Results for “data space inversion” — Page 5

DOE OSTI2019

Convolutional Neural Network Surrogate Models for the Mechanical Properties of Periodic Structures

The work in this paper describes neural network surrogate models for calculating the effective mechanical properties of a periodic composites. The models achieve good accuracy even when only provided with training data sampling a small portion of the design space. As an example, the surrogate models are applied to solving the inverse design problem of finding structures with optimal mechanical properties. The surrogate models are sufficiently accurate to recover optimal solutions in general agreement with established topology optimization methods. However, improvements will be required to develop robust, efficient neural network-based surrogate models and several directions for future research are highlighted here.

42 ENGINEERING↗

NASA NTRS1993

The soliton transform and a possible application to nonlinear Alfven waves in space

The inverse scattering transform (IST) based on the derivative nonlinear Schroedinger (DNLS) equation is applied to a complex time series of nonlinear Alfven wave data generated by numerical simulation. The IST describes the long-time evolution of quasi-parallel Alfven waves more efficiently than the Fourier transform, which is adapted to linear rather than nonlinear problems. When dissipation is added, so the conditions for the validity of the DNLS are not strictly satisfied, the IST continues to provide a compact description of the wavefield in terms of a small number of decaying envelope solitons.

Hada, T.↗

DOE OSTI2016

Fault geometry and slip distribution of the 2008 M w 7.9 Wenchuan, China earthquake, inferred from GPS and InSAR measurements

We revisit the problem of coseismic rupture of the 2008 M w 7.9 Wenchuan earthquake. Precise determination of the fault structure and slip distribution provides critical information about the mechanical behaviour of the fault system and earthquake rupture. We use all the geodetic data available, craft a more realistic Earth structure and fault model compared to previous studies, and employ a nonlinear inversion scheme to optimally solve for the fault geometry and slip distribution. Compared to a homogeneous elastic half-space model and laterally uniform layered models, adopting separate layered elastic structure models on both sides of the Beichuan fault significantly improved data fitting. Our results reveal that: (1) The Beichuan fault is listric in shape, with near surface fault dip angles increasing from ~36° at the southwest end to ~83° at the northeast end of the rupture. (2) The fault rupture style changes from predominantly thrust at the southwest end to dextral at the northeast end of the fault rupture. (3) Fault slip peaks near the surface for most parts of the fault, with~8.4mthrust and ~5 m dextral slip near Hongkou and ~6 m thrust and ~8.4 m dextral slip near Beichuan, respectively. (4) The peak slips are located around fault geometric complexities, suggesting that earthquake style and rupture propagation were determined by fault zone geometric barriers. Such barriers exist primarily along restraining left stepping discontinuities of the dextralcompressional fault system. (5) The seismic moment released on the fault above 20 km depth is 8.2 × 10 21 N m, corresponding to an M w 7.9 event. The seismic moments released on the local slip concentrations are equivalent to events of M w 7.5 at Yingxiu-Hongkou, M w 7.3 at Beichuan-Pingtong, M w 7.2 near Qingping, M w 7.1 near Qingchuan, and M w 6.7 near Nanba, respectively. (6) The fault geometry and kinematics are consistent with a model in which crustal deformation at the eastern margin of the Tibetan plateau is decoupled by differential motion across a decollement in the mid crust, above which deformation is dominated by brittle reverse faulting and below which deformation occurs by viscous horizontal shortening and vertical thickening.

