Predictive reduced order models of tsunamis via neural Galerkin-projection and heirarchical pooling

Reduced order models (ROMs) often posit that the state of a dynamical system can be decomposed into temporal weights that activate spatial bases. By projecting these bases back onto the state's governing partial differential equations, we form a system of ordinary differential equations that describe how those temporal weights evolve, called a Galerkin-Projection ROM (GP-ROM). New extensions of this method based on differentiable programming known as neuralGP-ROMs can then be used to stabilize these equations to unprecedented levels of accuracy. Since these neuralGP-ROMs are based on the spatial basis from which they are constructed, they are typically valid for some deviations from the original basis. In the case of tsunamis, this implies that spatial basis of one tsunami (a reference model) may also be used to describe another (a test model) nearby or of slightly varying earthquake magnitude, with acceptable accuracy. In this presentation, we describe how this can be accomplished using a hierarchical pooling method that parameterizes our neural GP-ROMs to ensure that our models provide interpretable, accurate representations of these tsunamis. We demonstrate that a neural GP-ROM built on the basis of one realization can be leveraged to model another realization's dynamics in the neighborhood and predict unseen trajectories.