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Rare Event Detection Using Error-corrected DNA and RNA Sequencing
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Numerical computation of rare events via large deviation theory
Tobias Grafke1, Eric Vanden-Eijnden2
1Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom.
Chaos (Woodbury, N.Y.)
|July 4, 2019
Summary
This study presents rare event algorithms grounded in large deviation theory (LDT), offering numerical schemes and best practices for complex systems. It explores extensions and connections to other methods for enhanced computational efficiency.
Area of Science:
- Computational Physics
- Applied Mathematics
- Statistical Mechanics
Background:
- Rare event algorithms are crucial for simulating systems with infrequent but significant occurrences.
- Large deviation theory (LDT) provides a powerful mathematical framework for analyzing rare events.
- Existing numerical methods face challenges with complex systems, degenerate forcing, and infinite dimensions.
Purpose of the Study:
- To provide a comprehensive overview of rare event algorithms based on LDT.
- To discuss numerical schemes, best practices, and implementation tradeoffs.
- To propose generalizations and extensions of minimum action methods.
Main Methods:
- Review of numerical schemes for computing large deviation minimizers.
- Application of minimum action methods to various setups.
- Exploration of generalizations to non-Gaussian noise and random parameters.
- Integration with importance sampling techniques like genealogical algorithms.
Main Results:
- Demonstration of algorithms on example problems highlighting common difficulties.
- Analysis of challenges arising from degenerate/multiplicative forcing and infinite-dimensional systems.
- Discussion of connections to stochastic field theory and optimal control.
Conclusions:
- LDT-based rare event algorithms offer robust solutions for complex systems.
- Proposed generalizations enhance applicability to a wider range of stochastic processes.
- The integration with importance sampling improves efficiency for rare event simulation.
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