Correlating Structure with Dynamics in Supercooled Liquids Using Machine Learning Tools Open Access
Obadiya, Tomilola M. (Spring 2025)
Abstract
Understanding the relationship between structure and dynamics in supercooled liquids remains a central challenge in glass physics. Machine learning techniques, particularly Support Vector Classification (SVC), have provided insights into structural predictors of dynamics, such as the “softness” order parameter, which correlates with energy barriers for particle rearrangements. This dissertation critically examines the methodology and interpretability of machine learning models in this context, focusing on their ability to predict rearrangement probabilities and energy barriers. We first investigate whether classification hyperplanes trained on structural data from high-temperature, diffusive regimes can predict energy barriers in the supercooled regime. By introducing a Z-score-based binning approach, we demonstrate that structural features associated with purely diffusive motion retain predictive power for activated events, challenging conventional assumptions about structure-dynamics correlations at high temperatures. Building on this, we explore the physical interpretability of various regression-based machine learning models, including Ridge Regression, Support Vector Regression, and Multilayer Perceptron, in predicting energy barriers. Our analysis, leveraging the iso-configurational ensembles, shows that these models capture similar structural signatures as SVC, reinforcing the idea that predictive success is rooted in the ability to learn high-dimensional structure-dynamics relationships. We then extend our investigation to the role of memory effects in supercooled liquids, using softness as a structural order parameter to probe system responses under thermal cycling. Preliminary findings suggest that supercooled liquids exhibit memory effects typically associated with glasses, raising new questions about the glass transition. This dissertation highlights key challenges in using machine learning to understand glassy dynamics, particularly regarding feature selection, model interpretability, and the physical significance of learned representations. Our findings contribute to ongoing efforts to develop more robust and interpretable machine learning frameworks for studying supercooled liquids and other complex systems.
Table of Contents
1. Introduction 1
1.1. Background and Motivation ....................... 1
1.2. Kob-Andersen glass model........................ 4
1.3. Dynamical Heterogeneity......................... 5
1.4. Relaxation Behavior in Supercooled Liquids . . . . . . . . . . . . . . 7
1.5. The Potential Energy Landscape .................... 13
1.6. Challenge in defining an order parameter correlating structure with dynamics ................................. 15
1.6.1. Particle Mobility from Iso-configurational ensemble . . . . . . 16
1.6.2. Correlating structure and dynamics through machine learning 17
1.7. Dissertation: Challenges in correlating structure with dynamics in supercooled liquids using machine learning tools . . . . . . . . . . . . . 23
1.8. Dissertation Outline and Contributions................. 24
2. Using fluid structures to encode predictions of glassy dynamics 27
2.1. Introduction................................ 27
2.2. Methods.................................. 30
2.2.1. Model and simulations ...................... 30
2.2.2. Local structure and dynamics .................. 32
2.2.3. Machine learning protocol .................... 33
2.3. Classification in the fluid phase ..................... 35
2.4. Interpretability of fluidity and softness . . . . . . . . . . . . . . . . . 38
2.5. Discussion................................. 40
3. Machine Learning of Energy Barriers to Rearrangements from Local Structure in Supercooled Liquids 46
3.1. Introduction................................ 47
3.2. Methods.................................. 50
3.2.1. Model and Simulations...................... 50
3.2.2. Identifying Rearrangements ................... 52
3.2.3. Structural descriptors....................... 52
3.2.4. Standard training datasets.................... 54
3.3. Inferring energy barriers with different data-driven approaches . . . . 54
3.3.1. Correlating structure with dynamics using linear models . . . 54
3.3.2. Inferring energy barriers ..................... 56
3.3.3. Correlating structure with dynamics using non-linear models . 61
3.4. Impact of structural descriptors on model performance . . . . . . . . 62
3.5. Impact of dynamical labels on model performance . . . . . . . . . . . 65
3.6. Conclusion................................. 66
4. Ongoing Work on Memory Effect in Supercooled Liquid 70
4.1. Introduction................................ 70
4.2. Methods.................................. 74
4.2.1. Model and Simulations...................... 74
4.2.2. Temperature Cycle ........................ 75
4.3. Results................................... 76
4.4. Discussion................................. 76
4.5. FutureDirections............................. 78
5. Conclusion 80
5.1. Open Questions and Future Directions ................. 81
5.2. Final Remarks............................... 83
Appendix A: Supplemental Information to Chapter 3 84
A.0.1. Mean trend for softness and log of the probability of rearrangement................................ 84
A.0.2. Definition of Cumulative Squared Displacement (CSD) ............................... 85
A.0.3. Influence of the ratio of training examples to model parameters........................ 86
Bibliography 87
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