58 GEOSCIENCES↗

NASA NTRSDate not supplied

Improving Boundary Layer Data Assimilation Using Observation Data from Multiple Observing Systems in the NASA GEOS System

The Planetary Boundary Layer (PBL) is a complex interface that mediates energy and moisture exchanges between the Earth’s surface and atmosphere. Accurate simulation and observation of PBL characteristics, such as PBL height and thermodynamic structure, have proven to be a challenge. In our latest efforts, we have focused on improving PBL thermodynamic structure using data from multiple observing systems in the Goddard Earth Observing System (GEOS), developed by the NASA Global Modeling and Assimilation Office (GMAO). We present strategies and results from assimilating PBL height data derived from radiosondes, GNSS radio occultation, space-based lidar (CALIPSO, CATS, IceSat-2), ground-based lidar (MPLNET), and radar wind profilers, including a novel global PBL height analysis dataset. We also discuss the impacts of better representing capping inversions by using PBL height data together with other observations in GEOS through adjustments to the background error covariance. Long-term statistics of the impact of assimilating and utilizing PBL height data in GEOS are presented. In addition, we explore an innovative approach to assimilate GNSS-RO refractivity data in the lower troposphere.

Eun-Gyeong Yang↗

NASA NTRS1991

Numerical recovery of certain discontinuous electrical conductivities

The inverse problem of recovering an electrical conductivity of the form Gamma(x) = 1 + (k-1)(sub Chi(D)) (Chi(D) is the characteristic function of D) on a region omega is a subset of 2-dimensional Euclid space from boundary data is considered, where D is a subset of omega and k is some positive constant. A linearization of the forward problem is formed and used in a least squares output method for approximately solving the inverse problem. Convergence results are proved and some numerical results presented.

Bryan, Kurt↗

DOE OSTI2016

Dynamical constraints on the core mass of hot Jupiter HAT-P-13B

HAT-P-13b is a Jupiter-mass transiting exoplanet that has settled onto a stable, short-period, and mildly eccentric orbit as a consequence of the action of tidal dissipation and perturbations from a second, highly eccentric, outer companion. Owing to the special orbital configuration of the HAT-P-13 system, the magnitude of HAT-P-13b's eccentricity (e{sub b}) is in part dictated by its Love number (k{sub 2{sub b}}), which is in turn a proxy for the degree of central mass concentration in its interior. Thus, the measurement of e{sub b} constrains k{sub 2{sub b}} and allows us to place otherwise elusive constraints on the mass of HAT-P-13b's core (M{sub core,b}). In this study we derive new constraints on the value of e{sub b} by observing two secondary eclipses of HAT-P-13b with the Infrared Array Camera on board the Spitzer Space Telescope. We fit the measured secondary eclipse times simultaneously with radial velocity measurements and find that e{sub b} = 0.00700 ± 0.00100. We then use octupole-order secular perturbation theory to find the corresponding k{sub 2{sub b}}=0.31{sub −0.05}{sup +0.08}. Applying structural evolution models, we then find, with 68% confidence, that M{sub core,b} is less than 25 Earth masses (M{sub ⊕}). The most likely value is M{sub core,b} = 11 M{sub ⊕}, which is similar to the core mass theoretically required for runaway gas accretion. This is the tightest constraint to date on the core mass of a hot Jupiter. Additionally, we find that the measured secondary eclipse depths, which are in the 3.6 and 4.5 μm bands, best match atmospheric model predictions with a dayside temperature inversion and relatively efficient day–night circulation.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1994

