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| Format: | Recurso digital |
| Language: | English |
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2025
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| Online Access: | https://doi.org/10.5281/zenodo.17124006 |
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| _version_ | 1866901379858038784 |
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| author | Lopez Lozano, Andres Felipe |
| author_facet | Lopez Lozano, Andres Felipe |
| contents | <p><span>Quantum mechanics provides rich mathematical frameworks for understanding electron </span> <span>behavior, yet bridging these abstract formulations with practical machine learning applica- </span> <span>tions remains challenging. This paper introduces a novel machine learning pipeline based </span> <span>on the Quantum Trail theory: a geometric reinterpretation of electrons as dynamic enti- </span> <span>ties leaving directional trails represented by vector fields derived from probability density </span> <span>gradients and quantum probability currents. I extracted 22 features from these trail fields, </span> <span>including density statistics, trail velocities, divergence patterns, vorticity measures, and </span> <span>streamline characteristics. Using a synthetic data set of 300 molecules with 2-8 atoms (H, </span> <span>C, N, O), I train gradient boosting and random forest models to predict HOMO-LUMO gaps </span> <span>and dipole moments, achieving R</span><span>² </span><span>scores of 0.5144 and 0.4351 respectively. In particular, </span> <span>quantum trail features such as trail velocity standard deviation (6.75% importance) and </span> <span>average streamline length (5.12% importance) rank highly among predictive features, vali- </span> <span>dating geometric interpretation. The implementation achieves numerical stability through </span> <span>4th-order finite differences and adaptive regularization, with deployment as a Google Cloud </span> <span>Function enabling real-time predictions. This work demonstrates that geometric interpreta- </span> <span>tions of quantum mechanics can yield practical ML features with potential applications in </span> <span>drug discovery, materials science, and quantum chemistry education.</span></p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17124006 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Machine Learning Applications of Quantum Trail Fields for Molecular Property Prediction Lopez Lozano, Andres Felipe <p><span>Quantum mechanics provides rich mathematical frameworks for understanding electron </span> <span>behavior, yet bridging these abstract formulations with practical machine learning applica- </span> <span>tions remains challenging. This paper introduces a novel machine learning pipeline based </span> <span>on the Quantum Trail theory: a geometric reinterpretation of electrons as dynamic enti- </span> <span>ties leaving directional trails represented by vector fields derived from probability density </span> <span>gradients and quantum probability currents. I extracted 22 features from these trail fields, </span> <span>including density statistics, trail velocities, divergence patterns, vorticity measures, and </span> <span>streamline characteristics. Using a synthetic data set of 300 molecules with 2-8 atoms (H, </span> <span>C, N, O), I train gradient boosting and random forest models to predict HOMO-LUMO gaps </span> <span>and dipole moments, achieving R</span><span>² </span><span>scores of 0.5144 and 0.4351 respectively. In particular, </span> <span>quantum trail features such as trail velocity standard deviation (6.75% importance) and </span> <span>average streamline length (5.12% importance) rank highly among predictive features, vali- </span> <span>dating geometric interpretation. The implementation achieves numerical stability through </span> <span>4th-order finite differences and adaptive regularization, with deployment as a Google Cloud </span> <span>Function enabling real-time predictions. This work demonstrates that geometric interpreta- </span> <span>tions of quantum mechanics can yield practical ML features with potential applications in </span> <span>drug discovery, materials science, and quantum chemistry education.</span></p> |
| title | Machine Learning Applications of Quantum Trail Fields for Molecular Property Prediction |
| url | https://doi.org/10.5281/zenodo.17124006 |