Super-resolution and uncertainty estimation from sparse sensors of dynamical physical systems

The goal of this study is to leverage emerging machine learning (ML) techniques to develop a framework for the global reconstruction of system variables from potentially scarce and noisy observations and to explore the epistemic uncertainty of these models. This work demonstrates the utility of exploiting the stochasticity of dropout and batch normalization schemes to infer uncertainty estimates of super-resolved field reconstruction from sparse sensor measurements. A Voronoi tessellation strategy is used to obtain a structured-grid representation from sensor observations, thus enabling the use of fully convolutional neural networks (FCNN) for global field estimation. An ensemble-based approach is developed using Monte-Carlo batch normalization (MCBN) and Monte-Carlo dropout (MCD) methods in order to perform approximate Bayesian inference over the neural network parameters, which facilitates the estimation of the epistemic uncertainty of predicted field values. We demonstrate these capabilities through numerical experiments that include sea-surface temperature, soil moisture, and incompressible near-surface flows over a wide range of parameterized flow configurations.