SchNet: A Continuous-Filter Convolutional Neural Network for Modeling Quantum Interactions

SchNet: A Continuous-Filter Convolutional Neural Network for Modeling Quantum Interactions Kristof T. Schütt Pieter-Jan Kindermans Huziel E. Sauceda Stefan Chmiela Alexandre Tkatchenko Klaus-Robert Müller

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SchNet: A Continuous-Filter Convolutional Neural Network for Modeling Quantum Interactions 2017 NeurIPS / arXiv 1706.08566 schutt2017-schnet schutt2017-schnet.txt, the project's staged copy 0b6e43106d5e02b7e2d8b4539b086ec0dbda4905 arxiv-open chemistry

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0 spans located by searching the stored text for the quote's exact words, allowing any whitespace between them method Quotation withheld because this record is not cleared for redistribution. modeling quantum interactions in molecules Quotation withheld because this record is not cleared for redistribution. system-or-tool-building system-or-tool-building Quotation withheld because this record is not cleared for redistribution. mechanisms continuous-filter convolutions over continuous atom positions (not a grid), preserving the physical information in molecular geometry Quotation withheld because this record is not cleared for redistribution. chemical compound space is vast and accurate quantum calculations are costly, preventing exhaustive exploration what this limits: any claim of coverage over chemical space: Quotation withheld [exploration] Quotation withheld because this record is not cleared for redistribution. The radial-basis filter parameters (number and range of centres) were not systematically studied. what this limits: the reported architecture choices: AN EXTENSIVE EVALUATION OF THE IMPACT OF THESE VARIABLES IS LEFT FOR FUTURE WORK Quotation withheld because this record is not cleared for redistribution. Training on forces roughly doubles the computational cost, because forces require a full forward and backward pass through the energy model. what this limits: the force-training results, which are not free: WE EXPECT TO SEE IMPROVED GENERALIZATION, HOWEVER, AT A COMPUTATIONAL COST Quotation withheld because this record is not cleared for redistribution. Performance on the new ISO17 benchmark, which combines chemical and conformational variation, is only promising rather than solved. what this limits: the ISO17 benchmark result: WHILE WE ACHIEVE PROMISING RESULTS ON THIS NEW BENCHMARK, MODELING CHEMICAL AND CONFORMATIONAL VARIATIONS REMAINS DIFFICULT AND NEEDS FURTHER IMPROVEMENT Quotation withheld because this record is not cleared for redistribution. A whole class of competing methods is excluded from force training by its REPRESENTATION - discrete binning and one-hot bond types - which makes their energy surface discontinuous. what this limits: a comparison of this model against circular fingerprints, graph convolutions or message-passing networks on forces: those methods cannot be trained with forces at all, because discrete binning or one-hot bond types put discontinuities in their potential energy surface Quotation withheld because this record is not cleared for redistribution. The main benchmark contains only equilibrium molecules, where the force term the paper exists to predict is zero by definition. what this limits: a QM9 result as evidence about force prediction: QM9 holds only equilibrium molecules, so the forces there are zero by definition and are not predicted at all Quotation withheld because this record is not cleared for redistribution. A named competitor is ruled out of one benchmark entirely, and its scaling behaviour is given as quadratic in both atoms and examples. what this limits: GDML as a baseline: its kernel matrix grows quadratically in both the number of atoms and the number of examples, and it is stated elsewhere in the paper that it cannot be used for the molecular-dynamics predictions Quotation withheld because this record is not cleared for redistribution. deep convolutional neural networks applied to model quantum interactions in molecules Quotation withheld because this record is not cleared for redistribution. comparison of force and energy prediction against a mean predictor as a baseline, on held-out MD trajectories eliminates: that SchNet's reported accuracy could be obtained by predicting the dataset mean, and that it comes from memorising conformations rather than generalising · outcome: held Quotation withheld because this record is not cleared for redistribution. continuous-filter convolution continuous-filter convolution Quotation withheld because this record is not cleared for redistribution. potential energy surface potential energy surface Quotation withheld because this record is not cleared for redistribution. interatomic forces interatomic forces Quotation withheld because this record is not cleared for redistribution. molecular energy molecular energy Quotation withheld because this record is not cleared for redistribution. rotational invariance rotational invariance Quotation withheld because this record is not cleared for redistribution. QM9 QM9 Quotation withheld because this record is not cleared for redistribution. the invariances - BY CONSTRUCTION, not measured: rotational equivariance of the forces follows from rotational invariance of the energy plus the architecture, so it is a guarantee rather than an empirical result, and must not be compared with a model's measured conservation Quotation withheld because this record is not cleared for redistribution. QM9 - AS A BENCHMARK OF THE SPECIAL CASE: equilibrium molecules only, which is precisely where the forces vanish, so the benchmark omits the regime the architecture was built for Quotation withheld because this record is not cleared for redistribution. the filter - CONTINUOUS RATHER THAN DISCRETE, because atom positions do not lie on a grid and their precise locations carry physical information that discretising destroys Quotation withheld because this record is not cleared for redistribution. extends → grid-based convolutional neural networks Quotation withheld because this record is not cleared for redistribution. extends → dynamic filter networks [34] Quotation withheld because this record is not cleared for redistribution. extends → deep tensor neural networks (DTNN), Schütt et al. [20] Quotation withheld because this record is not cleared for redistribution. builds-on → gradient-domain machine learning (GDML), Chmiela et al. [19] Quotation withheld because this record is not cleared for redistribution. builds-on → ResNet [36] residual connections Quotation withheld because this record is not cleared for redistribution. continuous-filter convolution —causes→ potential energy surface continuous-filter convolution potential energy surface the relation itself is separately evidenced · strength of the relation: 1 · the relation stated: the continuous-filter layers are what YIELD a continuous energy surface Audit 2026-09-28: DOUBTFUL - read against its full span and kept, but the span writes 'continuous-filter convolutional layers', not 'continuous-filter convolution'. Quotation withheld because this record is not cleared for redistribution. interatomic forces —operationalised-as→ molecular energy interatomic forces molecular energy strength of the relation: 1 Audit 2026-09-28: DOUBTFUL - read against its full span and kept, but the span says forces are RELATED to energy and obtained by differentiating it; operationalised-as is loose. Quotation withheld because this record is not cleared for redistribution. three — benchmark datasets used (QM9, MD17, ISO17) Quotation withheld because this record is not cleared for redistribution. SchNet yields a joint model of total energy and interatomic forces that follows fundamental quantum-chemical principles. about this quote: QUOTE REPAIRED: the extractor split a hyphen-space and the quote was recorded faithfully with the damage in it, which made it unanchorable. The repaired string is an EXACT SUBSTRING of the staged text - that is why it was accepted, not because a rule produced it. The text as originally recorded is kept in evidence as extracted. Quotation withheld because this record is not cleared for redistribution. SchNet delivers rotationally invariant energy predictions and rotationally equivariant force predictions. Quotation withheld because this record is not cleared for redistribution. total energy total energy Quotation withheld because this record is not cleared for redistribution. interatomic forces interatomic forces Quotation withheld because this record is not cleared for redistribution. continuous-filter convolutional layer continuous-filter convolutional layer about this quote: QUOTE REPAIRED: the extractor split a hyphen-space and the quote was recorded faithfully with the damage in it, which made it unanchorable. The repaired string is an EXACT SUBSTRING of the staged text - that is why it was accepted, not because a rule produced it. The text as originally recorded is kept in evidence as extracted. Quotation withheld because this record is not cleared for redistribution. potential energy surface potential energy surface Quotation withheld because this record is not cleared for redistribution.

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