用深度学习统一建模捕食者-猎物系统的时空动态,兼顾物理规律与计算效率。
Unified Spatiotemporal Physics-Informed Learning (USPIL): A Framework for Modeling Complex Predator-Prey Dynamics
- 融合物理约束与神经网络,统一处理微分方程组的时序与空间模式。
- 在1D系统中达98.9%相关性,2D螺旋波模式相关性0.94,损失低至0.0219。
- 支持参数发现与敏感性分析,适合生态预测与多尺度建模研究者。
生态系统表现出复杂的多尺度动态,传统建模方法面临挑战。本文提出统一时空物理信息学习框架(USPIL),结合物理信息神经网络(PINNs)与守恒定律,用于跨尺度建模捕食者-猎物动力学。该框架统一求解常微分方程(ODE)与偏微分方程(PDE)系统,同时描述时间振荡与反应-扩散模式。通过自动微分施加物理约束,并采用自适应损失权重平衡数据拟合与物理一致性。应用于洛特卡-沃尔泰拉系统,在1D时序动态中实现98.9%相关性(损失:0.0219,平均绝对误差:0.0184),在2D系统中成功捕捉复杂螺旋波(损失:4.7656,模式相关性:0.94)。验证表明守恒律偏差小于0.5%,推理速度比数值求解器快10-50倍。该框架支持可解释的物理约束,实现参数发现与敏感性分析,是纯数据驱动方法无法做到的。其跨维度建模能力为多尺度生态建模开辟新路径。这些特性使USPIL成为生态预测、保护规划与生态系统韧性研究的强大工具,确立了物理信息深度学习作为科学严谨范式的地位。
原文摘要 · Abstract (English)
Ecological systems exhibit complex multi-scale dynamics that challenge traditional modeling. New methods must capture temporal oscillations and emergent spatiotemporal patterns while adhering to conservation principles. We present the Unified Spatiotemporal Physics-Informed Learning (USPIL) framework, a deep learning architecture integrating physics-informed neural networks (PINNs) and conservation laws to model predator-prey dynamics across dimensional scales. The framework provides a unified solution for both ordinary (ODE) and partial (PDE) differential equation systems, describing temporal cycles and reaction-diffusion patterns within a single neural network architecture. Our methodology uses automatic differentiation to enforce physics constraints and adaptive loss weighting to balance data fidelity with physical consistency. Applied to the Lotka-Volterra system, USPIL achieves 98.9% correlation for 1D temporal dynamics (loss: 0.0219, MAE: 0.0184) and captures complex spiral waves in 2D systems (loss: 4.7656, pattern correlation: 0.94). Validation confirms conservation law adherence within 0.5% and shows a 10-50x computational speedup for inference compared to numerical solvers. USPIL also enables mechanistic understanding through interpretable physics constraints, facilitating parameter discovery and sensitivity analysis not possible with purely data-driven methods. Its ability to transition between dimensional formulations opens new avenues for multi-scale ecological modeling. These capabilities make USPIL a transformative tool for ecological forecasting, conservation planning, and understanding ecosystem resilience, establishing physics-informed deep learning as a powerful and scientifically rigorous paradigm.
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