An LSTM-PINN Hybrid Method to the specific problem of population forecasting
Ze Tao
TL;DR
This work addresses forecasting age-structured populations under fertility-policy changes by integrating domain knowledge with data-driven learning through physics-informed neural networks. It introduces two frameworks, PINN and LSTM-PINN, that embed policy-driven fertility functions into a transport-reaction PDE to model population evolution from $2024$ to $2054$, with LSTM-PINN adding memory to capture long-range temporal dependencies. Across three policy scenarios, the methods demonstrate stable training, interpretable policy-sensitive projections, and a principled pathway for data-informed demographic forecasting under policy interventions. The approach offers a scalable, extensible tool for long-term demographic planning and policy assessment, with code made publicly available on GitHub.
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.