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At least 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Closed-Form Approximation of the Total Variation Proximal Operator

Total variation (TV) is a widely used function for regularizing imaging inverse problems that is particularly appropriate for images whose underlying structure is piecewise constant. TV regularized optimization problems are typically solved using proximal methods, but the way in which they are applied is constrained by the absence of a closed-form expression for the proximal operator of the TV function. A closed-form approximation of the TV proximal operator has previously been proposed, but its accuracy was not theoretically explored in detail. Here, we address this gap by making several new theoretical contributions, proving that the approximation leads to a proximal operator of some convex function, it is equivalent to a gradient descent step on a smoothed version of TV, and that its error can be fully characterized and controlled with its scaling parameter. We experimentally validate our theoretical results on image denoising and sparse-view computed tomography (CT) image reconstruction.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Advancing the Frontiers of Deep Learning for Low-Dose 3D Cone-Beam CT Reconstruction

X-ray computed tomography (CT) is an important noninvasive medical imaging modality for studying the structural details of internal organs. Image reconstruction in CT is an inverse problem of recovering an object's internal structure from the absorption profile of X-ray beams (sinogram) measured using a detector. The classical variational approach for CT reconstruction minimizes an energy functional using an appropriate iterative algorithm. Motivated by the success of deep learning (DL), researchers have begun to leverage training data and enhanced computing capabilities in recent years to produce high-fidelity reconstructed images. Nonetheless, much of the academic research in DL algorithms for CT has focused primarily on the two-dimensional setting (with simplified forward operators and noise model) for proofs-of-concept, and a comprehensive benchmarking of various classical and data-driven CT reconstruction approaches has not beenundertaken. The key objective of our CT reconstruction grand challenge was to promote methodological advancements for both classical and DL-based approaches for clinical CT with a reasonably accurately simulated 3D CT forward operator and noise model. We have utilized the publicly available LIDC-IDRI dataset and simulated sinograms and FDK images corresponding to two dose levels (clinical- and low-dose, constituting two tracks of the challenge) starting from the normal-dose images as the ground truth. In this paper, we summarize the motivation, context, and results of our challenge, and highlight the future research directions in DL for clinical CT.

X-ray tomography↗
NASA NTRS1979

Wave tilt sounding of multilayered structures

The relationship between the wave tilt and the electrical parameters of a multilayered structure is investigated. Particular emphasis is placed on the inverse problem associated with the sounding planetary surfaces. An inversion technique, based on multifrequency wave tilt, is proposed and demonstrated with several computer models. It is determined that there is close agreement between the electrical parameters used in the models and those in the inversion values.

Warne, L.↗
NASA NTRS1997

Regularization for Atmospheric Temperature Retrieval Problems

Passive remote sensing of the atmosphere is used to determine the atmospheric state. A radiometer measures microwave emissions from earth's atmosphere and surface. The radiance measured by the radiometer is proportional to the brightness temperature. This brightness temperature can be used to estimate atmospheric parameters such as temperature and water vapor content. These quantities are of primary importance for different applications in meteorology, oceanography, and geophysical sciences. Depending on the range in the electromagnetic spectrum being measured by the radiometer and the atmospheric quantities to be estimated, the retrieval or inverse problem of determining atmospheric parameters from brightness temperature might be linear or nonlinear. In most applications, the retrieval problem requires the inversion of a Fredholm integral equation of the first kind making this an ill-posed problem. The numerical solution of the retrieval problem requires the transformation of the continuous problem into a discrete problem. The ill-posedness of the continuous problem translates into ill-conditioning or ill-posedness of the discrete problem. Regularization methods are used to convert the ill-posed problem into a well-posed one. In this paper, we present some results of our work in applying different regularization techniques to atmospheric temperature retrievals using brightness temperatures measured with the SSM/T-1 sensor. Simulation results are presented which show the potential of these techniques to improve temperature retrievals. In particular, no statistical assumptions are needed and the algorithms were capable of correctly estimating the temperature profile corner at the tropopause independent of the initial guess.

