Stochastic forest transition model dynamics and parameter estimation via deep learning

Satoshi Kumabe; Tianyu Song; Tôn Việt Tạ; Satoshi Kumabe; Tianyu Song; Tôn Việt Tạ

doi:10.3934/mbe.2025046

Mathematical Biosciences and Engineering

2025, Volume 22, Issue 5: 1243-1262. doi: 10.3934/mbe.2025046

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Research article

Stochastic forest transition model dynamics and parameter estimation via deep learning

1.
Joint Graduate School of Mathematics for Innovation, Kyushu University, 744 Motooka Nishi Ward, Fukuoka 819-0395, Japan
2.
Graduate School of Bioresource and Bioenvironmental Sciences, Kyushu University, 744 Motooka Nishi Ward, Fukuoka 819-0395, Japan
3.
Center for Promotion of International Education and Research, Faculty of Agriculture, Kyushu University, 744 Motooka Nishi Ward, Fukuoka 819-0395, Japan

Academic Editor: Yang Kuang

Received: 07 February 2025 Revised: 10 April 2025 Accepted: 15 April 2025 Published: 18 April 2025

Forest transitions, characterized by dynamic shifts between forest, agricultural, and abandoned lands, are complex phenomena. This study developed a stochastic differential equation model to capture the intricate dynamics of these transitions. We established the existence of global positive solutions for the model and conducted numerical analyses to assess the impact of model parameters on deforestation incentives. To address the challenge of parameter estimation, we proposed a novel deep learning approach that estimates all model parameters from a single sample containing time-series observations of forest and agricultural land proportions. This innovative approach enables us to understand forest transition dynamics and deforestation trends at any future time.
- forest transition,
- stochastic differential equations,
- deep learning
Citation: Satoshi Kumabe, Tianyu Song, Tôn Việt Tạ. Stochastic forest transition model dynamics and parameter estimation via deep learning[J]. Mathematical Biosciences and Engineering, 2025, 22(5): 1243-1262. doi: 10.3934/mbe.2025046

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Abstract

Forest transitions, characterized by dynamic shifts between forest, agricultural, and abandoned lands, are complex phenomena. This study developed a stochastic differential equation model to capture the intricate dynamics of these transitions. We established the existence of global positive solutions for the model and conducted numerical analyses to assess the impact of model parameters on deforestation incentives. To address the challenge of parameter estimation, we proposed a novel deep learning approach that estimates all model parameters from a single sample containing time-series observations of forest and agricultural land proportions. This innovative approach enables us to understand forest transition dynamics and deforestation trends at any future time.

References

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