Action Functional Gradient Descent algorithm for estimating escape paths in Stochastic Chemical Reaction Networks

Abstract

We first derive the Hamilton-Jacobi theory underlying continuous-time Markov processes, and then use the construction to develop a variational algorithm for estimating escape (least improbable or first passage) paths for a generic stochastic chemical reaction network that exhibits multiple fixed points. The design of our algorithm is such that it is independent of the underlying dimensionality of the system, the discretization control parameters are updated towards the continuum limit, and there is an easy-to-calculate measure for the correctness of its solution. We consider several applications of the algorithm and verify them against computationally expensive means such as the shooting method and stochastic simulation. While we employ theoretical techniques from mathematical physics, numerical optimization and chemical reaction network theory, we hope that our work finds practical applications with an inter-disciplinary audience including chemists, biologists, optimal control theorists and game theorists.

arXiv comment40 pages, 21 figures

References in corpus (12)

• A short introduction to the Lindblad Master Equation
• Functional determinants by contour integration methods
• A rare event algorithm links transitions in turbulent flows with activated nucleations
• Action Principle in Nonequilibrium Statistical Dynamics
• Large deviations and dynamical phase transitions in stochastic chemical networks
• Large-deviation principles, stochastic effective actions, path entropies, and the structure and meaning of thermodynamic descriptions
• Efficient Rare Event Simulation by Optimal Nonequilibrium Forcing
• Asymptotics of work distributions in a stochastically driven system
• Intrinsic and extrinsic thermodynamics for stochastic population processes with multi-level large-deviation structure
• Flows, scaling, and the control of moment hierarchies for stochastic chemical reaction networks
• Solving Moment Hierarchies for Chemical Reaction Networks
• Eikonal solutions for moment hierarchies of Chemical Reaction Networks in the limits of large particle number

Cited by in corpus (2)

• Field theories and quantum methods for stochastic reaction-diffusion systems
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