Velez-Reyes, Miguel↗
DOE OSTI2020

On the Derivation of Quasi-Newton Formulas for Optimization in Function Spaces

Newton’s method is usually preferred when solving optimization problems due to its superior convergence properties compared to gradient-based or derivative-free optimization algorithms. However, deriving and computing second-order derivatives needed by Newton’s method often is not trivial and, in some cases, not possible. In such cases quasi-Newton algorithms are a great alternative. In this paper, we provide a new derivation of well-known quasi-Newton formulas in an infinite-dimensional Hilbert space setting. Furthermore, it is known that quasi-Newton update formulas are solutions to certain variational problems over the space of symmetric matrices. In this paper, we formulate similar variational problems over the space of bounded symmetric operators in Hilbert spaces. By changing the constraints of the variational problem we obtain updates (for the Hessian and Hessian inverse) not only for the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method but also for Davidon–Fletcher–Powell (DFP), Symmetric Rank One (SR1), and Powell-Symmetric-Broyden (PSB). In addition, for an inverse problem governed by a partial differential equation (PDE), we derive DFP and BFGS “structured” secant formulas that explicitly use the derivative of the regularization and only approximates the second derivative of the misfit term. We show numerical results that demonstrate the desired mesh-independence property and superior performance of the resulting quasi-Newton methods.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1990

An approximation theory for the identification of linear thermoelastic systems

An abstract approximation framework and convergence theory for the identification of thermoelastic systems is developed. Starting from an abstract operator formulation consisting of a coupled second order hyperbolic equation of elasticity and first order parabolic equation for heat conduction, well-posedness is established using linear semigroup theory in Hilbert space, and a class of parameter estimation problems is then defined involving mild solutions. The approximation framework is based upon generic Galerkin approximation of the mild solutions, and convergence of solutions of the resulting sequence of approximating finite dimensional parameter identification problems to a solution of the original infinite dimensional inverse problem is established using approximation results for operator semigroups. An example involving the basic equations of one dimensional linear thermoelasticity and a linear spline based scheme are discussed. Numerical results indicate how the approach might be used in a study of damping mechanisms in flexible structures.

Rosen, I. G.↗
NASA NTRS1990

Inverse methods for assessing ship-of-opportunity networks and estimating circulation and winds from tropical expendable bathythermograph data

Inverse methods for estimating the surface ciculation of the equatorial Pacific by combining a linear reduced-gravity shallow-water model with the Tropical Ocean-Global Atmosphere ship-of-opportunity expendable bathythermograph (TOGA SOP XBT) observing program are examined. It is demonstrated that a simple linear model of the upper circulation of the equatorial Pacific can be successfully used as a weak constraint when smoothing the TOGA SOP XBT data. A circulation is sought as the weighted least squares fit to the dynamics and the data. The solution method is an expansion in representer functions, and the generalized inverse problem is thereby reduced from a functional problem to an algebraic problem for the coefficients of the representer. A specific inverse calculation using synthetic forcing and data is presented.

Bennett, Andrew F.↗
DOE OSTI2022

Invertible neural networks for E3SM land model calibration and simulation

We apply an invertible neural network (INN) for E3SM land model calibration and simulation with eight parameters at the Missouri Ozark AmeriFlux forest site. INN provides bijective (two-way) mappings between inputs and outputs, thus it can solve probabilistic inverse problems and forward approximations simultaneously. We demonstrate INN's inverse and forward capability in both synthetic and real-data applications. Results indicate that INN produces accurate parameter posterior distributions similar to Markov Chain Monte Carlo sampling and it generates model outputs close to the forward model simulations. Additionally, both the inverse and forward evaluations in INN are computationally efficient which allows for rapid integration of observations for parameter estimation and fast model predictions.

