Orateur
Description
Forecasting the future state of a dynamical system from observed time series is a central problem across science and engineering.
Classical autoregressive models offer simplicity and interpretability but struggle with complex nonlinear dynamics.
Deep learning architectures such as Recurrent Neural Networks overcome this limitation yet offer no physical guarantees, leading to unphysical extrapolations beyond the training window.
Hybrid approaches have emerged to combine the strengths of both paradigms: Physics-Informed Neural Networks (PINNs) incorporate known laws as penalty terms in the training loss, while Neural ODEs and Universal Differential Equations (UDEs) embed physical structure directly inside a differential equation.
In this talk, we present these different approaches and apply UDEs to forecasting water temperature at multiple depths in Lake Créteil (Paris region), where thermal stratification is crucial for predicting harmful algal blooms.
We benchmark the UDE against physics-based models and deep learning approaches, and also discuss the training methodology and new physics-coupling designs that improve learning.