Physics-informed neural networks

Another way to leverage machine learning models with first principles is using ‘‘physics-informed neural networks’’ (PINNs). PINNs are used for solving partial differential equations (PDEs) where the solution of these PDEs is parametrized with a neural network. To enable this, PINNs make use of the flexibility provided by automatic differentiation by enforcing the PDEs at so-called collocation points. We am interested in how PINNs can be used in a probabilistic setting [C22, W1], with a special focus on dynamical systems.

References

[C22] P. Pilar and N. Wahlström. Physics-informed neural networks with unknown measurement noise. Learning for Dynamics \& Control Conference, Oxford, July (2024).
[W1] [P. Pilar, M. Heinonen, and N. Wahlström. Repulsive Ensembles for Uncertainty Estimation in PINNs (2025) (working manuscript)