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At least 595 records · Page 33

Forward and inverse modeling of fault transmissibility in subsurface flows

Characterizing physical properties of faults, such as their transmissibility, is crucial for performing predictive numerical simulation of subsurface flows, such as those encountered in petroleum engineering and remediation of subsurface contamination. Here, this paper provides a complete investigation of the inverse problem for fault transmissibility in subsurface flow models, under appropriate assumptions on fault structure. In particular, the following aspects are considered: 1) fault modeling and well-posedness of the forward problem; 2) finite element (FEM) discretizations of the forward problem and their rigorous a priori convergence analysis; 3) Well-posedness of the Bayesian inverse problem, FEM discretization of the infinite dimensional Bayesian inverse formulation, and its rigorous a priori analysis. Moreover, computation of the maximum a posteriori (MAP) point via fast inexact Newton-conjugate gradient optimization and a Laplace approximation of the Bayesian posterior are also presented. Numerical results illustrate the use of the proposed fault model in forward and inverse problems for subsurface flows in two dimensional domains with multiple faults.

97 MATHEMATICS AND COMPUTING↗

A staggered-grid finite-difference scheme optimized in the time–space domain for modeling scalar-wave propagation in geophysical problems

For modeling scalar-wave propagation in geophysical problems using finite-difference schemes, optimizing the coefficients of the finite-difference operators can reduce numerical dispersion. Most optimized finite-difference schemes for modeling seismic-wave propagation suppress only spatial but not temporal dispersion errors. We develop a novel optimized finite-difference scheme for numerical scalar-wave modeling to control dispersion errors not only in space but also in time. Our optimized scheme is based on a new stencil that contains a few more grid points than the standard stencil. We design an objective function for minimizing relative errors of phase velocities of waves propagating in all directions within a given range of wavenumbers. Dispersion analysis and numerical examples demonstrate that our optimized finite-difference scheme is computationally up to 2.5 times faster than the optimized schemes using the standard stencil to achieve the similar modeling accuracy for a given 2D or 3D problem. Compared with the high-order finite-difference scheme using the same new stencil, our optimized scheme reduces 50 percent of the computational cost to achieve the similar modeling accuracy. This new optimized finite-difference scheme is particularly useful for large-scale 3D scalar-wave modeling and inversion.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Inverse Analysis with Variational Autoencoders: A Comparison of Shallow and Deep Networks

Inverse problems are applied to determine unknown properties by matching observational data with a physical model that often takes many parameters as input. To overcome the underconstrained nature of inverse problems and achieve good performance, an approach is presented involving regularization with a technique known as a variational autoencoder (VAE), which is trained to map a high-dimensional parameter space with a complex structure to a low-dimensional latent space with a simple structure. We apply this approach to unconditioned realizations of the parameters (heterogeneous hydraulic fields) for a hydrogeological inverse problem. Two types of hydraulic conductivity fields are used to evaluate the characterization for the different levels of heterogeneity complexity of the physical inputs. This approach keeps the computational cost of generating the training data low. The reason is unconditioned realizations neither rely on the observational data used to perform the inverse analysis nor require any groundwater flow model forward runs. In addition, this approach applies regularization on a low-dimensional latent space from the VAE and increases optimization efficiency through automatic differentiation. Furthermore, two different neural network (NN) structures are tested for their utility in using the VAE for inverse analysis. The performance of a deep, convolutional neural network strongly depends on the dimensionality of the latent space, which requires tuning. In contrast, a shallow, dense neural network provides consistently accurate characterization without tuning. Furthermore, our approach evaluates the advantages of the shallow, dense neural network over the deep, convolutional one and enables future application to a wide range of inverse problems.

