Uncertainty quantification in low-order machine learning models of unsteady aerodynamics

In aerodynamics, accurately estimating the flow around airfoils is pivotal for effective flow control and optimal decision-making. To achieve this, we seek to use sensors on the airfoil to capture the underlying flow state. This study presents a data-driven approach to reconstructing the vorticity field and lift from limited surface pressure measurements using a non-linear lift-augmented neural network. As in some recent studies, our approach leverages deep learning tools to reduce the dimensionality of the system to a few latent variables, revealing that the inference of flow and lift from sensor data can be captured via a low-dimensional space. However, typical deep learning models do not inherently account for uncertainties, which is crucial for reliable predictions. Accordingly, we quantify two types of uncertainties: aleatoric uncertainty, arising from noisy measurements, and epistemic uncertainty, stemming from limitations and lack of knowledge in the mapping from pressure to the flow field. The uncertainty quantification provided by our model can be used to highlight the sensitivity of predictions from sensor measurements, strategically place sensors, and significantly improve decision-making processes in aerodynamic applications.