Data-Driven Dynamics: Learning Vector Fields for Epidemic Forecasting with Neural ODEs

We explore the framework of Neural Ordinary Differential Equations (Neural ODEs), a continuous-depth generalization of Residual Networks. By defining the hidden state dynamics as a neural network, this approach treats the neural network as a learnable vector field rather than a discrete map. We illustrate this concept by reconstructing known dynamics from synthetic data, demonstrating the model’s ability to capture underlying physical laws. Finally, we apply Neural ODEs to real-world epidemiological forecasting. We compare their performance against traditional compartmental models, highlighting that while compartmental models offer rigid structural priors, Neural ODEs provide superior flexibility and robustness when handling complex, irregularly sampled observational data.

Nov 28, 2025 12:00 AM