Partition of Unity Physics-Informed Neural Networks (POU-PINN) is a framework that combines the strengths of PINNs and mixtures of experts to identify subdomains with distinct physical properties in an unsupervised manner. The method addresses Stokes flow problems, particularly in ice sheet and surface flow modeling applications, where diffusivity properties vary across regions. By leveraging the partition of unity networks, this approach enables accurate estimation of conductivity values ​​for the segmentation domain. Several examples, including manufactured solutions, e.g., in Darcy flow, demonstrate the effectiveness of POU-PINNs in capturing heterogeneous behavior. Work is also progressing, addressing challenges and future directions, including causality reinforcement, satellite data integration, and real-world geometric complexity.

This study combines physical experiments and computational models to analyze boundary layer transition in hypersonic flow for the behavior of blunt cone geometry. This work includes schlieren data from Wright-Patterson AFB's Ludwig Tube experiments and corresponding computational fluid dynamics simulations. The CFD setup includes mesh-independent laminar and turbulent flow simulation comparisons at Mach 6 conditions. Special attention is given to the effects of surface roughness on the flow transition. The results agree with the numerical and experimental data, validating the computational approach. This study is supported by NSF, AFOSR, and DOE, and acknowledges guidance from Prof. Steven P. Schneider on hypersonic flow transition.

This research investigates the nature of atmospheric turbulence cascades using multifractal analysis. We analyze energy dissipation using direct numerical simulations of the Johns Hopkins Turbulence Database and large-eddy simulations with OpenFOAM. Based on the Kolmogorov-5/3 power law, the study leverages the Meneveau multifractal to capture turbulence's anisotropic characteristics better. In this paper, we implement an analysis with Python, analyzing energy dissipation, applying box counting methods, and evaluating the fractal dimension of turbulence. The results indicate isotropic behavior in the simulated data, confirming theoretical expectations and highlighting the need to incorporate experimental data to model the phenomenon of turbulence in the atmosphere and extend the models for anisotropic flows.

This research explores the aerodynamic performance of airfoils at ultra-low Reynolds numbers using panel method simulations as a computationally efficient alternative to CFD. Focusing on micro-vehicle vehicles (MAVs), this study analyzes NACA 4404, 4402, and 0012 airfoils across a range of Reynolds numbers from 1000 to 4000. Using XFOIL panel method simulations, the investigation focuses on lift, drag, and pressure distributions, revealing how airfoil thickness impacts aerodynamic efficiency. The results demonstrate that low Reynolds numbers lead to delayed flow separation and thick boundary layers, significantly altering lift and drag behavior. The study confirms that panel method simulations provide reliable predictions in MAVs' early design and analysis stages, providing valuable insights into low-speed aerodynamics.

This research uses various image processing techniques to deblur optical images distorted by atmospheric turbulence. The research explains that deblurring images is an ill-posed and non-convex inverse problem, usually complicated by unknown blur characteristics. This study explores traditional approaches, including Wiener filters, regularized filtering, the Lucy-Richardson algorithm, and blind deblurring, each demonstrating strengths and limitations. A graph-based blind deblurring method is introduced as an adaptive method. This research highlights the promise of deep learning, which has shown superior performance in recent years despite higher computational demands. Future work involves leveraging transformer-based restoration models to improve restoration images under turbulent conditions.