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Action functional gradient descent algorithm for estimating escape paths in stochastic chemical reaction networks.

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  • 1Department of Physics, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA.

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We developed a new algorithm to estimate the most likely paths in complex chemical reaction networks. This method is dimension-independent and verified against existing techniques.

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Area of Science:

  • Mathematical Physics
  • Chemical Reaction Network Theory
  • Stochastic Processes

Background:

  • Continuous-time Markov processes are fundamental to modeling chemical reactions.
  • Estimating escape paths (first passage times) is crucial for understanding system dynamics.
  • Stochastic chemical reaction networks often exhibit complex behaviors with multiple stable states.

Purpose of the Study:

  • To derive the Hamilton-Jacobi theory for continuous-time Markov processes.
  • To develop a novel variational algorithm for estimating escape paths in stochastic chemical reaction networks.
  • To create a dimension-independent algorithm with verifiable accuracy.

Main Methods:

  • Derivation of Hamilton-Jacobi theory for Markov processes.
  • Development of a variational algorithm for path estimation.
  • Verification using shooting methods and stochastic simulations.

Main Results:

  • A dimension-independent variational algorithm for escape path estimation.
  • An easily calculable measure for solution correctness.
  • Successful verification against computationally intensive methods.

Conclusions:

  • The developed algorithm provides an efficient and accurate method for analyzing stochastic chemical reaction networks.
  • The approach bridges mathematical physics, numerical optimization, and chemical kinetics.
  • Potential applications span chemistry, biology, optimal control, and game theory.