贫困是一种复杂的动态挑战，难以通过预设的常微分方程充分刻画。当前，人工智能机器学习（ML）方法在建模真实世界动力系统方面已展现出显著潜力。其中，神经常微分方程（Neural ODEs）作为一种数据驱动方法，能够直接从观测数据中学习连续时间动力学，因而日益成为一种强大工具。本章将Neural ODE框架应用于印度奥里萨邦（Odisha）的贫困动态分析。具体而言，我们利用2007至2020年间关于经济发展与减贫关键指标的时间序列数据。在Neural ODE架构中，系统的时序梯度由一个多层感知机（MLP）表示；所得神经动力系统通过数值常微分方程（ODE）求解器进行积分，以获得状态变量随时间演化的轨迹。在反向传播过程中，采用伴随敏感性方法（adjoint sensitivity method）计算梯度，从而实现对ODE求解器的有效梯度回传。训练完成的Neural ODE模型能以高精度复现观测数据，表明其具备准确刻画混凝土结构住房家庭贫困指标动态演化的能力。结果表明，Neural ODE等机器学习方法可作为建模社会经济转型的有效工具，为政策制定者提供可靠的预测支持，助力更科学、更有效的减贫决策。

Poverty is a complex dynamic challenge that cannot be adequately captured using predefined differential equations. Nowadays, artificial machine learning (ML) methods have demonstrated significant potential in modelling real-world dynamical systems. Among these, Neural Ordinary Differential Equations (Neural ODEs) have emerged as a powerful, data-driven approach for learning continuous-time dynamics directly from observations. This chapter applies the Neural ODE framework to analyze poverty dynamics in the Indian state of Odisha. Specifically, we utilize time-series data from 2007 to 2020 on the key indicators of economic development and poverty reduction. Within the Neural ODE architecture, the temporal gradient of the system is represented by a multi-layer perceptron (MLP). The obtained neural dynamical system is integrated using a numerical ODE solver to obtain the trajectory of over time. In backpropagation, the adjoint sensitivity method is utilized for gradient computation during training to facilitate effective backpropagation through the ODE solver. The trained Neural ODE model reproduces the observed data with high accuracy. This demonstrates the capability of Neural ODE to capture the dynamics of the poverty indicator of concrete-structured households. The obtained results show that ML methods, such as Neural ODEs, can serve as effective tools for modeling socioeconomic transitions. It can provide policymakers with reliable projections, supporting more informed and effective decision-making for poverty alleviation.