E(3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials

Batzner, Simon; Musaelian, Albert; Sun, Lixin; Geiger, Mario; Mailoa, Jonathan P.; Kornbluth, Mordechai; Molinari, Nicola; Smidt, Tess; Kozinsky, Boris

doi:10.1038/s41467-022-29939-5

Cited by 727 publications

(713 citation statements)

References 43 publications

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“…For the rest of the paper, we will assume that they are encoded in spherical coordinates. This is in line with many equivariant models such as SOAP-GAP [2], SNAP [34], ACE [5,35] and its recursive implementations such as [36], NICE [37], NequIP [26], equivariant transformer [24], and SEGNNs [25]. By contrast, some equivariant MPNNs like NewtonNet [22], EGNN [20], or PaINN [21] express the features in Cartesian coordinates.…”

Section: Equivariant Messagessupporting

confidence: 64%

“…17 and U t is the update function for each layer. In most MPNNs, the k channel of the message corresponds to the dimension of the learned embedding of the chemical elements [14,26]. We further need to extend Eq.…”

Section: Atomic Basismentioning

confidence: 99%

“…As the message uses a sum operation, it gathers an average of neighbors' features. NequIP [26] proposed to normalise the sum by the square root of the average number of neighbors, so that λ = #N (k) k in Eq. ( 2).…”

Section: A Internal Normalizationmentioning

confidence: 99%

“…To create these equivariant features inside the network, they introduced a new type of nonlinear operation, an equivariant tensor-product, which couples feature via the Clebsch-Gordan coefficients resulting in output features of a desired symmetry. Several novel equivariant messagepassing models were recently published (e.g., EGNN [20], PaiNN [21], NewtonNet [22], GemNet [23], TorchMD-Net [24], and SEGNN [25]) of which the best results were achieved by the Neural Equivariant Interatomic Potential (NequIP) [26], improving on the previous state-ofthe-art accuracy by about a factor of two across multiple datasets. A strictly local equivariant deep learning interatomic potential was also introduced recently [27].…”

Section: Introductionmentioning

confidence: 99%

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

Batatia¹,

Batzner²,

Kovács³

et al. 2022

Preprint

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The rapid progress of machine learning interatomic potentials over the past couple of years produced a number of new architectures. Particularly notable among these are the Atomic Cluster Expansion (ACE), which unified many of the earlier ideas around atom density-based descriptors, and Neural Equivariant Interatomic Potentials (NequIP), a message passing neural network with equivariant features that showed state of the art accuracy. In this work, we construct a mathematical framework that unifies these models: ACE is generalised so that it can be recast as one layer of a multi-layer architecture. From another point of view, the linearised version of NequIP is understood as a particular sparsification of a much larger polynomial model. Our framework also provides a practical tool for systematically probing different choices in the unified design space. We demonstrate this by an ablation study of NequIP via a set of experiments looking at in-and out-of-domain accuracy and smooth extrapolation very far from the training data, and shed some light on which design choices are critical for achieving high accuracy. Finally, we present BOTNet (Body-Ordered-Tensor-Network), a much-simplified version of NequIP, which has an interpretable architecture and maintains accuracy on benchmark datasets.

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Section: Equivariant Messagessupporting

confidence: 64%

Section: Atomic Basismentioning

confidence: 99%

Section: A Internal Normalizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Batatia¹,

Batzner²,

Kovács³

et al. 2022

Preprint

Self Cite

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“…Priors of particular importance for 3D structure modeling include rotation [49] and translation [50] equivariance. Such priors form the basis of 3D Euclidean transformations that can now directly be found within neural network layers [51,52,12,53,54] to increase networks' data efficiency and generalization capabilities [55,56]. Our work follows that of [12] to incorporate E(3)-equivariance in our message passing neural network for 3D structure refinement and quality assessment.…”

Section: Related Workmentioning

confidence: 99%

EGR: Equivariant Graph Refinement and Assessment of 3D Protein Complex Structures

Morehead¹,

Chen²,

Wu³

et al. 2022

Preprint

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Protein complexes are macromolecules essential to the functioning and well-being of all living organisms. As the structure of a protein complex, in particular its region of interaction between multiple protein subunits (i.e., chains), has a notable influence on the biological function of the complex, computational methods that can quickly and effectively be used to refine and assess the quality of a protein complex's 3D structure can directly be used within a drug discovery pipeline to accelerate the development of new therapeutics and improve the efficacy of future vaccines. In this work, we introduce the Equivariant Graph Refiner (EGR), a novel E(3)-equivariant graph neural network (GNN) for multi-task structure refinement and assessment of protein complexes. Our experiments on new, diverse protein complex datasets, all of which we make publicly available in this work, demonstrate the state-of-the-art effectiveness of EGR for atomistic refinement and assessment of protein complexes and outline directions for future work in the field. In doing so, we establish a baseline for future studies in macromolecular refinement and structure analysis. 1 Preprint. Under review.

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Machine Learning in Soft Matter: From Simulations to Experiments

Zhang,

Gong,

Jiang

2024

Adv Funct Materials

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Soft matter with diverse functionalities that are easily designable has fascinated tremendous research interests in the past several decades. Nevertheless, the inherent confluence of time and length scale ubiquitous in soft matter immensely complicates the elucidation of the structure–property relationship and thereby severely impedes the function exploration of soft materials. Recently, the emergent machine learning (ML) techniques open new paradigms in property prediction and molecular design of functional materials, due to their extraordinarily distinguished performance in the aspect of trend identity and pattern extraction from data, and objective optimization by accelerating the guided search in high‐dimensional spaces. This review exclusively focuses on the current state‐of‐the‐art progress in the development of ML techniques applied in the realms of soft matter, ranging from coarse‐grained simulations to theoretical prediction on the structural formation and macroscopic properties, as well as the optimization and algorithm‐aided design in experiments. Finally, an outlook on the challenges and opportunities for this rapidly evolving field is discussed.

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E(3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials

Cited by 727 publications

References 43 publications

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

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

EGR: Equivariant Graph Refinement and Assessment of 3D Protein Complex Structures

Machine Learning in Soft Matter: From Simulations to Experiments

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