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| Main Author: | |
|---|---|
| Format: | Recurso digital |
| Language: | English |
| Published: |
Zenodo
2025
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| Online Access: | https://doi.org/10.5281/zenodo.17124006 |
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Table of 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>