Reduced Order Modeling of Geophysical Flows Using Physics-Based and Data-Driven Modeling Techniques

The growing advancements in computational power, algorithmic innovation, and the availability of data resources have started shaping the way we numerically model physical problems now and for years to come. Many of the physical phenomena, whether it be in natural sciences and engineering disciplines or social sciences, are described by a set of ordinary differential equations or partial differential equations which is referred as the mathematical model of a physical system. High-fidelity numerical simulations provide us valuable information about the flow behavior of the physical system by solving these sets of equations using suitable numerical schemes and modeling tools. However, despite the progress in software engineering and processor technologies, the computational burden of high-fidelity simulation is still a limiting factor for many practical problems in different research areas, specifically for the large-scale physical problems with high spatio-temporal variabilities such as atmospheric and geophysical flows. Therefore, the development of efficient and robust algorithms that aims at achieving the maximum attainable quality of numerical simulations with optimal computational costs has become an active research question in computational fluid dynamics community. As an alternative to existing techniques for computational cost reduction, reduced order modeling (ROM) strategies have been proven to be successful in reducing the computational costs significantly with little compromise in physical accuracy. In this thesis, we utilize the state of the art physics-based and data-driven modeling tools to develop efficient and improved ROM frameworks for large-scale geophysical flows by addressing the issues associated with conventional ROM approaches. We first develop an improved physics-based ROM framework by considering the analogy between dynamic eddy viscosity large eddy simulation (LES) model and truncated modal projection, then we present a hybrid modeling approach by combining projection based ROM and extreme learning machine (ELM) neural network, and finally, we devise a fully data-driven ROM framework utilizing long short-term memory (LSTM) recurrent neural network architecture. As a representative benchmark test case, we consider a two-dimensional quasi-geostrophic (QG) ocean circulation model which, in general, displays an enormous range of fluctuating spatial and temporal scales. Throughout the thesis, we demonstrate our findings in terms of time series evolution of the field values and mean flow patterns, which suggest that the proposed ROM frameworks are robust and capable of predicting such fluid flows in an extremely efficient way compared to the conventional projection based ROM framework

Image-Based Force Estimation and Haptic Rendering For Robot-Assisted Cardiovascular Intervention

Clinical studies have indicated that the loss of haptic perception is the prime limitation of robot-assisted cardiovascular intervention technology, hindering its global adoption. It causes compromised situational awareness for the surgeon during the intervention and may lead to health risks for the patients. This doctoral research was aimed at developing technology for addressing the limitation of the robot-assisted intervention technology in the provision of haptic feedback. The literature review showed that sensor-free force estimation (haptic cue) on endovascular devices, intuitive surgeon interface design, and haptic rendering within the surgeon interface were the major knowledge gaps. For sensor-free force estimation, first, an image-based force estimation methods based on inverse finite-element methods (iFEM) was developed and validated. Next, to address the limitation of the iFEM method in real-time performance, an inverse Cosserat rod model (iCORD) with a computationally efficient solution for endovascular devices was developed and validated. Afterward, the iCORD was adopted for analytical tip force estimation on steerable catheters. The experimental studies confirmed the accuracy and real-time performance of the iCORD for sensor-free force estimation. Afterward, a wearable drift-free rotation measurement device (MiCarp) was developed to facilitate the design of an intuitive surgeon interface by decoupling the rotation measurement from the insertion measurement. The validation studies showed that MiCarp had a superior performance for spatial rotation measurement compared to other modalities. In the end, a novel haptic feedback system based on smart magnetoelastic elastomers was developed, analytically modeled, and experimentally validated. The proposed haptics-enabled surgeon module had an unbounded workspace for interventional tasks and provided an intuitive interface. Experimental validation, at component and system levels, confirmed the usability of the proposed methods for robot-assisted intervention systems