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Neural Ordinary Differential Equations for Modeling Socio-Economic Dynamics

Sandeep Kumar Samota, Snehashish Chakraverty, Narayan Sethi

Abstract

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.

Neural Ordinary Differential Equations for Modeling Socio-Economic Dynamics

Abstract

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.

Paper Structure

This paper contains 25 sections, 31 equations, 8 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Residual Networks (ResNets)
  4. The Continuous-Time Analogy
  5. Neural Ordinary Differential Equations
  6. Numerical integration
  7. Training objective and gradients
  8. The Adjoint Sensitivity Method
  9. Neural ODEs for Poverty Dynamics
  10. Data Representation
  11. District Embeddings
  12. Encoder (GRU)
  13. District-Conditioned Neural ODE
  14. ODE Solver
  15. District-Conditioned Decoder
  16. ...and 10 more sections

Figures (8)

  • Figure 1: Visual representation of a Neural ODE. The input $\boldsymbol{z}(t_0)$ is evolved continuously to $\boldsymbol{z}(t_1)$ by an ODE solver. The dynamics of the evolution (the derivative) are defined by the neural network $f$, parameterized by $\theta$.
  • Figure 2: Schematic diagram of a GRU
  • Figure 3: Flow diagram of Neural ODE with district embeddings
  • Figure 4: Training Loss Curve: Log-scaled MSE loss over 1000 epochs, demonstrating stable convergence.
  • Figure 5: PCA Projection of Learned District Embeddings. Districts with similar poverty dynamics tend to cluster together, reflecting underlying structural groups.
  • ...and 3 more figures

Theorems & Definitions (1)

  • Definition 2.1: Neural ODE chen2018neural