Reduced Markovian models of dynamical systems

Giorgini, Ludovico Theo; Souza, Andre N.; Schmid, Peter J.

doi:10.1016/j.physd.2024.134393

Physica D: Nonlinear Phenomena

2024

DOI: 10.1016/j.physd.2024.134393

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Reduced Markovian models of dynamical systems

Ludovico Theo Giorgini,

Andre N. Souza,

Peter J. Schmid

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2024

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Representing turbulent statistics with partitions of state space. Part 1. Theory and methodology

Souza

2024

J. Fluid Mech.

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This is the first of a two-part paper. We formulate a data-driven method for constructing finite-volume discretizations of an arbitrary dynamical system's underlying Liouville/Fokker–Planck equation. A method is employed that allows for flexibility in partitioning state space, generalizes to function spaces, applies to arbitrarily long sequences of time-series data, is robust to noise and quantifies uncertainty with respect to finite sample effects. After applying the method, one is left with Markov states (cell centres) and a random matrix approximation to the generator. When used in tandem, they emulate the statistics of the underlying system. We illustrate the method on the Lorenz equations (a three-dimensional ordinary differential equation) saving a fluid dynamical application for Part 2 (Souza, J. Fluid Mech., vol. 997, 2024, A2).

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Representing turbulent statistics with partitions of state space. Part 1. Theory and methodology

Souza

2024

J. Fluid Mech.

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Reduced Markovian models of dynamical systems

Cited by 1 publication

References 31 publications

Representing turbulent statistics with partitions of state space. Part 1. Theory and methodology

Representing turbulent statistics with partitions of state space. Part 1. Theory and methodology

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