Speaker
Description
We present a novel hybrid computational framework designed to reconstruct the hidden dynamics of critical parameters in complex dynamical systems [1]. In many scientific applications, the predictive accuracy of physics-based models is often limited by the inaccurate extrapolation of time-varying parameters. To address this problem, we propose an hybrid framework that integrates Neural Ordinary Differential Equations (Neural ODEs) within a classical differential solver to learn the underlying evolution laws governing these parameters.
The architecture consists of a data-driven layer that models parameter trajectories as a function of exogenous signals and sample-specific latent variables. These learned parameters are then seamlessly integrated into a physics-based. To handle data heterogeneity and noise, we incorporate a data assimilation procedure that estimates latent input variables through an end-to-end optimization process.
From a numerical perspective, this approach leverages the flexibility of deep learning while maintaining the mathematical consistency of physical models. We validate the framework within the context of computational epidemiology, proving robustness with respect to noise and long-term stability compared to traditional emulators. Numerical results entail that this hybrid strategy is effective for discovering parameter laws and it is especially reliable for long-term forecasting in noisy, real-world scenarios.
[1] Ziarelli, G., Pagani, S., Parolini, N., Regazzoni, F., & Verani, M. (2025). A model learning framework for inferring the dynamics of transmission rate depending on exogenous variables for epidemic forecasts. Computer Methods in Applied Mechanics and Engineering, 437, 117796.