Lu, Dan↗
DOE OSTI2023

Machine learning based approach to predict ductile damage model parameters for polycrystalline metals

Damage models for ductile materials typically need to be parameterized, often with the appropriate parameters changing for a given material depending on the loading conditions. This can make parameterizing these models computationally expensive, since an inverse problem must be solved for each loading condition. Using standard inverse modeling techniques typically requires hundreds or thousands of high-fidelity computer simulations to estimate the optimal parameters. Additionally, the time of a human expert is required to set up the inverse model. Machine learning has recently emerged as an alternative approach to inverse modeling in these settings, where the machine learning model is trained in an offline manner and new parameters can be quickly generated on the fly, after training is complete. Here, this work utilizes such a workflow to enable the rapid parameterization of a ductile damage model called TEPLA with a machine learning inverse model. The machine learning model can efficiently estimate the model parameters much faster, as compared to previously employed methods, such as Bayesian calibration. The results demonstrate good accuracy on a synthetic test dataset and is validated against experimental data.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Machine learning for domain transfer between simulated and experimental 2D X-ray diffraction patterns using generative adversarial networks

X-ray diffraction (XRD) is a well-established technique for analyzing materials at an atomic level. Dynamic compression experiments (DCE), in which materials are subject to extreme pressures, can provide fundamental understanding to pressure-induced phase transitions and compression of the crystal lattice. The analysis of XRD patterns from highly compressed samples is non-trivial given the sparsity of data, high experimental costs, and the fact that the data is often marred with X-ray background and other artifacts. While accurate computational frameworks exist, they solve the forward problem—from structures and orientations to XRD patterns. Solving the inverse problem for 2D experimental diffraction patterns is currently a complex manual process of matching and comparing experimentally observed patterns to computationally generated ones. Machine learning is a promising tool for automating the matching process but often requires data-intensive architectures. Here, in this study, we use a CycleGAN to translate the domain of limited experimental data to a domain in which there is readily available simulated data. This domain shift allows data-intensive machine learning models that have only been trained on simulated XRD patterns to be used in the analysis of experiments.

Brozak, Samantha Jean [Sandia National Laboratorie↗
DOE OSTI2021

Inverse Aerodynamic Design of Gas Turbine Blades using Probabilistic Machine Learning

Abstract One of the critical components in Industrial Gas Turbines (IGT) is the turbine blade. Design of turbine blades needs to consider multiple aspects like aerodynamic efficiency, durability, safety and manufacturing, which make the design process sequential and iterative. The sequential nature of these iterations forces a long design cycle time, ranging from several months to years. Due to the reactionary nature of these iterations, little effort has been made to accumulate data in a manner that allows for deep exploration and understanding of the total design space. This is exemplified in the process of designing the individual components of the IGT resulting in a potential unrealized efficiency. To overcome the aforementioned challenges, we demonstrate a probabilistic inverse design machine learning framework, namely PMI (PMI), to carry out an explicit inverse design. PMI calculates the design explicitly without costly iteration and overcomes the challenges associated with ill-posed inverse problems. In this work the framework will be demonstrated on inverse aerodynamic design of three-dimensional turbine blades.

Engineering↗
DOE OSTI2021

Estimating Watershed Subsurface Permeability From Stream Discharge Data Using Deep Neural Networks

Subsurface permeability is a key parameter in watershed models that controls the contribution from the subsurface flow to stream flows. Since the permeability is difficult and expensive to measure directly at the spatial extent and resolution required by fully distributed watershed models, estimation through inverse modeling has had a long history in subsurface hydrology. The wide availability of stream surface flow data, compared to groundwater monitoring data, provides a new data source to infer soil and geologic properties using integrated surface and subsurface hydrologic models. As most of the existing methods have shown difficulty in dealing with highly nonlinear inverse problems, we explore the use of deep neural networks for inversion owing to their successes in mapping complex, highly nonlinear relationships. We train various deep neural network (DNN) models with different architectures to predict subsurface permeability from stream discharge hydrograph at the watershed outlet. The training data are obtained from ensemble simulations of hydrographs corresponding to an permeability ensemble using a fully-distributed, integrated surface-subsurface hydrologic model. The trained model is then applied to estimate the permeability of the real watershed using its observed hydrograph at the outlet. Our study demonstrates that the permeabilities of the soil and geologic facies that make significant contributions to the outlet discharge can be more accurately estimated from the discharge data. Their estimations are also more robust with observation errors. Compared to the traditional ensemble smoother method, DNNs show stronger performance in capturing the nonlinear relationship between permeability and stream hydrograph to accurately estimate permeability. Our study sheds new light on the value of the emerging deep learning methods in assisting integrated watershed modeling by improving parameter estimation, which will eventually reduce the uncertainty in predictive watershed models.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Data-Consistent Inversion for Stochastic Input-to-Output Maps

