Generalization and robustness of learned simulators (GRLSim)

Machine learning is increasingly used as a surrogate for numerical PDE solvers. Several methods have been proposed ranging from physics-informed neural networks to autoregressive and message-passing-based methods. With this project, we aim to analyze and improve the robustness and generalization behavior of ML-based surrogate models. Classical numerical solvers often trade off accuracy and computational efficiency. Their advantage is their ability to be accurate for any given PDE as long as the discretization and other parameters are properly chosen. While ML models are efficient at prediction time, they require a substantial amount of resources during training. In order to use machine learning-based surrogate models more flexibly, it would be necessary for them to generalize to situations unseen during training. Examples of such situations are (1) new parameter values of parametric PDEs; (2) generalization to higher spatial resolutions; and (3) generalization to more time steps into the future than experienced during training. While some existing ML methods have been shown to achieve limited success in either of these three settings, we are not aware of any principled study on the generalization behavior of surrogate model classes and methods that aim to generalize with respect to two or more generalization types. We aim to close this gap with the proposed project.