97 MATHEMATICS AND COMPUTING↗

Inverse Calculation of Burden Distribution Matrix Using B-spline Model Based PDF control in Blast Furnace Burden Charging Process

The inverse calculation of burden distribution matrix (BDM) is one of the most important challenges in the blast furnace operation in iron-making processes. In general, blast furnace consumes 65% of the total energy for the whole steel-making. Focusing on this practical challenge, this article proposes a new burden distribution spatial model in calculating burden charging process, and develops a B-spline approximation-based probability density function (PDF) control algorithm to assign the expected thickness distribution of burden layer and, thus, develops a new method for the required inverse calculation of BDM. First, a novel method for the thickness distribution of burden layer is given using B-spline model to produce an expected distribution shape subjected to a desired tracking within a specific spatial constraint. Then, according to the coexistence of continuous and bounded discrete variables in BDM, a novel hybrid optimization control method by combining integer programming and PDF tracking is further established for the effective inverse calculation of BDM. Finally, the proposed PDF-based iterative inverse calculation of BDM using B-spline models are tested using various data from industrial examples. Furthermore, the simulation results show that the proposed method is well suited to solve the BDM inverse calculation problem in practice.

42 ENGINEERING↗

Combined structures-controls optimization of lattice trusses

The role that distributed parameter model can play in CSI is demonstrated, in particular in combined structures controls optimization problems of importance in preliminary design. Closed form solutions can be obtained for performance criteria such as rms attitude error, making possible analytical solutions of the optimization problem. This is in contrast to the need for numerical computer solution involving the inversion of large matrices in traditional finite element model (FEM) use. Another advantage of the analytic solution is that it can provide much needed insight into phenomena that can otherwise be obscured or difficult to discern from numerical computer results. As a compromise in level of complexity between a toy lab model and a real space structure, the lattice truss used in the EPS (Earth Pointing Satellite) was chosen. The optimization problem chosen is a generic one: of minimizing the structure mass subject to a specified stability margin and to a specified upper bond on the rms attitude error, using a co-located controller and sensors. Standard FEM treating each bar as a truss element is used, while the continuum model is anisotropic Timoshenko beam model. Performance criteria are derived for each model, except that for the distributed parameter model, explicit closed form solutions was obtained. Numerical results obtained by the two model show complete agreement.

Balakrishnan, A. V.↗

Control Effector Unsaturation Modification to the Cascading Generalized Inverse Control Allocation Algorithm

Control allocation has sufficiently progressed such that it is used in front-line fighter aircraft such as the F-18Superhornet and the F-35 Joint Strike Fighter. Published literature shows the F-35 utilizes Nonlinear Dynamic Inversion in conjunction with an Effector Blender that incorporates the Cascading Generalized Inverse control allocation algorithm. While the Cascading Generalized Inverse algorithm is one of the premier generalized inverse methods, it does suffer from three deficiencies. In particular, it suffers from an inability to achieve some desired outcomes, it intermittently provides non-optimal solutions and generally fails to preserve moment direction near maximal achievable moments. An effector unsaturation method based on a Scalar Difference Quadratic was first introduced and implemented on the iterative Prediction Method control allocation algorithm which was shown to consistently achieve optimal (weighted) control allocation solutions throughout the entire Attainable Moment Set while preserving desired moment direction. In this paper, the shortcomings of the Cascading Generalized Inverse algorithm are addressed by augmenting the baseline algorithm with Scalar Difference Quadratic unsaturation identification and location at each iteration. Numerical case studies demonstrate that the Modified Cascading Generalized Inverse algorithm resolves the aforementioned deficiencies.

Michael J Acheson↗

3D Deep Learning Joint Inversion of Active Seismic Full Waveform and Passive Seismic Traveltime Data for Reservoir Imaging and Uncertainty Quantification