Heat transfer measurements for Stirling machine cylinders

The primary purpose of this study was to measure the effects of inflow-produced heat turbulence on heat transfer in Stirling machine cylinders. A secondary purpose was to provide new experimental information on heat transfer in gas springs without inflow. The apparatus for the experiment consisted of a varying-volume piston-cylinder space connected to a fixed volume space by an orifice. The orifice size could be varied to adjust the level of inflow-produced turbulence, or the orifice plate could be removed completely so as to merge the two spaces into a single gas spring space. Speed, cycle mean pressure, overall volume ratio, and varying volume space clearance ratio could also be adjusted. Volume, pressure in both spaces, and local heat flux at two locations were measured. The pressure and volume measurements were used to calculate area averaged heat flux, heat transfer hysteresis loss, and other heat transfer-related effects. Experiments in the one space arrangement extended the range of previous gas spring tests to lower volume ratio and higher nondimensional speed. The tests corroborated previous results and showed that analytic models for heat transfer and loss based on volume ratio approaching 1 were valid for volume ratios ranging from 1 to 2, a range covering most gas springs in Stirling machines. Data from experiments in the two space arrangement were first analyzed based on lumping the two spaces together and examining total loss and averaged heat transfer as a function of overall nondimensional parameter. Heat transfer and loss were found to be significantly increased by inflow-produced turbulence. These increases could be modeled by appropriate adjustment of empirical coefficients in an existing semi-analytic model. An attempt was made to use an inverse, parameter optimization procedure to find the heat transfer in each of the two spaces. This procedure was successful in retrieving this information from simulated pressure-volume data with artificially generated noise, but it failed with the actual experimental data. This is evidence that the models used in the parameter optimization procedure (and to generate the simulated data) were not correct. Data from the surface heat flux sensors indicated that the primary shortcoming of these models was that they assumed turbulence levels to be constant over the cycle. Sensor data in the varying volume space showed a large increase in heat flux, probably due to turbulence, during the expansion stroke.

Kornhauser, Alan A.↗

DOE OSTI2021

Anomalous temperature dependence of the experimental x-ray structure factor of supercooled water

The structural changes of water upon deep supercooling were studied through wide-angle x-ray scattering at SwissFEL. The experimental setup had a momentum transfer range of 4.5 Å-1, which covered the principal doublet of the x-ray structure factor of water. The oxygen–oxygen structure factor was obtained for temperatures down to 228.5 ± 0.6 K. Similar to previous studies, the second diffraction peak increased strongly in amplitude as the structural change accelerated toward a local tetrahedral structure upon deep supercooling. We also observed an anomalous trend for the second peak position of the oxygen–oxygen structure factor (q 2 ). We found that q 2 exhibits an unprecedented positive partial derivative with respect to temperature for temperatures below 236 K. Based on Fourier inversion of our experimental data combined with reference data, we propose that the anomalous q 2 shift originates from that a repeat spacing in the tetrahedral network, associated with all peaks in the oxygen–oxygen pair-correlation function, gives rise to a less dense local ordering that resembles that of low-density amorphous ice. The findings are consistent with that liquid water consists of a pentamer-based hydrogen-bonded network with low density upon deep supercooling.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Two transitions in complex eigenvalue statistics: Hermiticity and integrability breaking

Open quantum systems have complex energy eigenvalues which are expected to follow non-Hermitian random matrix statistics, when chaotic, or two-dimensional (2d) Poisson statistics, when integrable. We investigate the spectral properties of a many-body quantum spin chain, i.e., the Hermitian Heisenberg model with imaginary disorder. Its rich complex eigenvalue statistics is found to separately break both Hermiticity and integrability at different scales of the disorder strength. With no disorder, the system is integrable and Hermitian, with spectral statistics corresponding to the 1d Poisson point process. At very small disorder, we find a transition from 1d Poisson statistics to an effective D -dimensional Poisson point process, showing Hermiticity breaking. At intermediate disorder, we find integrability breaking, as inferred from the statistics matching that of non-Hermitian complex symmetric random matrices in class AI † . For large disorder, as the spins align, we recover the expected integrability (now in the non-Hermitian setup), indicated by 2d Poisson statistics. These conclusions are based on fitting the spin-chain data of numerically generated nearest- and next-to-nearest-neighbor spacing distributions to an effective 2d Coulomb gas description at inverse temperature β . We confirm that such an effective description of random matrices also applies in classes AI † and AII † up to next-to-nearest-neighbor spacings. Published by the American Physical Society 2025

Akemann, Gernot (ORCID:0000000217104258)↗

DOE OSTI2020

Learning and meta-learning of stochastic advection–diffusion–reaction systems from sparse measurements

