Simulation of Wave Propagation
http://hdl.handle.net/20.500.11824/8
2022-12-09T03:01:45ZDeep Learning for Inverting Borehole Resistivity Measurements
http://hdl.handle.net/20.500.11824/1536
Deep Learning for Inverting Borehole Resistivity Measurements
Rivera, J.A
There exist multiple traditional methods to solve inverse problems, mainly, gradient-based or statistics-based methods. However, these methods have severe limitations. In particular, they often need to compute the forward problem hundreds of times, which is computationally expensive in three-dimensional (3D) problems.
In this dissertation, we propose the use of Deep Learning (DL) techniques to solve inverse problems. Although the training stage of a Deep Neural Network (DNN) may be time-consuming, after the network is properly trained it can forecast the solution in a fraction of a second, facilitating real-time operations. In the first part of this dissertation, we investigate appropriate loss functions to train a DNN when dealing with an inverse problem.
Additionally, to properly train a DNN that approximates the inverse solution, we require a large dataset containing the solution of the forward problem. To create such dataset, we need to solve aPartial Differential Equation (PDE) thousands of times. Building a dataset may be time-consuming, especially for two and three-dimensional problems since solving PDEs using traditional methods, such as the Finite Element Method (FEM), is computationally expensive. Thus, we want to reduce the computational cost of building the database needed to train the DNN. For this, we propose the use of rIGA methods.
In addition, we explore the possibility of using DL techniques to solve PDEs, which is the main computational bottleneck when solving inverse problems. Our main goal is to develop a fast forward simulator for solving parametric PDEs. As a first step, in this dissertation we analyze the quadrature problems that appear while solving PDEs using DNNs and propose different integration methods to overcome these limitations.
2022-11-25T00:00:00ZZindler-type hypersurfaces in R^4
http://hdl.handle.net/20.500.11824/1519
Zindler-type hypersurfaces in R^4
Martinez-Maure, Y.; Rochera, D.
In this paper the definition of Zindler-type hypersurfaces is introduced in $\mathbb{R}^4$ as a generalization of planar Zindler curves. After recalling some properties of planar Zindler curves, it is shown that Zindler hypersurfaces satisfy similar properties. Techniques from quaternions and symplectic geometry are used. Moreover, each Zindler hypersurface is fibrated by space Zindler curves that correspond, in the convex case, to some space curves of constant width lying on the associated hypersurface of constant width and with the same symplectic area.
2022-09-08T00:00:00ZThe DPG Method for the Convection-Reaction Problem, Revisited
http://hdl.handle.net/20.500.11824/1512
The DPG Method for the Convection-Reaction Problem, Revisited
Demkowicz, L.; Roberts, N.V.; MuĂ±oz-Matute, J.
We study both conforming and non-conforming versions of the practical DPG method for the convection-reaction problem. We determine that the most common approach for DPG stability analysis - construction of a local Fortin operator - is infeasible for the convection-reaction problem. We then develop a line of argument based on a direct proof of discrete stability; we find that employing a polynomial enrichment for the test space does not suffice for this purpose, motivating the introduction of a (two-element) subgrid mesh. The argument combines mathematical analysis with numerical experiments.
2022-01-01T00:00:00ZMachining-induced characteristics of microstructure-supported LPBF-IN718 curved thin walls
http://hdl.handle.net/20.500.11824/1508
Machining-induced characteristics of microstructure-supported LPBF-IN718 curved thin walls
Mishra, S.; Escudero, G.; Gonzalez, H.; Calleja, A.; Martinez, S.; Barton, M.; Lopez de Lacalle, N.; Mishra
The microstructure-supported design of engineering components is recently gaining attention due to their high strength-to-weight and high stiffness-to-weight properties. The present study investigates the hybrid manufacturing of Inconel 718 curved thin walls with internal microstructural supports fabricated by laser powder bed fusion (LPBF). Printed walls contain a fixed curvature and thickness, whereas the internal microstructures were varied at different inclination angles. In this research, a finish milling operation has been performed at different milling parameters. Machining-induced damages on the internal microstructures have been studied and correlated with geometrical deviation and surface integrity features on the outer thin wall surfaces.
2022-07-01T00:00:00Z