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

arXiv: https://arxiv.org/abs/2505.01819 · HTML: https://mlsanity.com/paper/2505.01819/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 14 references that are in the map.
- First posted on arXiv 3 May 2025.

## Builds on (most cited first, 2 of 2)

- [A Data-driven Crowd Simulation Framework Integrating Physics-informed Machine Learning with Navigation Potential Fields](https://mlsanity.com/paper/2410.16132/) (2024)
- [Modeling a demographic problem using the Leslie matrix](https://mlsanity.com/paper/2409.15147/) (2024)

## Built on by (most cited first, 1 of 1)

- [Forecasting India's Demographic Transition Under Fertility Policy Scenarios Using hybrid LSTM-PINN Model](https://mlsanity.com/paper/2512.00760/) (2025)

## Abstract (arXiv)

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.