Physics-informed neural networks (PINNs) were recently proposed in [18] as an alternative way to solve partial differential equations (PDEs). A neural network (NN) represents the solution, while a PDE-induced NN is coupled to the solution NN, and all differential operators are treated using automatic differentiation. Here, we first employ the standard PINN and a stochastic version, sPINN, to solve forward and inverse problems governed by a non-linear advection–diffusion–reaction (ADR) equation, assuming we have some sparse measurements of the concentration field at random or pre-selected locations. Subsequently, we attempt to optimise the hyper-parameters of sPINN by using the Bayesian optimisation method (meta-learning) and compare the results with the empirically selected hyper-parameters of sPINN. In particular, for the first part in solving the inverse deterministic ADR, we assume that we only have a few high-fidelity measurements, whereas the rest of the data is of lower fidelity. Hence, the PINN is trained using a composite multi-fidelity network, first introduced in [12], that learns the correlations between the multi-fidelity data and predicts the unknown values of diffusivity, transport velocity and two reaction constants as well as the concentration field. For the stochastic ADR, we employ a Karhunen–Loève (KL) expansion to represent the stochastic diffusivity, and arbitrary polynomial chaos (aPC) to represent the stochastic solution. Correspondingly, we design multiple NNs to represent the mean of the solution and learn each aPC mode separately, whereas we employ a separate NN to represent the mean of diffusivity and another NN to learn all modes of the KL expansion. For the inverse problem, in addition to stochastic diffusivity and concentration fields, we also aim to obtain the (unknown) deterministic values of transport velocity and reaction constants. The available data correspond to 7spatial points for the diffusivity and 20 space–time points for the solution, both sampled 2000 times. We obtain good accuracy for the deterministic parameters of the order of 1–2% and excellent accuracy for the mean and variance of the stochastic fields, better than three digits of accuracy. In the second part, we consider the previous stochastic inverse problem, and we use Bayesian optimisation to find five hyper-parameters of sPINN, namely the width, depth and learning rate of two NNs for learning the modes. Here, we obtain much deeper and wider optimal NNs compared to the manual tuning, leading to even better accuracy, i.e., errors less than 1% for the deterministic values, and about an order of magnitude less for the stochastic fields.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

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↗

DOE OSTI2020

Three-dimensional seismic characterization and imaging of the Soda Lake geothermal field

Accurate characterization of subsurface geophysical properties and detection of the fault system are essential for geothermal energy exploration and production. The Soda Lake geothermal field is in western Nevada with a complex fault system. Previous seismic characterization only produced a low-resolution, smooth velocity model along with a simple, conceptual fault model. Using optimized correlation-based full-waveform inversion, wavefield-separation-based reverse-time migration, and automatic fault detection techniques, we present 3D seismic characterization for the Soda Lake geothermal field using 3D surface seismic data acquired with Vibroseis sources. Here, we obtain 3D high-resolution velocity, density, and acoustic impedance models, 3D seismic images with different grid spacings, and a high-resolution fault system. Consistency check between the constructed faults and currently active injection and production geothermal wells verifies that our seismic inversion and imaging results and detected faults are reliable. These results can provide valuable information for optimizing well placement and geothermal energy production at the Soda Lake geothermal field.

15 GEOTHERMAL ENERGY↗

DOE OSTI2018

A spacetime derivation of the Lorentzian OPE inversion formula

Caron-Huot has recently given an interesting formula that determines OPE data in a conformal field theory in terms of a weighted integral of the four-point function over a Lorentzian region of cross-ratio space. We give a new derivation of this formula based on Wick rotation in spacetime rather than cross-ratio space. The derivation is simple in two dimensions but more involved in higher dimensions. We also derive a Lorentzian inversion formula in one dimension that sheds light on previous observations about the chaos regime in the SYK model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2023

A Novel Approach to Map Permeability Using Passive Seismic Emission Tomography

Newly acquired magnetotelluric data and passive seismic data collected with tightly spaced geophone arrays are combined with historic drilling, active seismic, and potential fields data to generate 3-D permeability maps. A cooperative inversion methodology has been developed using active seismic, magnetotelluric, and gravity data in order to produce more robust velocity models for passive seismic data processing without requiring expensive 3-D active seismic surveys. The cooperative inversion estimates velocities from other geophysical data where no prior seismic velocity information is available at two geothermal sites in Nevada: San Emidio and Crescent Valley.

