ensembles compared to machine learning and cheminformatics methods in terms of both RMSD and chemical properties  ...  This work was supported by the Machine Learning for Pharmaceutical Discovery and Synthesis (MLPDS) consortium, the Abdul Latif Jameel Clinic for Machine Learning in Health, the DTRA Discovery of Medical  ... 
arXiv:2206.01729v1 fatcat:w5xekbfru5apzi7gjpntu2q2ta
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