Inference Design for the Uncertainty Quantification of Extreme-Scale Fluid Dynamics Simulations

Abstract

The quantification of uncertainties in modern computational fluid dynamics solvers poses significant computational challenges with individual simulations costing 100’s of thousands of CPU or GPU hours. Approaching such large simulation workflows with Bayesian Uncertainty Quantification, Bayesian inference at its core, hence requires the commitment of inordinate computational resources to the inference routine. To enable such large routines we hence have to exploit inherent model hierarchies to the fullest extent possible. To accelerate the sampling we build on advances in fields adjacent to uncertainty quantification, such as machine-learning based design, sequential decision making, and reinforcement learning to pose our problem as the design of a Multifidelity inference routine with intelligent sampling agents at its core. The intuition here is that the sampling agents learn the task- and problem-structure in their attention-based policy networks, which can then later be fine-tuned to similar inference problems. In this work we present a machine-learning based design approach to Bayesian Uncertainty Quantification inference routines, which is based on a graph network representation of the inference routine in combination with a Transformer-based placement network to exploit the available model hierarchies. The excessive training costs of the learned inference routine are amortized across later inference studies.