Here, we present deep learning (DL) networks for three-dimensional (3D) joint inversion of active seismic full waveform and passive seismic traveltime data to image reservoirs and their properties and quantify imaging uncertainties. Active seismic full-waveform data can provide high-resolution monitoring images but are collected only intermittently because of their high acquisition cost. In contrast, passive seismic data can be gathered at relatively low cost between regular active surveys, although their imaging quality can be compromised by factors such as low signal-to-noise ratios and limited ray coverage of the target. Although these datasets are routinely acquired together at CO 2 storage sites, their combined inversion within a 3D DL framework has not been previously demonstrated. To our knowledge, this is the first study to address this gap, combining the strength of both data types. For efficient data storage and DL training with large 3D seismic datasets, we use a 3D data matrix in which a random number of passive seismic traveltime data are stored as parabolic envelopes using one-hot encoding and a 3D full-waveform data matrix in which multiple shot gathers are summed. Two network architectures are evaluated: a single-encoder U-Net for single-data type inversion and a dual-encoder U-Net for joint inversion of active and passive seismic data. We also evaluate the single-encoder U-Net for joint inversion by concatenating full-waveform data and traveltime data. We propose a systematic approach for selecting an optimal dropout rate that balances regularization during training and Monte Carlo dropout-based uncertainty quantification during prediction by examining the correlation coefficient between standard deviation and prediction error, along with the training misfit, across a range of dropout rates. 3D DL inversion experiments include five different network configurations, with evaluations under ideal, noisy and dropout-enabled conditions. Both model and data uncertainties are assessed, as well as their combined effects. Across all conditions, the networks consistently predict accurate CO 2 saturation models with low prediction errors, such as a structural similarity index of 0.993 and CO 2 difference of 1.1%. Uncertainty estimates show strong spatial correlation with prediction errors, confirming the effectiveness of the proposed dropout selection approach. The results demonstrate that our DL approach, utilizing compact data representations and appropriate uncertainty quantification, yields accurate subsurface images under various inversion conditions and provides valuable insights into the reliability of predictions.

Um, Evan Schankee [Lawrence Berkeley National Labo↗

Optimal utilization of total elastic scattering cross section data for the determination of interatomic potentials

The problem of inversion is considered in relation to absolute total cross sections Q(v) for atom-atom collisions and their velocity dependence, and the glory undulations and the transition to high velocity behavior. There is a limit to the amount of information available from Q(v) even when observations of good accuracy (e.g., + or - 0.25%) are in hand over an extended energy range (from thermal energies upward by a factor of greater than 1000 in relative kinetic energy). Methods were developed for data utilization, which take full advantage of the accuracy of the experimental Q(v) measurements.

Bernstein, R. B.↗

Numerical convergence and validation of the DIMP inverse particle transport model

The data integration with modeled predictions (DIMP) model is a promising inverse radiation transport method for solving the special nuclear material (SNM) holdup problem. Unlike previous methods, DIMP is a completely passive nondestructive assay technique that requires no initial assumptions regarding the source distribution or active measurement time. DIMP predicts the most probable source location and distribution through Bayesian inference and quasi-Newtonian optimization of predicted detector re-sponses (using the adjoint transport solution) with measured responses. DIMP performs well with for-ward hemispherical collimation and unshielded measurements, but several considerations are required when using narrow-view collimated detectors. DIMP converged well to the correct source distribution as the number of synthetic responses increased. DIMP also performed well for the first experimental validation exercise after applying a collimation factor, and sufficiently reducing the source search vol-ume's extent to prevent the optimizer from getting stuck in local minima. DIMP's simple point detector response function (DRF) is being improved to address coplanar false positive/negative responses, and an angular DRF is being considered for integration with the next version of DIMP to account for highly collimated responses. Overall, DIMP shows promise for solving the SNM holdup inverse problem, especially once an improved optimization algorithm is implemented.

42 ENGINEERING↗

An Active Subspace Method for Accelerating Convergence in Delaunay-Based Optimization via Dimension Reduction

Delaunay-based derivative-free optimization, ∆DOGS, is an efficient and provably-convergent global optimization method for the problems which has computationally expensive objection function and the analytical expression for the objective function is not available. ∆-DOGS is a novel optimization scheme in the family of response surface methods (RSMs); however, it suffers from the curse of dimensionality since the computational cost increases dramatically as the number of design parameters increases. As a result, the number of design parameters in ∆-DOGS algorithm is relatively low (n.10). To avoid such problems, this paper proposes a combination of derivative-free optimization, seeking the global minimizer of an expensive and nonconvex objective function f(x) and active subspace method, detecting the directions of the most variability using evaluations of the gradient. The contribution of other directions to the objective function is bounded by a sufficiently small constant. This new algorithm iteratively applied Delaunay-based derivative-free optimization to seek the minimizer on the d-dimensional active subspace that has most function variation. Inverse mapping is needed to project data from active subspace to full-model for evaluating function values. This task is overcome by solving an inequality constrained problem that curves the response surface of the objective function. The test results show that this strategy is effective on a handful of optimization problems.

