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Analyzing Russia–Ukraine War Patterns Based on Lanchester Model Using SINDy Algorithm

Author

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  • Daewon Chung

    (Department of Mathematics, Keimyung University, Daegu 42601, Republic of Korea)

  • Byeongseon Jeong

    (Department of Mathematics, Keimyung University, Daegu 42601, Republic of Korea)

Abstract

In this paper, we present an effective method for analyzing patterns in the Russia–Ukraine war based on the Lanchester model. Due to the limited availability of information on combat powers of engaging forces, we utilize the loss of armored equipment as the primary data source. To capture the intricate dynamics of modern warfare, we partition the combat loss data into disjoint subsets by examining their geometric properties. Separate systems of ordinary differential equations for these subsets are then identified using the Sparse Identification of Nonlinear Dynamics (SINDy) algorithm under a generalized formulation of the historical Lanchester model. We provide simulations of our method to demonstrate its effectiveness and performance in analyzing contemporary warfare dynamics.

Suggested Citation

  • Daewon Chung & Byeongseon Jeong, 2024. "Analyzing Russia–Ukraine War Patterns Based on Lanchester Model Using SINDy Algorithm," Mathematics, MDPI, vol. 12(6), pages 1-14, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:6:p:851-:d:1356953
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    References listed on IDEAS

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    1. Wei, Baolei, 2022. "Sparse dynamical system identification with simultaneous structural parameters and initial condition estimation," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    2. Duffey, Romney B, 2017. "Dynamic theory of losses in wars and conflicts," European Journal of Operational Research, Elsevier, vol. 261(3), pages 1013-1027.
    3. N. Cangiotti & M. Capolli & M. Sensi, 2023. "A generalization of unaimed fire Lanchester’s model in multi-battle warfare," Operational Research, Springer, vol. 23(2), pages 1-19, June.
    4. Dean S. Hartley & Robert L. Helmbold, 1995. "Validating Lanchester's square law and other attrition models," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(4), pages 609-633, June.
    5. Herbert K. Weiss, 1966. "Combat Models and Historical Data: The U.S. Civil War," Operations Research, INFORMS, vol. 14(5), pages 759-790, October.
    6. R. H. Peterson, 1967. "Letter to the Editor—On the “Logarithmic Law” of Attrition and its Application to Tank Combat," Operations Research, INFORMS, vol. 15(3), pages 557-558, June.
    7. Marvin B. Schaffer, 1968. "Lanchester Models of Guerrilla Engagements," Operations Research, INFORMS, vol. 16(3), pages 457-488, June.
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