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Inexact iterative numerical linear algebra for neural network-based spectral estimation and rare-event prediction
John Strahan1, Spencer C Guo1, Chatipat Lorpaiboon1
1Department of Chemistry and James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA.
The Journal of Chemical Physics
|July 6, 2023
Summary
We developed new spectral estimation methods to analyze complex system dynamics. These techniques improve predictions of future events from trajectory data, aiding in fields like reinforcement learning.
Area of Science:
- Complex systems analysis
- Computational dynamics
- Machine learning
Background:
- Analyzing complex systems is difficult due to numerous degrees of freedom.
- Identifying key dynamics for predicting events is often challenging.
- Leading eigenfunctions of the transition operator aid visualization and statistical predictions.
Purpose of the Study:
- To develop inexact iterative linear algebra methods for spectral estimation.
- To enable predictions from datasets of short, finite-interval trajectories.
- To apply these methods to both low- and high-dimensional systems.
Main Methods:
- Inexact iterative linear algebra for spectral estimation.
- Computation of leading eigenfunctions of the transition operator.
- Application to simulated and biomolecular trajectory data.
Main Results:
- Successful computation of eigenfunctions for spectral estimation.
- Accurate prediction of event likelihood and average time from trajectory data.
- Demonstration on low- and high-dimensional models.
Conclusions:
- Developed efficient methods for spectral estimation and prediction in complex systems.
- These methods provide insights into system dynamics and aid event prediction.
- Potential applications in reinforcement learning and biomolecular dynamics are highlighted.
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