Lipid nanoparticles and micro-droplets serve as vital vectors in modern targeted therapeutics, acting as protective vehicle bubbles that transport delicate medical payloads directly through the human bloodstream. Optimizing these drug delivery systems requires a deep understanding of how these bubbles deform, rupture, and interact with ambient blood plasma under complex hydrodynamic forces. With this as a primary motivating application, this project concerns the development of surrogate models to accurately model these interactions for large-scale problems where the number of droplets would make a classical simulation approach prohibitively expensive, even on extreme-scale computing architectures. A core goal focuses on the development of high-fidelity neural surrogate models designed to approximate continuous velocity fields and boundary spatial gradients around deforming elliptical droplets in Stokes flows. This framework serves as a high-efficiency sub-resolution module embedded within a larger, macroscopic surrogate Stokes solver pipeline. The purpose of the neural network component is to accurately resolve complex boundary layer dynamics and capture high-curvature deformation states. We are investigating multiple candidate neural network architectures. This exploration includes a cascaded multi-scale approach that pairs smooth global background networks with harmonic Fourier embedding layers to isolate challenging localized fluid phenomena. Having successfully developed and validated prototype implementations on local workstations, we request cluster access to transition from small-scale baseline testing to full architectural optimization. This compute pipeline is to be integrated with an existing surrogate solver to extract continuous hydrodynamic traction forces and evaluate cell deformations. The project is being carried out in the research group of professor Sara Zahedi (KTH) in collaboration with assistant professor Davide Pradovera (Stockholm University).