Browsing by Subject "Inverse problem"
- Results Per Page
- Sort Options
Item Open Access Coding Strategies and Implementations of Compressive Sensing(2016) Tsai, Tsung-HanThis dissertation studies the coding strategies of computational imaging to overcome the limitation of conventional sensing techniques. The information capacity of conventional sensing is limited by the physical properties of optics, such as aperture size, detector pixels, quantum efficiency, and sampling rate. These parameters determine the spatial, depth, spectral, temporal, and polarization sensitivity of each imager. To increase sensitivity in any dimension can significantly compromise the others.
This research implements various coding strategies subject to optical multidimensional imaging and acoustic sensing in order to extend their sensing abilities. The proposed coding strategies combine hardware modification and signal processing to exploiting bandwidth and sensitivity from conventional sensors. We discuss the hardware architecture, compression strategies, sensing process modeling, and reconstruction algorithm of each sensing system.
Optical multidimensional imaging measures three or more dimensional information of the optical signal. Traditional multidimensional imagers acquire extra dimensional information at the cost of degrading temporal or spatial resolution. Compressive multidimensional imaging multiplexes the transverse spatial, spectral, temporal, and polarization information on a two-dimensional (2D) detector. The corresponding spectral, temporal and polarization coding strategies adapt optics, electronic devices, and designed modulation techniques for multiplex measurement. This computational imaging technique provides multispectral, temporal super-resolution, and polarization imaging abilities with minimal loss in spatial resolution and noise level while maintaining or gaining higher temporal resolution. The experimental results prove that the appropriate coding strategies may improve hundreds times more sensing capacity.
Human auditory system has the astonishing ability in localizing, tracking, and filtering the selected sound sources or information from a noisy environment. Using engineering efforts to accomplish the same task usually requires multiple detectors, advanced computational algorithms, or artificial intelligence systems. Compressive acoustic sensing incorporates acoustic metamaterials in compressive sensing theory to emulate the abilities of sound localization and selective attention. This research investigates and optimizes the sensing capacity and the spatial sensitivity of the acoustic sensor. The well-modeled acoustic sensor allows localizing multiple speakers in both stationary and dynamic auditory scene; and distinguishing mixed conversations from independent sources with high audio recognition rate.
Item Open Access Deep Learning for the modeling and design of artificial electromagnetic materials(2023) Ren, SimiaoArtificial electromagnetic materials (AEMs) are materials that exhibit unusual electromagnetic properties. With sub-wavelength, periodic structures, AEMs can achieve incredible abilities to manipulate light, like the cloaking effect of the “invisibility cloak” in the Harry Potter movie. Apart from the cinematic application of invisibility, AEMs have important applications ranging from high-efficiency solar panels to next-generation communications systems. The major goal of this thesis is to develop deep learning tools to design materials that have increasingly customized interactions with electromagnetic waves, thus enabling more useful technologies. In turn, this necessitates the modeling and design of increasingly complicated materials. Modeling of these materials is difficult because (i) the physics of advanced materials is intrinsically more complicated with no simple analytical form, (ii) the manufacture of such nano-structures is prohibitively expensive, and (iii) the computational electromagnetic simulation software is too slow to iterative through trail-n-error. Recently, the advancement of deep learning bring new perspectives on such a problem. In this thesis, we explore deep learning for the modeling and design of advanced photonic materials. In particular, we explore and make important contributions to two fundamental areas: inverse design, and active learning. In inverse design, we develop an accurate method, “Neural-adjoint,” and show its dominance not only in simple inverse problems but also in contemporary AEM design problems. We further analyze and benchmark eight state-of-the-art deep inverse approaches in the AEM inverse design and discover that the one-to-manyness of the problem is an important factor in such a problem. Then, motivated by the immediate drawback that all deep inverse models require a large set of labeled data, we investigate the benefit of active learning in the setting of AEM design and scientific computing in general. By setting the problem close to a real application where pool size is unknown, we find the majority of deep regression pool-based active learning methods in our benchmark lack robustness and don’t outperform even random sampling consistently.
