ArticleInternational journal for numerical methods in biomedical engineering2019
DG-GL: Differential geometry-based geometric learning of molecular datasets.
Article in International journal for numerical methods in biomedical engineering, 2019. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 33 papers.
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33 citing papers in PubMed.
- Article
- Structural Knowledge Is What Matters in Protein-Ligand Binding Affinity Prediction.Molecules (Basel, Switzerland) · 2026Article
- Correlated clustering and projection for dimensionality reduction.Machine learning: science and technology · 2026Article
- Topological data analysis and topological deep learning beyond persistent homology: a review.Artificial intelligence review · 2026Article
- A Review of Topological Data Analysis and Topological Deep Learning in Molecular Sciences.Journal of chemical information and modeling · 2025Review
- Enhancing energy predictions in multi-atom systems with multiscale topological learning.Journal of materials chemistry. A · 2025Article
- Persistent Directed Flag Laplacian (PDFL)-Based Machine Learning for Protein-Ligand Binding Affinity Prediction.Journal of chemical theory and computation · 2025Article
- Multiscale Differential Geometry Learning for Protein Flexibility Analysis.Journal of computational chemistry · 2025Article
- The algebraic extended atom-type graph-based model for precise ligand-receptor binding affinity prediction.Journal of cheminformatics · 2025Article
- Curvature estimation techniques for advancing neurodegenerative disease analysis: a systematic review of machine learning and deep learning approaches.American journal of neurodegenerative disease · 2025Review
- Position: Topological Deep Learning is the New Frontier for Relational Learning.Proceedings of machine learning research · 2024Article
- Regression Study of Odorant Chemical Space, Molecular Structural Diversity, and Natural Language Description.ACS omega · 2024Article
- Multiscale differential geometry learning of networks with applications to single-cell RNA sequencing data.Computers in biology and medicine · 2024Article
- Persistent de Rham-Hodge Laplacians in Eulerian representation for manifold topological learning.AIMS mathematics · 2024Article
- Artificial intelligence-aided protein engineering: from topological data analysis to deep protein language models.Briefings in bioinformatics · 2023Review
- Protein-ligand binding affinity prediction exploiting sequence constituent homology.Bioinformatics (Oxford, England) · 2023Article
- Article
- Mathematical Geometry and Groups for Low-Symmetry Metal Complex Systems.Molecules (Basel, Switzerland) · 2023Article
- Multiscale Laplacian Learning.Applied intelligence (Dordrecht, Netherlands) · 2023Article
- Multi-shelled ECIF: improved extended connectivity interaction features for accurate binding affinity prediction.Bioinformatics advances · 2023Article
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Abstract
motivationDespite its great success in various physical modeling, differential geometry (DG) has rarely been devised as a versatile tool for analyzing large, diverse, and complex molecular and biomolecular datasets because of the limited understanding of its potential power in dimensionality reduction and its ability to encode essential chemical and biological information in differentiable manifolds.
resultsWe put forward a differential geometry-based geometric learning (DG-GL) hypothesis that the intrinsic physics of three-dimensional (3D) molecular structures lies on a family of low-dimensional manifolds embedded in a high-dimensional data space. We encode crucial chemical, physical, and biological information into 2D element interactive manifolds, extracted from a high-dimensional structural data space via a multiscale discrete-to-continuum mapping using differentiable density estimators. Differential geometry apparatuses are utilized to construct element interactive curvatures in analytical forms for certain analytically differentiable density estimators. These low-dimensional differential geometry representations are paired with a robust machine learning algorithm to showcase their descriptive and predictive powers for large, diverse, and complex molecular and biomolecular datasets. Extensive numerical experiments are carried out to demonstrate that the proposed DG-GL strategy outperforms other advanced methods in the predictions of drug discovery-related protein-ligand binding affinity, drug toxicity, and molecular solvation free energy. AVAILABILITY AND IMPLEMENTATION: http://weilab.math.msu.edu/DG-GL/ Contact: wei@math.msu.edu.
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