Pressure Field Reconstruction with SIREN: A Mesh-Free Approach for Image Velocimetry in Complex Noisy Environments

Abstract: This work presents a novel approach for pressure field reconstruction from image velocimetry data using SIREN (Sinusoidal Representation Network), emphasizing its effectiveness as an implicit neural representation in noisy environments and its mesh-free nature. While we briefly assess two recently proposed methods - one-shot matrix-omnidirectional integration (OS-MODI) and Green's function integral (GFI) - the primary focus is on the advantages of the SIREN approach. The OS-MODI technique performs well in noise-free conditions and with structured meshes but struggles when applied to unstructured meshes with high aspect ratio. Similarly, the GFI method encounters difficulties due to singularities inherent from the Newtonian kernel. In contrast, the proposed SIREN approach is a mesh-free method that directly reconstructs the pressure field, bypassing the need for an intrinsic grid connectivity and, hence, avoiding the challenges associated with ill-conditioned cells and unstructured meshes. This provides a distinct advantage over traditional mesh-based methods. Moreover, it is shown that changes in the architecture of the SIREN can be used to filter out inherent noise from velocimetry data. This work positions SIREN as a robust and versatile solution for pressure reconstruction, particularly in noisy environments characterized by the absence of mesh structure, opening new avenues for innovative applications in this field.