Koopman Mode Analysis of agent-based models of logistics processes
Autoři:
James Hogg aff001; Maria Fonoberova aff001; Igor Mezić aff001; Ryan Mohr aff001
Působiště autorů:
Aimdyn, Inc., Santa Barbara, CA, United States of America
aff001; University of California Santa Barbara, Santa Barbara, CA, United States of America
aff002
Vyšlo v časopise:
PLoS ONE 14(9)
Kategorie:
Research Article
doi:
https://doi.org/10.1371/journal.pone.0222023
Souhrn
Modern logistics processes and systems can feature extremely complicated dynamics. Agent Based Modeling is emerging as a powerful modeling tool for design, analysis and control of such logistics systems. However, the complexity of the model itself can be overwhelming and mathematical meta-modeling tools are needed that aggregate information and enable fast and accurate decision making and control system design. Here we present Koopman Mode Analysis (KMA) as such a tool. KMA uncovers exponentially growing, decaying or oscillating collective patterns in dynamical data. We apply the methodology to two problems, both of which exhibit a bifurcation in dynamical behavior, but feature very different dynamics: Medical Treatment Facility (MTF) logistics and ship fueling (SF) logistics. The MTF problem features a transition between efficient operation at low casualty rates and inefficient operation beyond a critical casualty rate, while the SF problem features a transition between short mission life at low initial fuel levels and sustained mission beyond a critical initial fuel level. Both bifurcations are detected by analyzing the spectrum of the associated Koopman operator. Mathematical analysis is provided justifying the use of the Dynamic Mode Decomposition algorithm in punctuated linear decay dynamics that is featured in the SF problem.
Klíčová slova:
Physical sciences – Mathematics – Algebra – Linear algebra – Eigenvalues – Applied mathematics – Algorithms – Systems science – Agent-based modeling – Bifurcation theory – Materials science – Materials – Fuels – Chemistry – Chemical reactions – Decomposition – Engineering and technology – Energy and power – Research and analysis methods – Simulation and modeling – Computer and information sciences – Biology and life sciences – Psychology – Behavior – Social sciences
Zdroje
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PLOS One
2019 Číslo 9
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