An LSTM-PINN Hybrid Method to the specific problem of population forecasting
This work addresses the challenge of demographic forecasting for policy planning, though it appears incremental as it combines existing methods (LSTM and PINN) for a specific domain.
The authors tackled the problem of forecasting age-structured population dynamics under policy-driven fertility changes by proposing physics-informed deep learning frameworks (PINN and LSTM-PINN), which simulated population evolution from 2024 to 2054 and demonstrated the models' ability to reflect policy-sensitive demographic shifts.
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.