MP-PINN: A Multi-Phase Physics-Informed Neural Network for Epidemic Forecasting

TL;DR

A new hybrid method called MP-PINN (Multi-Phase Physics-Informed Neural Network) is proposed to overcome the limitations of these two major approaches to long-term forecasting of temporal processes such as virus spreading in epidemics.

Abstract

Forecasting temporal processes such as virus spreading in epidemics often requires more than just observed time-series data, especially at the beginning of a wave when data is limited. Traditional methods employ mechanistic models like the SIR family, which make strong assumptions about the underlying spreading process, often represented as a small set of compact differential equations. Data-driven methods such as deep neural networks make no such assumptions and can capture the generative process in more detail, but fail in long-term forecasting due to data limitations. We propose a new hybrid method called MP-PINN (Multi-Phase Physics-Informed Neural Network) to overcome the limitations of these two major approaches. MP-PINN instils the spreading mechanism into a neural network, enabling the mechanism to update in phases over time, reflecting the dynamics of the epidemics due to policy interventions. Experiments on COVID-19 waves demonstrate that MP-PINN achieves superior performance over pure data-driven or model-driven approaches for both short-term and long-term forecasting.

Figures (6)

• Figure 1: A representative case of forecasting COVID-19 at 35 days of the wave. Our hybrid multi-phase method $\text{MP-PINN}$ strikes a balance between model-driven and data-driven approaches, and hence is more accurate in both short/long-term forecasting.
• Figure 2: Multi-phase Physics-Informed Neural Network ($\text{MP-PINN}$) Framework for Epidemic Forecasting. The framework illustrates the integration of expert knowledge and data-driven approaches to estimate parameters in a multi-phase scenario, where key parameters such as infection rate $\left(\beta\right)$ and recovery rate $\left(\gamma\right)$ vary across phases.
• Figure 3: The map of Italy with 21 regions created using Geopandas geopandas and data from the GeoJSON file openpolis2024.
• Figure 4: Forecasting examples of short-term (next 30 days) and long-term (beyond 30 days) demonstrating the superior performance of PINNs like $\text{SP-PINN}$ and $\text{MP-PINN}$ compared to pure model-driven (SIR) and data-driven (MLP) methods. The background colours indicate the training period (white), short-term forecasting horizon (blue), and long-term forecasting horizon (red).
• Figure 5: Forecasting examples showcasing the importance of multi-phase modelling in $\text{MP-PINN}$. When the dynamics changes, single models are inadequate. The background colours indicate the training period (white), short-term forecasting horizon (blue), and long-term forecasting horizon (red).