Bewley, Thomas R.↗

SU-E-J-161: Inverse Problems for Optical Parameters in Laser Induced Thermal Therapy

Purpose: Magnetic resonance-guided laser-induced thermal therapy (MRgLITT) is investigated as a neurosurgical intervention for oncological applications throughout the body by active post market studies. Real-time MR temperature imaging is used to monitor ablative thermal delivery in the clinic. Additionally, brain MRgLITT could improve through effective planning for laser fiber's placement. Mathematical bioheat models have been extensively investigated but require reliable patient specific physical parameter data, e.g. optical parameters. This abstract applies an inverse problem algorithm to characterize optical parameter data obtained from previous MRgLITT interventions. Methods: The implemented inverse problem has three primary components: a parameter-space search algorithm, a physics model, and training data. First, the parameter-space search algorithm uses a gradient-based quasi-Newton method to optimize the effective optical attenuation coefficient, μ-eff. A parameter reduction reduces the amount of optical parameter-space the algorithm must search. Second, the physics model is a simplified bioheat model for homogeneous tissue where closed-form Green's functions represent the exact solution. Third, the training data was temperature imaging data from 23 MRgLITT oncological brain ablations (980 nm wavelength) from seven different patients. Results: To three significant figures, the descriptive statistics for μ-eff were 1470 m{sup −1} mean, 1360 m{sup −1} median, 369 m{sup −1} standard deviation, 933 m{sup −1} minimum and 2260 m{sup −1} maximum. The standard deviation normalized by the mean was 25.0%. The inverse problem took <30 minutes to optimize all 23 datasets. Conclusion: As expected, the inferred average is biased by underlying physics model. However, the standard deviation normalized by the mean is smaller than literature values and indicates an increased precision in the characterization of the optical parameters needed to plan MRgLITT procedures. This investigation demonstrates the potential for the optimization and validation of more sophisticated bioheat models that incorporate the uncertainty of the data into the predictions, e.g. stochastic finite element methods.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Optimal experimental design for prediction based on push-forward probability measures

Incorporating experimental data is essential for increasing the credibility of simulation-aided decision making and design. This paper presents a method which uses a computational model to guide the optimal acquisition of experimental data to produce data-informed predictions of quantities of interest (QoI). Many strategies for optimal experimental design (OED) select data that maximize some utility that measures the reduction in uncertainty of uncertain model parameters, for example the expected information gain between prior and posterior distributions of these parameters. In this paper, we seek to maximize the expected information gained from the pushforward of an initial (prior) density to the push-forward of the updated (posterior) density through the parameter-to-prediction map. The formulation presented is based upon the solution of a specific class of stochastic inverse problems which seeks a probability density that is consistent with the model and the data in the sense that the push-forward of this density through the parameter-to-observable map matches a target density on the observable data. While this stochastic inverse problem forms the mathematical basis for our approach, we develop a one-step algorithm, focused on push-forward probability measures, that leverages inference-for-prediction to bypass constructing the solution to the stochastic inverse problem. A number of numerical results are presented to demonstrate the utility of this optimal experimental design for prediction and facilitate comparison of our approach with traditional OED.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Aerodynamic Rotor Design for a 25 MW Offshore Downwind Turbine

