Source-linked AI summary
Geometric Deep Learning on Molecular Representations
Kenneth Atz, Francesca Grisoni, Gisbert Schneider
TL;DR
Molecular GDL uses symmetry-aware neural architectures across diverse molecular representations for drug discovery, synthesis prediction, and quantum chemistry. This review harmonizes the field and examines learned molecular features alongside classical descriptors. It finds representation-specific strengths while highlighting missing systematic evaluation of learned features and applicability domains.
Problem
Molecular GDL spans diverse representations and applications, but the usefulness of learned features and their relationship to classical descriptors remain insufficiently systematically evaluated.
Method
The review provides a structured and harmonized synthesis of molecular GDL applications, representation-specific properties, learned features, challenges, and future opportunities.
Results
Molecular strings are particularly suited to generative tasks, molecular graphs to property prediction, and 3D information to quantum-chemistry modeling, with representation-specific trade-offs.
Takeaways & Limitations
GDL offers flexible alternatives to classical human-engineered molecular features, but model complexity, interpretability, and chemistry-aware design remain important considerations.
Takeaways & Limitations
No framework currently enables systematic evaluation of data-driven molecular features, and contemporary GDL studies generally lack applicability-domain assessment.
Abstract
from arXiv · showhide
Geometric deep learning (GDL), which is based on neural network architectures that incorporate and process symmetry information, has emerged as a recent paradigm in artificial intelligence. GDL bears particular promise in molecular modeling applications, in which various molecular representations with different symmetry properties and levels of abstraction exist. This review provides a structured and harmonized overview of molecular GDL, highlighting its applications in drug discovery, chemical synthesis prediction, and quantum chemistry. Emphasis is placed on the relevance of the learned molecular features and their complementarity to well-established molecular descriptors. This review provides an overview of current challenges and opportunities, and presents a forecast of the future of GDL for molecular sciences.
1 Introduction
Deep learning is promising for molecular science because it can process diverse molecular representations and learn features directly from data. This review organizes molecular GDL applications across drug discovery, quantum chemistry, and synthesis planning, emphasizing learned features.
- Motivation: Deep learning can process molecular data represented as sequences, images, graphs, and other forms.Molecular representations capture properties at varying levels of abstraction.
- Motivation: Feature learning produces data-driven molecular features without manual intervention.This complements classical machine-learning approaches based on established molecular descriptors.
- Geometric deep learning: GDL incorporates geometric priors describing the structure and symmetry of molecular inputs.These priors are intended to improve the information captured by neural-network models.
- Molecular representations: Molecular representations range from 2D depictions and graphs to SMILES strings, 3D graphs, and molecular surfaces.The examples use the penam substructure of penicillin.
- Review scope: The review provides a structured overview of GDL applications in drug discovery, quantum chemistry, and computer-aided synthesis planning.It also delineates research directions and forecasts future impact, with particular attention to learned molecular features.
2 Principles of geometric deep learning
GDL extends neural networks with geometric priors and symmetry-aware behavior. Molecular tasks often require invariant or equivariant outputs because many molecular properties should remain consistent under specified transformations.
- Symmetry: The term geometric deep learning was coined in 2017 and now includes methods incorporating geometric priors.Symmetries include transformations such as translation, reflection, rotation, scaling, and permutation.
- Symmetry: Equivariance means transforming the input transforms the network output correspondingly: F(T(X)) = T′F(X).The output follows the transformation through an action of the same symmetry group.
- Symmetry: Invariance is the special case of equivariance in which the output is unchanged: F(T(X)) = F(X).Here, T′ is the identity action.
- Molecular features: Molecular features inherit symmetry behavior from both the input representation and the neural-network architecture.Many molecular descriptors are designed to be invariant to rotation and translation.
- Molecular properties: Equivariant architectures are desirable for properties invariant under predefined symmetries, with chiral and vector properties as exceptions.Examples of generally invariant properties include equilibrium energies, atomic charges, permeability, lipophilicity, and solubility.
- Geometric priors: GDL incorporates geometric priors about the structure space and symmetry properties of inputs.It applies to Euclidean and non-Euclidean domains including graphs, manifolds, meshes, and strings.
3 Molecular GDL
Molecular GDL addresses the challenge that one molecule can have multiple valid representations capturing different structural and physicochemical information. The review distinguishes these representations and summarizes relevant molecular-learning terminology.
- Molecular representations: Multiple valid molecular representations capture different abstraction levels and physicochemical or geometrical aspects.Each representation is suitable for some purposes but not others.
- Terminology: In this review, representation means a human-made molecular model, whereas feature means a numerical description obtained by rules or neural networks.Examples of representations include molecular graphs, 3D conformers, and SMILES strings.
- Glossary: The glossary defines CoMFA and CoMSIA as 3D QSAR methods using grids to capture molecular-feature distributions for bioactivity prediction.It also defines convolution as a neural-network operation that transforms one feature space into another while capturing local information.
3.1 Learning on molecular graphs
Molecular graphs represent atoms and their connections, enabling graph neural networks to learn molecular features through iterative message passing. These models support applications across quantum chemistry, drug discovery, property prediction, molecule generation, and synthesis planning, while equivariant architectures extend this approach to 3D structures.
