Reduced Order Modelling for the Drone Flow Field: Autoencoder-Driven Nonlinear Compression Versus Pod

Abstract Reduced-order modelling (ROM) is a computational technique that approximates the high-dimensional fidelity data by projecting onto a lower-dimensional subspace, while preserving dominant physical features of the multi-physics simulation data. This study presents a systematic comparison of two established dimensionality-reduction techniques – proper orthogonal decomposition (POD) and autoencoders (AEs) – for reducing dimensionality, while preserving the dominant physical features of the drone flow field. While POD employs linear subspace projection through singular value decomposition (SVD) to capture the energy dominant modes, the effectiveness of capturing the nonlinear relationship is limited. Since drone flow field data represents a complex multi-physics relationship, POD exhibits lesser capability of capturing maximum nonlinearity in the dataset while projecting onto subspace. In contrast, AE demonstrates superior reconstruction from the latent space, which the author of the study quantifies using performance metrics such as Mean Square Error (MSE) and the coefficient of determination (R 2 ). POD achieves lower MSE of 0.0352 vs. AE achieved a reconstruction error of 0.0491 and demonstrated superior variance retention with R 2 = 0.951 (95.1 %) compared to POD’s R 2 = 0.781 (78.1 %), indicating stronger preservation of nonlinear features. With regard to data compression, the second aspect for the ROM selection, AE outperformed in the compression ratio of 23.37x compared to 3.61x of POD. This study explores computational requirements, revealing that AE demands greater resources than POD. While POD relies on a single SVD, AE requires training and testing with iterative gradient descent across multiple layers and back-propagation to capture the effective representations of a nonlinear dataset.