# Controlling mean exit time of stochastic dynamical systems based on quasipotential and machine learning

@article{Li2022ControllingME, title={Controlling mean exit time of stochastic dynamical systems based on quasipotential and machine learning}, author={Yang Li and Shenglan Yuan and Shengyuan Xu}, journal={ArXiv}, year={2022}, volume={abs/2209.13098} }

The mean exit time escaping basin of attraction in the presence of white noise is of practical importance in various scientiﬁc ﬁelds. In this work, we propose a strategy to control mean exit time of general stochastic dynamical systems to achieve a desired value based on the quasipotential concept and machine learning. Speciﬁcally, we develop a neural network architecture to compute the global quasipotential function. Then we design a systematic iterated numerical algorithm to calculate the…

## One Citation

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## References

SHOWING 1-10 OF 37 REFERENCES

### Machine learning framework for computing the most probable paths of stochastic dynamical systems.

- Computer SciencePhysical review. E
- 2021

A machine learning framework to compute the most probable paths in the sense of Onsager-Machlup action functional theory and reformulate the boundary value problem of a Hamiltonian system and design a neural network to remedy the shortcomings of the shooting method.

### A machine learning method for computing quasi-potential of stochastic dynamical systems

- Computer ScienceNonlinear Dynamics
- 2022

A machine learning method to compute the quasi-potential of stochastic dynamical systems via WKB approximation based on the Hamilton-Jacobi equation, which provides an effective tool in exploring the internal mechanisms of rare events triggered by random perturbations in various scientific fields.

### Most probable dynamics of stochastic dynamical systems with exponentially light jump fluctuations.

- PhysicsChaos
- 2020

Although the most probable exit paths are analogous to the Gaussian case for the isotropic noise, the anisotropic noise leads to significant changes in the structure of the exit paths and shed light on the underlying qualitative mechanism and quantitative feature of theexit phenomenon induced by non-Gaussian noise.

### Stochastic bifurcation for two-time-scale dynamical system with α-stable Lévy noise

- Mathematics
- 2021

This work focuses on stochastic bifurcation for a slow–fast dynamical system driven by non-Gaussian α-stable Lévy noise. We prove the main result for the stochastic equilibrium states for the…

### A Data-Driven Approach for Discovering Stochastic Dynamical Systems with Non-Gaussian Levy Noise

- Computer ScienceArXiv
- 2020

### Slow manifolds for dynamical systems with non-Gaussian stable Lévy noise

- MathematicsAnalysis and Applications
- 2019

This work is concerned with the dynamics of a class of slow–fast stochastic dynamical systems driven by non-Gaussian stable Lévy noise with a scale parameter. Slow manifolds with exponentially…

### The geometric minimum action method: A least action principle on the space of curves

- Computer Science
- 2008

An algorithm to compute the quasi‐potential in the theory is proposed, which is the key object to quantify the dynamics on long time scales when the effect of the noise becomes ubiquitous: the equilibrium distribution of the system, the pathways of transition between metastable states and their rate, etc., can all be expressed in terms of the quasi-potential.

### Limiting Exit Location Distributions in the Stochastic Exit Problem

- MathematicsSIAM J. Appl. Math.
- 1997

It is shown using formal methods that the asymptotic form of the exit location distribution on $\partial\Omega$ is generically non-Gaussian and asymmetric, and classify the possible limiting distributions.

### Crossing the quasi-threshold manifold of a noise-driven excitable system

- PhysicsProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2017

It is found that varying the noise term in the slow variable would dramatically raise the whole level of quasi-potentials, leading to significant changes in both patterns of optimal paths and exit locations.

### A Primer on Noise-Induced Transitions in Applied Dynamical Systems

- PhysicsSIAM Rev.
- 2018

An overview of the theory underlying the dynamics of rare events for stochastic models along with some example applications is provided.