Continuously increasing offshore wind turbine scales require rotor designs that maximize power and performance. Downwind rotors offer advantages in lower mass due to reduced potential for tower strike, and is especially true at large scales, e.g., for a 25 MW turbine. In this study, three 25 MW downwind rotors, each with different prescribed lift coefficient distributions were designed (chord, geometry, and twist) and compared to maximize power production at unprecedented scales and Reynolds numbers, including a new approach to optimize rotor tilt and coning based on aeroelastic effects. To achieve this objective the design process was focused on achieving high power coefficients, while maximizing swept area and minimizing blade mass. Maximizing swept area was achieved by prescribing pre-cone and shaft tilt angles to ensure the aeroelastic orientation when the blades point upwards was nearly vertical at nearly rated conditions. Maximizing the power coefficient was achieved by prescribing axial induction factor and lift coefficient distributions which were then used as inputs for an inverse rotor design tool. The resulting rotors were then simulated to compare performance and subsequently optimized for minimum rotor mass. To achieve these goals, a high Reynolds number design space was developed using computational predictions as well as new empirical correlations for flatback airfoil drag and maximum lift. Within this design space, three rotors of small, medium and large chords were considered for clean airfoil conditions (effects of premature transition were also considered but did not significantly modify the design space). The results indicated that the medium chord design provided the best performance, producing the highest power in Region 2 from simulations while resulting in the lowest rotor mass, both of which support minimum LCOE. The methodology developed herein can be used for the design of other extreme-scale (upwind and downwind) turbines.

downwind rotors↗

Is the exquisite specificity of lymphocytes generated by thymic selection or due to evolution?

We have previously argued that the antigen receptors of T and B lymphocytes evolved to be sufficiently specific to avoid massive deletion of clonotypes by negative selection. Their optimal ‘specificity’ level, i.e., probability of binding any particular epitope, was shown to be inversely related to the number of self-antigens that the cells have to be tolerant to. Experiments have demonstrated that T lymphocytes also become more specific during negative selection in the thymus, because cells expressing the most crossreactive receptors have the highest likelihood of binding a self-antigen, and hence to be tolerized (i.e., deleted, anergized, or diverted into a regulatory T cell phenotype). Thus, there are two —not mutually exclusive— explanations for the exquisite specificity of T cells, one involving evolution and the other thymic selection. To better understand the impact of both, we extend a previously developed mathematical model by allowing for T cells with very different binding probabilities in the pre-selection repertoire. We confirm that negative selection tends to tolerize the most crossreactive clonotypes. As a result, the average level of specificity in the functional post-selection repertoire depends on the number of self-antigens, even if there is no evolutionary optimization of binding probabilities. However, the evolutionary optimal range of binding probabilities in the pre-selection repertoire also depends on the number of self-antigens. Species with more self antigens need more specific pre-selection repertoires to avoid excessive loss of T cells during thymic selection, and hence mount protective immune responses. We conclude that both evolution and negative selection are responsible for the high level of specificity of lymphocytes.

59 BASIC BIOLOGICAL SCIENCES↗

Input-response space-filling designs

Traditional space-filling designs are a convenient way to explore throughout an input space of flexible dimension and have design points close to any region where future predictions might be of interest. In some applications, there may be a model connecting the input factors to the response(s), which provides an opportunity to consider the spacing not only in the input space but also in the response space. In this paper, we present an approach for leveraging current understanding of the relationship between inputs and responses to generate designs that allow the experimenter to flexibly balance the spacing in these two regions to find an appropriate design for the experimental goals. Applications where good spacing of the observed response values include calibration problems where the goal is to demonstrate the adequacy of the model across the range of the responses, sensitivity studies where the outputs from a submodel may be used as inputs for subsequent models, and inverse problems where the outputs of a process will be used in the inverse prediction for the unknown inputs. Here, we use the multi-objective optimization method of Pareto fronts to generate multiple non-dominated designs with different emphases on the input and response space-filling criteria from which the experimenter can choose. The methods are illustrated through several examples and a chemical engineering case study.