15 GEOTHERMAL ENERGY↗

NASA NTRS2005

Modeling and Inverse Controller Design for an Unmanned Aerial Vehicle Based on the Self-Organizing Map

The next generation of aircraft will have dynamics that vary considerably over the operating regime. A single controller will have difficulty to meet the design specifications. In this paper, a SOM-based local linear modeling scheme of an unmanned aerial vehicle (UAV) is developed to design a set of inverse controllers. The SOM selects the operating regime depending only on the embedded output space information and avoids normalization of the input data. Each local linear model is associated with a linear controller, which is easy to design. Switching of the controllers is done synchronously with the active local linear model that tracks the different operating conditions. The proposed multiple modeling and control strategy has been successfully tested in a simulator that models the LoFLYTE UAV.

Cho, Jeongho↗

DOE OSTI2024

Multi‐Scale Seismic Imaging of the Ridgecrest, CA, Region With Waveform Inversion of Regional and Dense Array Data

Abstract We develop an inversion procedure for deriving multi‐scale velocity models with waveform inversions of earthquake and ambient noise data at multi‐frequency bands recorded by regional and dense sensor configurations. The method is applied for the area around the 2019 Ridgecrest earthquake rupture zones, utilizing data recorded by regional stations and dense 2D and 1D arrays with station spacings of ∼5 km and ∼100 m, respectively. Starting with regional Vp, Vs models and locations of Ridgecrest aftershocks, the velocity models and event locations are improved iteratively by inversions of waveforms recorded by regional stations and the 2D array, using a minimum spectral element size of ∼600 m. Waveforms from local events recorded by dense 1D arrays across the M7.1 rupture zone with frequencies of up to 10 Hz are used to resolve small‐scale features of the rupture zone and shallow crust with a local spectral element size of 80 m. The refined models provide self‐consistent descriptions of the rupture zone and the shallow crust embedded in the regional structures. The results reveal pronounced low Vs and high Vp/Vs in the M6.4 and M7.1 rupture zones coinciding with concentrations of seismicity, and also around the Garlock fault and in several local basins. We also observe clear velocity contrasts across the Garlock fault with polarity reversals along strike and with depth. The obtained multi‐scale velocity models can be used to improve derivations of earthquake source properties, simulations of dynamic ruptures and ground motions, and the understanding of fault and tectonic processes in the region.

Geochemistry & Geophysics↗

DOE OSTI2019

Active Subspace Methods for Data-Intensive Inverse Problems (Final Report)