Item Open Access Fluid Flow and Electromagnetic Fields Modeling for Geophysical Subsurface Sensing(2018) Hu, YunyunCrosswell electromagnetic (EM) fields measurement has been widely applied in oil industry which has a reservoir scale detection range. One of the limitation of this technique is that the EM singals are usually too weak to be detected. In order to overcome the disadvantage, nanoparticles (NP) designed with high contrast EM properties (conductivity, permittivity and magnetic permeability) are introduced to enhance the signals. They are injected into the formation and moving with the fluids. The movement of NP with the flow in a porous medium is modeled by solving the flow transport equations. The 3-D spectral-element time domain method (SETD) based on Gauss-Lobatto-Legendre (GLL) polynomials is employed to solve the flow equation to obtain the NP concentration distribution as a function of time. Since the method shows a spectral accuracy, i.e., the error decreases exponentially with the order of basis functions, less unknown is needed to achieve a given accuracy with a high order basis function.
The injected fluids with high contrast NP increase the electric conductivity and magnetic permeability in the flooded zone. The effective EM properties of the mixed fluids are calculated by the mixing theory, e.g., Bruggeman mixing rule. The increased EM property values produce higher EM signals in the receivers. The EM fields are then modeled by the volume integral equations (VIE), thus realizing the coupling of fluid flow and EM measurements. Based on the coupling, the detection range of the high contrast NP can be analyzed. Different types of NP are investigated under both electric and magnetic dipole sources.
The magnetic contrast NP excited by a magnetic dipole source can generate a detectable signal, while the electric contrast NP is more sensitive to an electric dipole. Using a magnetic dipole source, it is hard to generate detectable signals at receivers with high dielectric particles, however, increasing the frequency will improve the signals.
The coupling technique can also be used to evaluate the heterogeneity of the formation. When the high contrast agents are injected into a heterogeneous medium, e.g., with a low permeable region. The EM responses at the four producers are different. The signals at the producer near the barrier are lower than the other producers, since the fluids containing the high contrast NP is blocked. The proposed multiphysics coupling technique of fluid flow and EM measurements provides guidance for NP field application and help monitor the flow movement in reservoirs.
One of the applications of the high contrast agents is used for hydraulic fractures detection. Hydraulic fracturing is a technique to crack rocks by pumping high pressure fluid into a segment of a well. The created fractures serve as a pathway to release the hydrocarbon resource such as oil or natural gas from the rock. It is an efficient technology to increase the oil/gas production in tight formations. Successful fracture imaging is important to evaluate the created fractures. This is a part of a large project of the Advanced Energy Consortium (AEC) to image large-scale hydraulic fractures in deep underground with high contrast proppants injection. A group of small-scaled fracturing field tests are performed by AEC to investigate the feasibility of injecting high contrast proppants to detect fractures. The injected proppants are designed with high conductivity and permittivity to generate detectable signals at electrode-type sensors. To map the created fractures, an efficient 3-D EM inversion method with physical constraint on the inverted unknowns is developed to simultaneously reconstruct conductivity and permittivity profiles.
The inversion solver is firstly applied to a theoretical model with the noise-polluted synthetic data to reconstruct the fracture, and then applied to two hydraulic fracturing field tests with injected high conductive proppants, Loresco Coke Breeze and steel shot. The fracture conductivity and permittivity are reconstructed based on the scattered voltage signals which are the difference between the post-fracturing and pre-fracturing data. The post-fracturing data are the signals measured after the fracturing and the pre-fracturing data are measured before the fracturing. The difference signals are regarded as from the created fracture. The reconstructed fracture profiles are compared with the coring data to show the reliability of the inversion results. Their good agreement demonstrates the effectiveness of the inverse solver to estimate the fracture size and location.