42 ENGINEERING↗

Electrical switching of a p-wave magnet

Magnetic states with zero magnetization but non-relativistic spin splitting are outstanding candidates for the next generation of spintronic devices. Their electronvolt (eV)-scale spin splitting, ultrafast spin dynamics and nearly vanishing stray fields make them particularly promising for several applications. A variety of such magnetic states with non-trivial spin textures have been identified recently, including even-parity d-wave, g-wave or i-wave altermagnets and odd-parity p-wave magnets. Achieving voltage-based control of the non-uniform spin polarization of these magnetic states is of great interest for realizing energy-efficient and compact devices for information storage and processing. Spin-spiral type II multiferroics are optimal candidates for such voltage-based control, as they exhibit an inversion-symmetry-breaking magnetic order that directly induces ferroelectric polarization, allowing for symmetry-protected cross-control between spin chirality and polar order. Here we combine photocurrent measurements, first-principles calculations and group-theory analysis to provide direct evidence that the spin polarization of the spin-spiral type II multiferroic NiI 2 exhibits odd-parity character connected to the spiral chirality. The symmetry-protected coupling between chirality and polar order enables electrical control of a primarily non-relativistic spin polarization. Our findings represent an observation of p-wave magnetism in a spin-spiral type II multiferroic, which may lead to the development of voltage-based switching of non-relativistic spin polarization in compensated magnets.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

RIFTA: A Robust Iterative Fourier Transform-based dwell time Algorithm for ultra-precision ion beam figuring of synchrotron mirrors

With the rapid evolution of synchrotron X-ray sources, the demand for high-precision X-ray mirrors has greatly increased. Single nanometer profile error is required to keep imaging capability at the diffraction limit. Ion Beam Figuring (IBF), as a highly deterministic surfacing technique, has been used for ultra-precision finishing of mirrors. One crucial step that guides the IBF process is dwell time calculation. A valid dwell time solution should be non-negative and duplicate the shape of the desired removal map. Another important aspect is to minimize the total dwell time. In this study, we propose a Robust Iterative Fourier Transform-based dwell time Algorithm (RIFTA) that automatically fulfills these requirements. First, the thresholded inverse filtering in Fourier transform-based deconvolution is stabilized and automated by optimizing the threshold value using the Nelder-Mead simplex algorithm. Second, a novel two-level iterative scheme is proposed to guarantee the minimized total dwell time with its non-negativity at each dwell point. Third, a bicubic resampling is employed to flexibly adapt the calculated dwell time map to any IBF process intervals. The performance of RIFTA is first studied with simulation, followed by a comparison with the other state-of-the-art dwell time algorithms. We then demonstrate with an experiment that, using the dwell time calculated by the RIFTA, the total dwell time is shortened by a factor of two and the RMS in a 5 × 50 mm clear aperture was reduced from 3.4 nm to 1.1 nm after one IBF run, which proves the effectiveness and the efficiency of the proposed algorithm.

42 ENGINEERING↗

Improving small-scale CMB lensing reconstruction

Over the past decade, the gravitational lensing of the Cosmic Microwave Background (CMB) has become a powerful tool for probing the matter distribution in the Universe. The standard technique used to reconstruct the CMB lensing signal employs the quadratic estimator (QE) method, which has recently been shown to be suboptimal for lensing measurements on very small scales in temperature and polarization data. We implement a simple, more optimal method for the small-scale regime, which involves taking the direct inverse of the background gradient. We derive new techniques to make continuous maps of lensing using this "Gradient-Inversion" (GI) method and validate our method with simulated data, finding good agreement with predictions. For idealized simulations of lensing cross- and autospectra that neglect foregrounds, we demonstrate that our method performs significantly better than previous quadratic estimator methods in temperature; at $L=5000-9000$, it reduces errors on the lensing auto-power spectrum by a factor of $\sim 4$ for both idealized CMB-S4 and Simons Observatory-like experiments and by a factor of $\sim 2.6$ for cross-correlations of CMB-S4-like lensing reconstruction and the true lensing field. Finally, we caution that the level of the neglected small-scale foreground power, while low in polarization, is very high in temperature; though we briefly outline foreground mitigation methods, further work on this topic is required. Nevertheless, our results show the future potential for improved small-scale CMB lensing measurements, which could provide stronger constraints on cosmological parameters and astrophysics at high redshifts.

79 ASTRONOMY AND ASTROPHYSICS↗