Towards an Observationally Meaningful, Explainable Emulator for the Boussinesq equation

The demand for emulators of expensive computational models is rapidly surging, as search, optimization, and uncertainty quantification tasks become increasingly more relevant than the computation of single simulation configurations. Along with traditional methods that explore a model’s configuration space efficiently and accurately, relatively more recent AI algorithms have started to play a role in the construction of simulation emulators. In particular, auto-encoder networks have been deployed in a variety of domains, as they not only can ingest simulation data and enable the fast evaluation of specific observables, but also provide a degree of transparency into the evaluation process and relate the predicted values to the model’s configuration variables through simple, low-dimensional representations. We apply a recent proposal, based on a modified Variational Auto-Encoder architecture, to a 2D coastal inundation model based on the Boussinesq equation, and evaluate its ability to learn the relationship between the model controls and the observed water levels at a predefined location. We also propose two routes to use this representation as the central component of an emulator, and assess their respective viability.