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We use Gaussian stochastic weight averaging (SWAG) to assess the model-formuncertainty associated with neural-network-based function approximationrelevant to fluid flows. SWAG approximates a posterior Gaussian distribution ofeach weight, given training data, and a constant learning rate. Having accessto this distribution, it is able to create multiple models with variouscombinations of sampled weights, which can be used to obtain ensemblepredictions. The average of such an ensemble can be regarded as the `meanestimation', whereas its standard deviation can be used to construct`confidence intervals', which enable us to perform uncertainty quantification(UQ) with regard to the training process of neural networks. We utilizerepresentative neural-network-based function approximation tasks for thefollowing cases: (i) a two-dimensional circular-cylinder wake; (ii) the DayMETdataset (maximum daily temperature in North America); (iii) a three-dimensionalsquare-cylinder wake; and (iv) urban flow, to assess the generalizability ofthe present idea for a wide range of complex datasets. SWAG-based UQ can beapplied regardless of the network architecture, and therefore, we demonstratethe applicability of the method for two types of neural networks: (i) globalfield reconstruction from sparse sensors by combining convolutional neuralnetwork (CNN) and multi-layer perceptron (MLP); and (ii) far-field stateestimation from sectional data with two-dimensional CNN. We find that SWAG canobtain physically-interpretable confidence-interval estimates from theperspective of model-form uncertainty. This capability supports its use for awide range of problems in science and engineering.

Assessments of epistemic uncertainty using Gaussian stochastic weight averaging for fluid-flow regression