A Review of Topological Data Analysis and Topological Deep Learning in Molecular Sciences
Bibliographic record
Abstract
Topological data analysis (TDA) has emerged as a powerful framework for extracting robust, multiscale, and interpretable features from complex molecular data for artificial intelligence (AI) modeling and topological deep learning (TDL). This review provides a comprehensive overview of the development, methodologies, and applications of TDA in molecular sciences. We trace the evolution of TDA from early qualitative tools to advanced quantitative and predictive models, highlighting innovations such as persistent homology, persistent Laplacians, and topological machine learning. The paper explores TDA's transformative impact across diverse domains, including biomolecular stability, protein-ligand interactions, drug discovery, materials science, topological sequence analysis, and viral evolution. Special attention is paid to recent advances in integrating TDA with machine learning and AI, enabling breakthroughs in protein engineering, solubility, and toxicity prediction, and the discovery of novel materials and therapeutics. We also discuss the limitations of current TDA approaches and outline future directions, including the integration of TDA with advanced AI models and the development of new topological invariants. This review aims to serve as a foundational reference for researchers seeking to harness the power of topology in molecular sciences.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.004 | 0.005 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 0.002 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".