Fostered by advances in computing, simulation and data science have emerged as the third and fourth paradigms enabling scientific discovery. Many mathematical challenges arise when integrating these paradigms to produce new knowledge. One of the most important challenges is the inverse or calibration problem: find the inputs of a simulation such that its outputs agree with a given set of measurements. As both the cost of the complex simulations and the volume of measurement data sets increase, intuition-driven trial-and-error methods for calibration quickly become untenable; modern scientists need more computationally efficient and mathematically rigorous methods. When measurements and simulated predictions contain uncertainty, the Bayesian perspective on statistical inference provides a popular mathematical framework for developing computational methods to solve inverse problems. Markov chain Monte Carlo (MCMC) methods are a mainstay of this framework; they characterize a probability distribution on the space of model inputs that is conditioned on the given measurements. However, despite recent advances, MCMC methods remain impractical for expensive simulations with more than a handful of inputs. At its heart, MCMC searches the space of inputs for corresponding outputs that match measurements, and so it is afflicted with the curse of dimensionality. Additionally, MCMC methods become less efficient as the volume of the measurement data increases, particularly if the measurements are redundant. To make MCMC—and Bayesian methods, in general—amenable to today’s computer models with millions of inputs and terabytes of measurement data, one must devise methods to reduce the dimension of both the simulation inputs and the measurements. For many models used in practice, the outputs vary primarily on a low-dimensional manifold of the nominally high-dimensional input space. Recently developed active subspace methods discover this low-dimensional manifold and exploit it to enable analyses typically suited for low-dimensional settings (e.g., statistical inversion of complex systems). We hypothesize that active subspace methods can provide the necessary dimension reduction, enabling existing Bayesian methods to find solutions for a large class of otherwise intractable statistical inverse problems. We will test the hypothesis with a series of mathematical analyses and computational experiments that will proceed along three research veins: (i) integrating active subspace methods into methods for statistical inversion, (ii) addressing current challenges in active subspace methods, and (iii) incorporating methods for nonlinear dimensionality reduction into active subspace methods. We will apply the methods we develop to real inverse problems in chemical kinetics and turbulent flame modeling. Our team combines expertise in methods for inverse problems, dimension reduction, and reduced order modeling. With a history of active collaboration and thoughtful engagement, we bring enthusiasm and fresh perspectives to a well studied subject. We are excited by the potential opportunity to work together to extend and apply active subspace methods to data-intensive inverse problems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

Active Subspace Methods for Data-Intensive Inverse Problems

Fostered by advances in computing, simulation and data science have emerged as the third and fourth paradigms enabling scientific discovery. Many mathematical challenges arise when integrating these paradigms to produce new knowledge. One of the most important challenges is the inverse or calibration problem: find the inputs of a simulation such that its outputs agree with a given set of measurements. As both the cost of the complex simulations and the volume of measurement data sets increase, intuition-driven trial-and-error methods for calibration quickly become untenable; modern scientists need more computationally efficient and mathematically rigorous methods. When measurements and simulated predictions contain uncertainty, the Bayesian perspective on statistical inference provides a popular mathematical framework for developing computational methods to solve inverse problems. Markov chain Monte Carlo (MCMC) methods are a mainstay of this framework; they characterize a probability distribution on the space of model inputs that is conditioned on the given measurements. However, despite recent advances, MCMC methods remain impractical for expensive simulations with more than a handful of inputs. At its heart, MCMC searches the space of inputs for corresponding outputs that match measurements, and so it is afflicted with the curse of dimensionality. Additionally, MCMC methods become less efficient as the volume of the measurement data increases, particularly if the measurements are redundant. To make MCMC—and Bayesian methods, in general—amenable to today’s computer models with millions of inputs and terabytes of measurement data, one must devise methods to reduce the dimension of both the simulation inputs and the measurements. For many models used in practice, the outputs vary primarily on a low-dimensional manifold of the nominally high-dimensional input space. Recently developed active subspace methods discover this low-dimensional manifold and exploit it to enable analyses typically suited for low-dimensional settings (e.g., statistical inversion of complex systems). We hypothesize that active subspace methods can provide the necessary dimension reduction, enabling existing Bayesian methods to find solutions for a large class of otherwise intractable statistical inverse problems. We will test the hypothesis with a series of mathematical analyses and computational experiments that will proceed along three research veins: (i) integrating active subspace methods into methods for statistical inversion, (ii) addressing current challenges in active subspace methods, and (iii) incorporating methods for nonlinear dimensionality reduction into active subspace methods. We will apply the methods we develop to real inverse problems in chemical kinetics and turbulent flame modeling. Our team combines expertise in methods for inverse problems, dimension reduction, and reduced order modeling. With a history of active collaboration and thoughtful engagement, we bring enthusiasm and fresh perspectives to a well studied subject. We are excited by the potential opportunity to work together to extend and apply active subspace methods to data-intensive inverse problems.

97 MATHEMATICS AND COMPUTING↗