Data-consistent inversion is a recently developed measure-theoretic framework for solving a stochastic inverse problem involving models of physical systems. The goal is to construct a probability measure on model inputs (i.e., parameters of interest) whose associated push-forward measure matches (i.e., is consistent with) a probability measure on the observable outputs of the model (i.e., quantities of interest). Previous implementations required the map from parameters of interest to quantities of interest to be deterministic. This work generalizes this framework for maps that are stochastic, i.e., contain uncertainties and variation not explainable by variations in uncertain parameters of interest. Generalizations of previous theorems of existence, uniqueness, and stability of the data-consistent solution are provided while new theoretical results address the stability of marginals on parameters of interest. A notable aspect of the algorithmic generalization is the ability to query the solution to generate independent identically distributed samples of the parameters of interest without requiring knowledge of the so-called stochastic parameters. This work therefore extends the applicability of the data-consistent inversion framework to a much wider class of problems. This includes those based on purely experimental and field data where only a subset of conditions are either controllable or can be documented between experiments while the underlying physics, measurement errors, and any additional covariates are either uncertain or not accounted for by the researcher. Finally, numerical examples demonstrate application of this approach to systems with stochastic sources of uncertainties embedded within the modeling of a system and a numerical diagnostic is summarized that is useful for determining if a key assumption is verified among competing choices of stochastic maps.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Local convergence analysis of an inexact trust-region method for nonsmooth optimization

In Baraldi, we introduced an inexact trust-region algorithm for minimizing the sum of a smooth nonconvex function and a nonsmooth convex function in Hilbert space—a class of problems that is ubiquitous in data science, learning, optimal control, and inverse problems. Furthermore, this algorithm has demonstrated excellent performance and scalability with problem size. In this paper, we enrich the convergence analysis for this algorithm, proving strong convergence of the iterates with guaranteed rates. In particular, we demonstrate that the trust-region algorithm recovers superlinear, even quadratic, convergence rates when using a second-order Taylor approximation of the smooth objective function term.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1988

Vertical resolution of middle atmospheric measurements by ground-based microwave radiometry

The vertical resolution obtainable through measurement of trace constituents in the middle atmosphere by ground-based microwave spectroscopy has remained somewhat ambiguous. In order to explore this question, the Backus-Gilbert (1967, 1968, 1970) inversion technique, which automatically yields quantitative estimates of the inversion spatial resolution was applied to this particular inverse problem. This indicated that the optimum resolution of Backus-Gilbert inversions of microwave spectroscopic measurements is about 10 km. A general technique, based on inversion of delta function simulated profiles, was then developed, for evaluating the resolution of any inversion technique and applied to the Chahine (1970) inversion technique. These results indicated that the optimum resolution of the Chahine technique is about 6 or 7 km, or nearly a factor of 2 better than the equivalent Backus-Gilbert results.

Bevilacqua, Richard M.↗
DOE OSTI2023

NSGA-PINN: A Multi-Objective Optimization Method for Physics-Informed Neural Network Training

This paper presents NSGA-PINN, a multi-objective optimization framework for the effective training of physics-informed neural networks (PINNs). The proposed framework uses the non-dominated sorting genetic algorithm (NSGA-II) to enable traditional stochastic gradient optimization algorithms (e.g., ADAM) to escape local minima effectively. Additionally, the NSGA-II algorithm enables satisfying the initial and boundary conditions encoded into the loss function during physics-informed training precisely. We demonstrate the effectiveness of our framework by applying NSGA-PINN to several ordinary and partial differential equation problems. In particular, we show that the proposed framework can handle challenging inverse problems with noisy data.

Lu, Binghang (ORCID:0009000160016632)↗