In recent several decades, EM fields from layered media have attracted considerable attention concerning various applications including geophysical exploration, microwave remote sensing, wave propagation, microstrip circuits, antennas, etc. Especially, the EM waves in anisotropic laminates are of much concern. For geophysical problems, anisotropy happens commonly in many formations, e.g., shale formation. To accurately evaluate the anisotropic medium, a forward solver capable of handling arbitrary anisotropy is needed.
In this work, the formulations for EM fields in multilayered general anisotropic media are derived. Maxwell's equations in the spectral domain are written into a first-order differential (in $z$) equation concerning the transverse electric and magnetic field components in the spectral domain. The equation can be solved to obtain the EM fields in a homogeneous anisotropic medium. For fields in layered anisotropic media, the local transmission and reflection matrices, the global reflection matrices and the recursion relations of the wave amplitudes at interfaces are derived and used to express the EM fields in arbitrary layers. The electric and magnetic dipole sources can locate in arbitrary layers and the medium can possess an arbitrary anisotropy.
To transform the spectral domain solution into the spatial domain involves the inverse Fourier transform which needs integration from $-\infty$ to $+\infty$. The speed of integration calculation depends on the decaying of the integrands. The singular behavior of the fields in the close vicinity of the dipole source needs to be considered since the integrand usually converges very slowly. In this work, it is handled by subtracting the direct fields in the spectral domain, since the direct fields contribute most of the singular problem. The contributions of the subtracted part in the spatial domain are calculated and added afterwards. An example is modeled to show the convergence of the integrands with / without the singularity subtraction. The subtraction makes the integrands decaying rapidly as functions of $k_x$ and $k_y$.
To validate the algorithm, a multilayer full anisotropic medium is modeled and compared with the finite element method (FEM) results. It is also applied to the geophysical EM well logging by modeling the triaxial induction logging tool. The responses in vertical and deviated wells are computed and compared with FEM results. The good agreement between the two results further validates the algorithm and shows the capability of modeling induction logging tools in multilayered general anisotropic media.
The scattering of EM fields from anisotropic objects has been studied intensively in recent years. Most of the work studies the inhomogeneities in homogeneous isotropic background media and a few work has been done on uniaxial anisotropic media. This work extends to inhomogeneities embedded in layered general anisotropic media. The volume integral equation based on the electric dyadic Green's function is derived and solved efficiently with the fast Fourier transform (FFT) based BCGS method. The FFT technique is employed to calculate the convolution and correlation efficiently involved in the integral equation which reduces the computation cost from $O(N^2)$ to $O (N log N)$. A series of numerical examples are modeled and compared with FEM results to validate the algorithm.
Item Open Access Multiscale forward and inverse problems with the DGFD method and the deep learning method(2020) Zhang, RunrenA fast electromagnetic (EM) forward solver has been developed for the subsurface detection, with application includes producing synthetic logging data and instructing large-scale field test and inversion. A deep learning based full wave inversion method has also been developed to reconstruct the underground anomaly.
Since the gas and oil industry has very high demands for the forward modeling speed when doing inversion, the inversion model is usually simplified to a 1D or 2D problem by supposing the geometry of object invariant in two or one direction. The full 3D inversion is still a hot topic for research, which requires both fast 3D forward solver and efficient inversion method. The bottleneck for the forward solver is how to solve the large-scale linear system efficiently; the bottleneck for the inversion is how to pick the global minimum from lots of local minimums efficiently for the inverse problem.
For the forward part, the domain decomposition method (DDM) inspired discontinuous Galerkin frequency domain (DGFD) method has been extended to model the vertical open borehole resistivity measurement with structured gradient meshes; besides, the DGFD method has been extended to model the logging-while-drilling (LWD) resistivity measurement in high-angle and horizontal (HA/HZ) well and curved layers with a flipped total field/scattered field (TF/SF) mixed solver. An approximated casing model has also been proposed to accelerate the large-scale curved casing modeling with borehole-to-surface measurements.
