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Closed-loop Neuro-robotic Experiments to Test Computational Properties of Neuronal Networks

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Predicting rare events using neural networks and short-trajectory data.

John Strahan¹, Justin Finkel², Aaron R Dinner^1,3

¹Department of Chemistry and James Franck Institute, the University of Chicago, Chicago, IL 60637.

Journal of Computational Physics

|June 19, 2023

Summary

Predicting rare events in complex systems is challenging. This study introduces a neural network approach to solve Feynman-Kac equations, enabling accurate statistical predictions from short simulation data, even for high-dimensional models.

Keywords:

Feynman-Kac equation Holton-Mass model adaptive sampling high-dimensional PDE neural network rare event

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Area of Science:

Computational Science
Applied Mathematics
Atmospheric Science

Background:

Accurate estimation of rare event statistics is crucial for modeling stochastic dynamical systems.
Direct simulation is often infeasible for rare events due to timescale mismatches.
Feynman-Kac equations offer a powerful framework for calculating these statistics.

Purpose of the Study:

To develop a novel method for solving Feynman-Kac equations using neural networks.
To enable accurate prediction of rare event statistics in complex systems.
To demonstrate the method's applicability to high-dimensional models and observational data.

Main Methods:

Training neural networks on short-trajectory data to approximate solutions to Feynman-Kac equations.
Employing a Markov approximation without assuming underlying model dynamics.
Developing an adaptive sampling strategy for efficient data acquisition.

Main Results:

The neural network approach accurately solves Feynman-Kac equations for rare event statistics.
The method is applicable to complex computational models and observational data.
Accurate statistics were computed for a 75-dimensional sudden stratospheric warming model.

Conclusions:

Neural network-based solutions to Feynman-Kac equations provide an effective approach for rare event statistics.
The method offers a flexible and powerful tool for complex dynamical systems.
This technique advances the ability to model and predict rare phenomena in various scientific domains.