Deep Neural Networks to Correct Sub-Precision Errors in CFD
This addresses precision-related errors in CFD simulations for researchers and engineers, but it is incremental as it extends existing machine learning techniques to a new error type.
The paper tackled errors in computational fluid dynamics (CFD) simulations caused by low 16-bit floating-point precision, by developing a hybrid solver combining a convolutional neural network with a differentiable 16-bit solver to improve accuracy metrics.
Information loss in numerical physics simulations can arise from various sources when solving discretized partial differential equations. In particular, errors related to numerical precision ("sub-precision errors") can accumulate in the quantities of interest when the simulations are performed using low-precision 16-bit floating-point arithmetic compared to an equivalent 64-bit simulation. On the other hand, low-precision computation is less resource intensive than high-precision computation. Several machine learning techniques proposed recently have been successful in correcting errors due to coarse spatial discretization. In this work, we extend these techniques to improve CFD simulations performed with low numerical precision. We quantify the precision-related errors accumulated in a Kolmogorov forced turbulence test case. Subsequently, we employ a Convolutional Neural Network together with a fully differentiable numerical solver performing 16-bit arithmetic to learn a tightly-coupled ML-CFD hybrid solver. Compared to the 16-bit solver, we demonstrate the efficacy of the hybrid solver towards improving various metrics pertaining to the statistical and pointwise accuracy of the simulation.