For the inversion part, a convolutional neural network based inversion has been developed to reconstruct the lateral extent and direction of the hydraulic fracture through scattered electromagnetic field data under borehole-to-surface measurements; further, the deep transfer learning is applied in the same scenario to improve the performance of the inversion. Additionally, a fully connected neural network has been developed for the Devine field data and successfully reconstruct the shape of the hydraulic fracture with good agreement to the conventional inversion.
Item Open Access Theoretical and Computational Aspects of the Optimized Effective Potential Approach within Density Functional Theory(2009) Heaton-Burgess, TimThe computational success of density functional theory relies on the construction of suitable approximations to the exchange-correlation energy functional. Use of functional approximations depending explicitly upon the density alone appear unable to address all aspects of many-body interactions, such as the fundamental constraint that the ground state energy is a piecewise linear function of the total number of electrons, and the ability to model nonlocal effects. Functionals depending explicitly upon occupied and unoccupied Kohn–Sham orbitals are considered necessary to address these and other issues. This dissertation considers certain issues relevant to the successful implementation of explicitly orbital-dependent functionals through the optimized effective potential (OEP) approach, as well as extending the potential functional formalism that provides the formal basis for the OEP approach to systems in the presence of noncollinear magnetic fields.
The self-consistent implementation of orbital-dependent energy functionals is correctly done through the optimized effective potential approach—minimization of the ground state energy with respect to the Kohn–Sham potential that generates the set of orbitals employed in the energy evaluation. The focus on the potential can be problematic in finite basis set approaches as determining the exchange-correlation potential in this manner is an inverse problem which, depending upon the combination of orbital and potential basis sets employed, is often ill-posed. The ill-posed nature manifests itself as nonphysical exchange-correlation potentials and total energies. We address the problem of determining meaningful exchange-correlation potentials for arbitrary combinations of orbital and potential basis sets through an L-curve regularization approach based on biasing towards smooth potentials in the energy minimization. This approach generates physically reasonable potentials for any combination of basis sets as shown by comparisons with grid-based OEP calculations on atoms, and through direct comparison with DFT calculations employing functionals not depending on orbitals for which OEP can also be performed. This work ensures that the OEP methodology can be considered a viable many-body computational methodology.
A separate issue of our OEP implementation is that it can suffer from a lack of size-extensivity—the total energy of a system of infinitely separated monomers may not scale linearly with the total number of monomers depending upon how we construct the Kohn–Sham potential. Typically, a fixed reference potential is employed to aid in the convergence of a finite basis set expansion of the Kohn–Sham potential. This reference potential can be utilized to ensure other desirable properties of the resulting potential. In particular, it can enforce the correct asymptotic behavior. The Fermi–Amaldi potential is often used for this purpose but suffers from size-nonextensivity owing to the explicit dependence of the potential on the total number of electrons. This error is examined and shown to be rather small and rapidly approaches a limiting linear behavior. A size-extensive reference potential with the correct asymptotic behavior is suggested and examined.
We also consider a formal aspect of the potential-based approach that provides the underlying justification of the OEP methodology. The potential functional formalism of Yang, Ayers, and Wu is extended to include systems in the presence of noncollinear magnetic fields. In doing so, a solution to the nonuniqueness issue associated with mapping between potentials and wave functions in such systems is provided, and a computational implementation of the OEP in noncollinear systems is suggested.
Finally, as an example of an issue for which orbital-dependent functionals seem necessary to obtain a correct description, we consider the ground state structures of C4N + 2 rings which are believed to exhibit a geometric transition from angle-alternation (N ≤ 2) to bond-alternation (N > 2). So far, no published DFT approach has been able to reproduce this behavior owing to the tendency of common density functional approximations to bias towards delocalized electron densities. Calculations are presented with the rCAM-B3LYP exchange-correlation functional that correctly predict the structural evolution of this system. This is rationalized in terms of the recently proposed delocalization error for which rCAM-B3LYP explicitly attempts to address.