A Koopman-PINN Framework for Epidemic Models: Parameter Inference and Forecasting

2026-06-16 · Source: stat.ML updates on arXiv.org · Field: Science & Research — Mathematics & Computational Sciences, Health & Medical Research, Research Methodology & Innovation · Depth: Expert, extended

Summary

A Koopman-enhanced physics-informed neural network (K–PINN) framework is proposed for parameter inference and forecasting in nonlinear epidemic models. This method integrates Koopman operator theory, which maps epidemic states into a latent observable space for approximately linear dynamics, with physics-informed learning, enforcing governing equations via automatic differentiation. This combination enhances interpretability, parameter identifiability, and long-term predictive stability. The framework was applied to a normalized SEIRSD epidemic model, evaluated using synthetic monkeypox (Mpox) data and real-world SARS-CoV-2 datasets from Germany, Morocco, and Sweden. Numerical results consistently demonstrate that K–PINN achieves superior parameter estimation, trajectory reconstruction, and long-term forecasting compared to classical PINNs and Koopman-EDMD methods.

Key takeaway

For AI Scientists developing robust epidemic models, the Koopman-enhanced PINN (K–PINN) framework offers superior long-term forecasting and parameter identifiability. You should consider integrating this hybrid approach, which combines Koopman operator theory for latent linearization with physics-informed learning, to overcome limitations of classical methods. This is particularly beneficial when working with sparse or noisy real-world epidemiological data, ensuring more accurate and stable predictions.

Key insights

The K–PINN framework combines Koopman linearization with physics-informed learning for robust epidemic modeling and forecasting.

Principles

• Koopman operators linearize nonlinear dynamics in a lifted observable space.
• Physics-informed learning enforces governing equations through automatic differentiation.
• Combining these improves parameter identifiability and predictive stability.

Method

The K–PINN uses a neural lifting architecture to learn Koopman observables, evolves latent variables linearly, reconstructs states via a decoder, and enforces SEIRSD equations through a physics-informed loss function.

In practice

• Use NSFD schemes for generating reliable synthetic training data.
• Employ a two-stage optimization: Adam for exploration, L-BFGS for refinement.
• Parameterize rates (e.g., β, σ, γ, μ) using exp(˜·) for unconstrained optimization.

Topics

• Epidemic Modeling
• Koopman Operator Theory
• Physics-Informed Neural Networks
• Parameter Estimation
• Time Series Forecasting
• SEIRSD Model
• Nonstandard Finite Difference

Code references

• jgehrcke/covid-19-germany-gae

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.