Kapil Aryal

ORCID Identifier(s)


Graduation Semester and Year




Document Type


Degree Name

Doctor of Philosophy in Aerospace Engineering


Mechanical and Aerospace Engineering

First Advisor

Brian Dennis


Despite significant advancements in computer capabilities for numerical simulations, engineers continue to face limitations when dealing with large-scale full-order model(FOM) simulations. These simulations often necessitate repeated solves, such as those encountered in inverse design, real-time solution prediction, error quantification, and solver convergence, among others. To address these challenges, reduced order modeling (ROM) has emerged as a valuable approach. This thesis focuses on the development of an ROM framework that combines Proper Orthogonal Decomposition (POD) with machine learning techniques. This integrated approach is applied to a diverse range of heat transfer and fluid flow inverse design problems. POD constructs optimal sets of basis vectors from high fidelity numerical simulations which can be used in linear superposition to predict the FOM solution. The unknowns in the model are the coefficients of the basis vectors. To obtain these coefficients, various methods can be employed, such as Galerkin projection or other optimization techniques, particularly when the solution field is known. Then such data can be utilized to train (ANNs), which will then be capable of making real time predictions of the coefficients for new sets of parameters. These coefficients when used with POD bases constructs the full solution field quickly. This versatile ROM framework is applied to address various heat transfer and fluid flow problems, enhancing computational efficiency in a range of scenarios. Firstly, it is applied to 3D linear heat conduction within a deforming mesh configuration in a pipe, where the internal surface is governed by 20 parameters. The ROM accurately predicts the full temperature field with errors of less than 3.5% compared to the actual values. All 20 parameters are approximated within a remarkable 0.7% of the actual parameters. This framework establishes itself as a notably robust technique, surpassing other methods that rely directly on ANNs. The ROM demonstrates strong resilience to simulated errors in the target temperature. Secondly, the ROM is applied to determine the detailed internal flow and temperature in a multiphysics, nonlinear conjugate heat and mass transfer problem within a hollow cylindrical channel with a spherical heat source at its center, for varying inlet flow rates. As flow rate information may not always be available, three nodal temperatures from the surface of the cylinder or the sphere are used to re-parameterize the problem. The ROM exhibits satisfactory accuracy when temperature sensors are placed on the cylinder’s surface and responds poorly to simulated errors. However, when the ROM is updated with sensors on the surface of the heated sphere, its performance significantly improves, providing highly accurate predictions even in the presence of substantial Gaussian noise in the sensor temperatures. Impressively, the ROM predicts temperature and absolute velocity within 0.5% and 2.5%, respectively, with errors not exceeding 5% for both temperature and velocity when subjected to Gaussian noise within the range of ±10°C. In the final phase of the study, the ROM is applied to predict the pressure field for various 4-digit NACA airfoils at different angles of attack—a nonlinear 2D deforming mesh fluid flow problem. The predicted nodal pressure values are within 4% of the actual values for 25 test cases. In inverse approximation, the ROM demonstrates remarkable accuracy, recovering parameters and AOA within 2.5% of actual values, even when facing substantial Gaussian noise (equivalent to 5% of the highest pressure value). A groundbreaking discovery is made that this ROM is capable of eliminating multiple local minima (resembling noise) in the objective function. The objective of this comprehensive investigation is to establish a generalized procedure applicable to a wide range of applications. By scrutinizing key factors such as modal trajectories, sample sizes for POD and ANN, the number of modes, and sampling techniques, the research aims to develop a versatile ROM framework capable of accommodating various scenarios.


Reduced order model, Proper orthogonal decomposition, Inverse design, Inverse shape, Artificial neural network, Predictive modeling, Heat transfer, Fluid flow, Multiphysics, Optimization, Principal Component analysis


Aerospace Engineering | Engineering | Mechanical Engineering


Degree granted by The University of Texas at Arlington