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

• URL: http://arxiv.org/abs/2505.01819v1
• Date: Sat, 03 May 2025 13:50:53 GMT
• Title: An LSTM-PINN Hybrid Method to the specific problem of population forecasting
• Abstract summary: Policy-aware fertility functions are incorporated into a transport-reaction partial differential equation to simulate population evolution from 2024 to 2054.<n>The standard PINN model enforces the governing equation and boundary conditions via collocation-based training.<n>The LSTM-PINN framework integrates sequential memory mechanisms to effectively capture long-range dependencies in the age-time domain.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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