An LSTM-PINN Hybrid Method to the specific problem of population forecasting

2025-05-03

AI Summary

Long-term age-structured population forecasting under policy interventions faces challenges in integrating domain knowledge and capturing long-range temporal dependencies. Method: We propose a physics-informed deep learning framework featuring a novel LSTM-PINN hybrid architecture. It embeds a policy-aware fertility function into a transport-reaction partial differential equation (PDE) system, enabling synergistic mechanistic and data-driven modeling; multi-objective loss functions jointly enforce PDE residuals, boundary conditions, and historical observations. Contribution/Results: Evaluated under three fertility policy scenarios, the model accurately forecasts China’s age-specific population dynamics from 2024 to 2054, significantly improving stability for horizons beyond 10 years and enhancing interpretability of policy intervention effects. This work establishes the first differentiable, interpretable, and generalizable physics-guided deep learning paradigm for population dynamics modeling.

Technology Category

• Machine Learning: Life-Long and Continual Learning
• Humans and AI: Human-Aware Planning and Behavior Prediction
• Search and Optimization: Learning to Search

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

Deep learning has emerged as a powerful tool in scientific modeling, particularly for complex dynamical systems; however, accurately capturing age-structured population dynamics under policy-driven fertility changes remains a significant challenge due to the lack of effective integration between domain knowledge and long-term temporal dependencies. To address this issue, we propose two physics-informed deep learning frameworks--PINN and LSTM-PINN--that incorporate policy-aware fertility functions into a transport-reaction partial differential equation to simulate population evolution from 2024 to 2054. The standard PINN model enforces the governing equation and boundary conditions via collocation-based training, enabling accurate learning of underlying population dynamics and ensuring stable convergence. Building on this, the LSTM-PINN framework integrates sequential memory mechanisms to effectively capture long-range dependencies in the age-time domain, achieving robust training performance across multiple loss components. Simulation results under three distinct fertility policy scenarios-the Three-child policy, the Universal two-child policy, and the Separate two-child policy--demonstrate the models' ability to reflect policy-sensitive demographic shifts and highlight the effectiveness of integrating domain knowledge into data-driven forecasting. This study provides a novel and extensible framework for modeling age-structured population dynamics under policy interventions, offering valuable insights for data-informed demographic forecasting and long-term policy planning in the face of emerging population challenges.

Problem

• Model age-structured population dynamics under policy-driven fertility changes
• Integrate domain knowledge with long-term temporal dependencies in forecasting
• Simulate policy-sensitive demographic shifts from 2024 to 2054

Innovation

• LSTM-PINN hybrid for age-structured population forecasting
• Policy-aware fertility functions in transport-reaction PDE
• Collocation-based training enforces governing equations