Recovering missing CFD data for high-order discretizations using deep neural networks and dynamics learning
For practitioners of large-scale CFD simulations, this work offers a way to reduce disk storage requirements while enabling accurate post-hoc data recovery, though it is an incremental improvement combining existing techniques.
The paper addresses the bottleneck of data I/O in large-scale CFD simulations by proposing a two-stage method (autoencoders + PCA for dimensionality reduction, kernel methods for dynamics learning) that recovers missing high-order CFD data from sparse time samples. On a 13-million-degree-of-freedom example, the method accurately reconstructs field quantities a posteriori.
Data I/O poses a significant bottleneck in large-scale CFD simulations; thus, practitioners would like to significantly reduce the number of times the solution is saved to disk, yet retain the ability to recover any field quantity (at any time instance) a posteriori. The objective of this work is therefore to accurately recover missing CFD data a posteriori at any time instance, given that the solution has been written to disk at only a relatively small number of time instances. We consider in particular high-order discretizations (e.g., discontinuous Galerkin), as such techniques are becoming increasingly popular for the simulation of highly separated flows. To satisfy this objective, this work proposes a methodology consisting of two stages: 1) dimensionality reduction and 2) dynamics learning. For dimensionality reduction, we propose a novel hierarchical approach. First, the method reduces the number of degrees of freedom within each element of the high-order discretization by applying autoencoders from deep learning. Second, the methodology applies principal component analysis to compress the global vector of encodings. This leads to a low-dimensional state, which associates with a nonlinear embedding of the original CFD data. For dynamics learning, we propose to apply regression techniques (e.g., kernel methods) to learn the discrete-time velocity characterizing the time evolution of this low-dimensional state. A numerical example on a large-scale CFD example characterized by nearly 13 million degrees of freedom illustrates the suitability of the proposed method in an industrial setting.