用物理信息神经网络拟合捕食-掠食者-腐食者模型,提升生态预测精度。
Predator Prey Scavenger Model using Holling's Functional Response of Type III and Physics-Informed Deep Neural Networks
- 基于霍林Ⅲ型功能响应构建三物种生态模型。
- 在美森林数据集上通过神经网络与优化算法估计参数。
- 结合物理约束与实测数据,实现动态系统稳定性分析。
非线性数学模型揭示自然界中物理与生物相互作用的关系。经典的洛特卡-沃尔泰拉模型描述了捕食者与猎物的互动,但真实生态系统中捕食者、腐食者和猎物共存,且腐食者可依赖捕食者尸体生存。本文提出并模拟了捕食-猎物-腐食者模型,假设猎物对捕食者的响应符合霍林Ⅲ型功能响应。模型在多种情景下表现良好。随后,使用美国森林数据集进行参数估计,采用物理信息深度神经网络结合Adam反向传播方法,有效避免参数更新中的梯度爆炸问题。网络训练目标为均方误差与物理约束误差。训练后,利用BFGS算法对参数进行微调。最终,基于真实数据估计的参数通过雅可比稳定性分析验证其稳定性。未来工作包括降低参数误差、分岔分析及参数敏感性研究。
原文摘要 · Abstract (English)
Nonlinear mathematical models introduce the relation between various physical and biological interactions present in nature. One of the most famous models is the Lotka-Volterra model which defined the interaction between predator and prey species present in nature. However, predators, scavengers, and prey populations coexist in a natural system where scavengers can additionally rely on the dead bodies of predators present in the system. Keeping this in mind, the formulation and simulation of the predator prey scavenger model is introduced in this paper. For the predation response, respective prey species are assumed to have Holling's functional response of type III. The proposed model is tested for various simulations and is found to be showing satisfactory results in different scenarios. After simulations, the American forest dataset is taken for parameter estimation which imitates the real-world case. For parameter estimation, a physics-informed deep neural network is used with the Adam backpropagation method which prevents the avalanche effect in trainable parameters updation. For neural networks, mean square error and physics-informed informed error are considered. After the neural network, the hence-found parameters are fine-tuned using the Broyden-Fletcher-Goldfarb-Shanno algorithm. Finally, the hence-found parameters using a natural dataset are tested for stability using Jacobian stability analysis. Future research work includes minimization of error induced by parameters, bifurcation analysis, and sensitivity analysis of the parameters.
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