TY - JOUR

T1 - Probabilistic neural networks for fluid flow surrogate modeling and data recovery

AU - Maulik, Romit

AU - Fukami, Kai

AU - Ramachandra, Nesar

AU - Fukagata, Koji

AU - Taira, Kunihiko

N1 - Funding Information:
This material was based upon work supported by the U.S. Department of Energy (DOE), Office of Science, Office of Advanced Scientific Computing Research, under Contract No. DE-AC02-06CH11357. This research was funded in part and used resources of the Argonne Leadership Computing Facility, which is a DOE Office of Science User Facility supported under Contract No. DE-AC02-06CH11357. R.M. acknowledges support from the ALCF Margaret Butler Fellowship. K. Fukami and K. Fukagata are grateful for support from Japan Society for the Promotion of Science (KAKENHI Grant No. 18H03758). K.T. acknowledges generous support from the U.S. Army Research Office (Grant No. W911NF-17-1-0118) and U.S. Air Force Office of Scientific Research (Grant No. FA9550-16-1-0650). The authors acknowledge Dr. M. Gopalakrishnan Meena (University of California, Los Angeles) for sharing his DNS data.
Publisher Copyright:
© 2020 American Physical Society.

PY - 2020/10

Y1 - 2020/10

N2 - We consider the use of probabilistic neural networks for fluid flow surrogate modeling and data recovery. This framework is constructed by assuming that the target variables are sampled from a Gaussian distribution conditioned on the inputs. Consequently, the overall formulation sets up a procedure to predict the hyperparameters of this distribution which are then used to compute an objective function given training data. We demonstrate that this framework has the ability to provide for prediction confidence intervals based on the assumption of a probabilistic posterior, given an appropriate model architecture and adequate training data. The applicability of the present framework to cases with noisy measurements and limited observations is also assessed. To demonstrate the capabilities of this framework, we consider canonical regression problems of fluid dynamics from the viewpoint of reduced-order modeling and spatial data recovery for four canonical data sets. The examples considered in this study arise from (i) the shallow-water equations, (ii) a two-dimensional cylinder flow, (iii) the wake of a NACA0012 airfoil with a Gurney flap, and (iv) the NOAA sea surface temperature data set. The present results indicate that the probabilistic neural network not only produces a machine-learning-based fluid flow surrogate model but also systematically quantifies the uncertainty therein to assist with model interpretability.

AB - We consider the use of probabilistic neural networks for fluid flow surrogate modeling and data recovery. This framework is constructed by assuming that the target variables are sampled from a Gaussian distribution conditioned on the inputs. Consequently, the overall formulation sets up a procedure to predict the hyperparameters of this distribution which are then used to compute an objective function given training data. We demonstrate that this framework has the ability to provide for prediction confidence intervals based on the assumption of a probabilistic posterior, given an appropriate model architecture and adequate training data. The applicability of the present framework to cases with noisy measurements and limited observations is also assessed. To demonstrate the capabilities of this framework, we consider canonical regression problems of fluid dynamics from the viewpoint of reduced-order modeling and spatial data recovery for four canonical data sets. The examples considered in this study arise from (i) the shallow-water equations, (ii) a two-dimensional cylinder flow, (iii) the wake of a NACA0012 airfoil with a Gurney flap, and (iv) the NOAA sea surface temperature data set. The present results indicate that the probabilistic neural network not only produces a machine-learning-based fluid flow surrogate model but also systematically quantifies the uncertainty therein to assist with model interpretability.

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U2 - 10.1103/PhysRevFluids.5.104401

DO - 10.1103/PhysRevFluids.5.104401

M3 - Article

AN - SCOPUS:85093358179

VL - 5

JO - Physical Review Fluids

JF - Physical Review Fluids

SN - 2469-990X

IS - 10

M1 - 104401

ER -