- Molecular graphs encode atoms as vertices and their connections as edges, optionally enriched with vertex and edge features.
- Message passing neural networks iteratively update vertex features using learnable functions and permutation-invariant local aggregation.
- Graph neural networks have been applied to quantum chemistry, drug discovery, computer-aided synthesis planning, and molecular property prediction.
- Including 3D information generally improves drug-relevant property prediction, while single and multiple conformers show no marked difference in network training.
- GNNs support de novo molecule generation and synthesis planning, but current synthesis approaches are limited to reactions involving removal of one bond between products and reactants.
- SE(3)- and E(3)-equivariant GNNs use 3D coordinates and achieve high accuracy for energies, molecular-dynamics potentials, and wave-functions.
3.2 Learning on grids
Grid representations impose regular spatial structure that supports convolutional processing and translation invariance. In molecular modeling, 3D grids capture spatial property distributions, while 2D grids are used mainly for visualization.
- Grids represent systems at regularly spaced intervals in one, two, three, or higher dimensions.
- Grid vertices have fixed ordering and identical local connectivity, giving local convolutions a geometric prior for translation invariance.
- Molecular grid representations can map learned features to atomic or molecular properties after feature labeling, updating, and aggregation.
- 2D molecular grids are generally more useful for visualization than prediction, whereas 3D grids capture spatial distributions of molecular properties.
3.3 Learning on molecular surfaces
Molecular surfaces represent 3D structures as meshes whose points carry chemical and geometric features. Mesh-based GNNs can address limitations of conventional 2D CNN approaches, but have not yet been applied to molecular systems.
- Molecular surfaces enclose 3D structures and can encode hydrophobic, electrostatic, shape, and curvature features at surface points.
- 2D CNNs applied to molecular meshes require rotational data augmentation and homogeneous mesh resolution because they are not rotation-equivariant.
- Mesh-based GNNs incorporate rotational equivariance and heterogeneous mesh resolution, but have not yet found applications to molecular systems.
- 3D voxel-based surface representations have been used with 3D CNNs for protein-ligand affinity and protein binding-site prediction.
3.4 Learning on string representations
String representations treat molecules as chemical languages with syntax and semantics, enabling sequence models such as RNNs and Transformers. These models support molecular generation, property prediction, synthesis planning, and feature extraction, with SMILES remaining the dominant representation.
- Molecular strings encode chemical structures as linear sequences whose syntax constrains validity and whose semantics relate symbol combinations to molecular properties.
- SMILES encodes atoms, bonds, connectivity, branching, and stereochemistry and remains the de facto representation for chemical language modeling.
- RNNs process sequences through hidden states and commonly predict the next token autoregressively.
- Transformers represent sequences as fully connected or sequentially connected graphs and use positional information during processing.
- RNNs learn SMILES syntax and high-level physicochemical and biological features for de novo molecular generation, with randomization and bidirectional learning improving chemical-language quality.
- RNN-learned features have outperformed traditional molecular descriptors and graph-convolution methods for virtual screening and property prediction.
4 Conclusions and outlook
GDL offers flexible molecular modeling across representations, with representation-specific strengths and unresolved challenges in feature evaluation, applicability assessment, interpretability, and complexity.
- GDL leverages symmetries in molecular representations to increase flexibility and versatility in molecular structure generation.
- SMILES are particularly suited to generative tasks, whereas their non-univocity can limit molecular property prediction.Their syntax facilitates next-token and sequence-to-sequence prediction.
- Molecular graphs are useful for property prediction, while 3D information is especially useful for quantum chemistry modeling.In drug discovery, 3D graph approaches have often failed to clearly outweigh their increased model complexity.
- Molecular grids are a standard 3D representation for large molecular systems because they support user-defined resolution and Euclidean input structure.
- Systematic benchmarks are still missing for evaluating the usefulness of AI-learned molecular features, despite mixed evidence relative to classical descriptors.Studies have reported both benefits and failures of GDL-learned representations.
- Current GDL studies generally lack applicability-domain assessment, and future work must balance algorithmic complexity, performance, interpretability, and domain communication.The review also identifies molecular surfaces and electronic structure as promising directions.
6 Competing interest
The authors disclose a potential financial conflict involving pharmaceutical consulting and co-founded-company ownership.
- G.S. declares a potential financial conflict of interest as co-founder of inSili.com LLC and as a scientific consultant to the pharmaceutical industry.
7 List of abbreviations
The paper defines abbreviations used for methods, representations, symmetry groups, and molecular-science applications.
- GDL denotes Geometric Deep Learning, while GNN, CNN, and RNN denote graph, convolutional, and recurrent neural networks.
- CASP denotes Computer-aided Synthesis Planning, and QSAR denotes Quantitative Structure-Activity Relationship.
- E(3) and SE(3) denote the Euclidean and Special Euclidean Symmetry Groups, respectively.
- SMILES denotes Simplified Molecular Input Line Entry Systems, and XAI denotes Explainable Artificial Intelligence.