Actuation manifold from snapshot data

Data-driven manifold learning has emerged as a promising technique for extracting low-dimensional representations from complex high-dimensional data. In this study, we propose a data-driven methodology to learn a low-dimensional manifold for controlled flows, referred to as an actuation manifold.

Our approach begins with resolving post-transient snapshot flow data for a representative ensemble of actuations. Key enablers of the method include isometric feature mapping (ISOMAP) as an encoder and a combination of a neural network and k-nearest neighbor interpolation as the decoder.

The proposed methodology is tested on the fluidic pinball, a cluster of three parallel cylinders in uniform flow, forming an equilateral triangle. The flow is manipulated by the constant rotation of the cylinders, described by three actuation parameters, at a Reynolds number of 30. The unforced flow yields a one-dimensional limit cycle of periodic shedding. Our method produces a five-dimensional manifold with minimal representation error, revealing physically meaningful parameters. Two dimensions describe downstream vortex shedding, while the other three describe near-field actuation, including boat-tailing strength, the Magnus effect, and forward stagnation point.

The discovered manifold is shown to be a key enabler for control-oriented flow estimation.