Abstract:

Scientific simulations in the natural sciences are mathematical and computational models that are being used to represent physical processes and interactions from real-world phenomenon such as radiative transfer, cloud formation or turbulent mixing. Traditional equation-based simulation methods are usually captured by Partial Differential Equations (PDEs), which are expensive to solve numerically. Recently, deep learning-based methods have been developed for accelerating these simulations themselves, contributing to faster PDE solvers through deep learning based surrogate models. Since in simulation studies it is of interest to predict and generate possible futures, generative models pose an attractive model candidate. In this research proposal, we propose the use of normalizing flows, a class of invertible generative models which exhibit stable training procedure, efficient sampling and inference properties and allows for predictive uncertainty quantification while allowing for exact log-likelihood computation on continuous data. We hypothesize the method would be of orders of magnitude faster than traditional time-dependent PDE solvers, as well as performance gains in terms of computational efficiency and stability in terms of accuracy over long rollout periods.