# Modeling COVID-19 Dynamics in German States Using Physics-Informed Neural Networks

arXiv: https://arxiv.org/abs/2510.06776 · HTML: https://mlsanity.com/paper/2510.06776/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 32 references that are in the map.
- First posted on arXiv 8 Oct 2025.

## Builds on (most cited first, 5 of 5)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Activation Functions in Deep Learning: A Comprehensive Survey and Benchmark](https://mlsanity.com/paper/2109.14545/) (2021)
- [Data-driven approaches for predicting spread of infectious diseases through DINNs: Disease Informed Neural Networks](https://mlsanity.com/paper/2110.05445/) (2021)
- [Approaching epidemiological dynamics of COVID-19 with physics-informed neural networks](https://mlsanity.com/paper/2302.08796/) (2023)

## Abstract (arXiv)

The COVID-19 pandemic has highlighted the need for quantitative modeling and analysis to understand real-world disease dynamics. In particular, post hoc analyses using compartmental models offer valuable insights into the effectiveness of public health interventions, such as vaccination strategies and containment policies. However, such compartmental models like SIR (Susceptible-Infectious-Recovered) often face limitations in directly incorporating noisy observational data. In this work, we employ Physics-Informed Neural Networks (PINNs) to solve the inverse problem of the SIR model using infection data from the Robert Koch Institute (RKI). Our main contribution is a fine-grained, spatio-temporal analysis of COVID-19 dynamics across all German federal states over a three-year period. We estimate state-specific transmission and recovery parameters and time-varying reproduction number (R_t) to track the pandemic progression. The results highlight strong variations in transmission behavior across regions, revealing correlations with vaccination uptake and temporal patterns associated with major pandemic phases. Our findings demonstrate the utility of PINNs in localized, long-term epidemiological modeling.