Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “inverse problem”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 523 records · Page 29
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

KKT Preconditioners for PDE-Constrained Optimization with the Helmholtz Equation

This paper considers preconditioners for the linear systems that arise from optimal control and inverse problems involving the Helmholtz equation. Specifically, we explore an all-at-once approach. The main contribution centers on the analysis of two block preconditioners. Variations of these preconditioners have been proposed and analyzed in prior works for optimal control problems where the underlying partial differential equation is a Laplace-like operator. In this paper, we extend some of the prior convergence results to Helmholtz-based optimization applications. Our analysis examines situations where control variables and observations are restricted to subregions of the computational domain. We prove that solver convergence rates do not deteriorate as the mesh is refined or as the wavenumber increases. More specifically, for one of the preconditioners we prove accelerated convergence as the wavenumber increases. Additionally, in situations where the control and observation subregions are disjoint, we observe that solver convergence rates have a weak dependence on the regularization parameter. We give a partial analysis of this behavior. We illustrate the performance of the preconditioners on control problems motivated by acoustic testing.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

DOLCE: A Model-Based Probabilistic Diffusion Framework for Limited-Angle CT Reconstruction

Limited-Angle Computed Tomography (LACT) is a non-destructive evaluation technique used in a variety of applications ranging from security to medicine. The limited angle coverage in LACT is often a dominant source of severe artifacts in the reconstructed images, making it a challenging inverse problem. We present DOLCE, a new deep model-based framework for LACT that uses a conditional diffusion model as an image prior. Diffusion models are a recent class of deep generative models that are relatively easy to train due to their implementation as image denoisers. DOLCE can form high-quality images from severely under-sampled data by integrating data-consistency updates with the sampling updates of a diffusion model, which is conditioned on the transformed limited-angle data. We show through extensive experimentation on several challenging real LACT datasets that, the same pre-trained DOLCE model achieves the SOTA performance on drastically different types of images. Additionally, we show that, unlike standard LACT reconstruction methods, DOLCE naturally enables the quantification of the reconstruction uncertainty by generating multiple samples consistent with the measured data.

Kim, Hyojin↗
DOE OSTI2021

pnnl/neuromancer

Dynamics-based deep learning methods to modernize current scientific computing methods. Neuromancer is currently capable of solving inverse problems for a system of ordinary differential equations. The functionality includes system identification and constrained optimal control of unknown or partially known ODEs.

Skomski, Elliott↗
DOE OSTI2024

Prime VI

SAND2025-03757O Prime VI is a distribution-of-disease outbreak model calibration code based on variational inference. It accompanies a publication for submission to Statistics in Medicine journal, and the code will be maintained for open-source use on Sandia's GitLab. The software provides methods for calibrating an epidemiological model to measured case-count data for a multitude of correlated spatial regions. The code solves a Bayesian inverse problem for model calibration where the posterior over-model parameters are approximated through a custom implementation of variational inference. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Safta, Cosmin↗
DOE OSTI2025

Application of physics-informed neural networks (PINNs) solution to coupled thermal and hydraulic processes in silty sands

Abstract The accurate modeling of water and heat transport in soils is crucial for both geo-environmental and geothermal engineering. Traditional modeling methods are problematic because they require well-defined boundaries and initial conditions. Recently, physics-informed neural networks (PINNs), which incorporate partial differential equations (PDEs) to solve forward and inverse problems, have attracted increasing attention in machine learning research. In this study, we applied PINNs to tackle hydraulic and thermal transport coupling forward problems in silty sands. A fully connected deep neural network was utilized for training. This neural network model leverages automatic differentiation to apply the governing equations as constraints, based on the mathematical approximations established by the neural network itself. We conducted forward problems and compared the solutions derived from PINNs with those from Finite Element Method (FEM) simulations. The forward problem results demonstrate the PINNs model’s capability in predicting hydraulic transport, heat transport, and thermal–hydraulic coupling in silty sands under various boundary conditions. The PINNs exhibited great performance in simulating the thermal–hydraulic coupling problem. The accuracy of the PINNs solutions shows its potential for simulation in geotechnical engineering.

Feng, Yuan↗
DOE OSTI2020

Imaging of a fluid injection process using geophysical data — A didactic example

In many subsurface industrial applications, fluids are injected into or withdrawn from a geologic formation. It is of practical interest to quantify precisely where, when, and by how much the injected fluid alters the state of the subsurface. Routine geophysical monitoring of such processes attempts to image the way that geophysical properties, such as seismic velocities or electrical conductivity, change through time and space and to then make qualitative inferences as to where the injected fluid has migrated. The more rigorous formulation of the time-lapse geophysical inverse problem forecasts how the subsurface evolves during the course of a fluid-injection application. Using time-lapse geophysical signals as the data to be matched, the model unknowns to be estimated are the multiphysics forward-modeling parameters controlling the fluid-injection process. Properly reproducing the geophysical signature of the flow process, subsequent simulations can predict the fluid migration and alteration in the subsurface. The dynamic nature of fluid-injection processes renders imaging problems more complex than conventional geophysical imaging for static targets. This work intents to clarify the related hydrogeophysical parameter estimation concepts.

58 GEOSCIENCES↗
DOE OSTI2024

Dynamic Graph Sequence Data from Simulated Neutron Reflectometry Measurements

This dataset comprises dynamic graph sequences derived from simulated in-situ neutron reflectometry measurements, capturing the gradual evolution of a layer structure over time. Each graph sequence represents a synthetic sample, with node features detailing the scattering vector and corresponding reflectivity measurements, while adjacency matrices have corresponding reference material parameters attached as metadata. The dataset spans multiple sets, each with a different number of sequences, offering a comprehensive basis for training models that handle dynamic input sequences with embedded physics. This dataset is particularly suited for tackling inverse problems with hidden physical states that evolve over time, challenges that are typically difficult to address using conventional iterative fitting methods.

36 MATERIALS SCIENCE↗
DOE OSTI2022

A refined assessment of nuclear data target accuracy requirements for ALFRED

The interest in target accuracy assessment has been recently renewed within the OECD/NEA Working Party on International Nuclear Data Evaluation Cooperation with an update exercise, thanks to the invaluable initiative of Massimo Salvatores. This work, moving from evaluations on the main core integral parameters of the Advanced Lead-cooled Fast Reactor European Demonstrator (ALFRED), and the identification of the associated target accuracies needed for improving its design, approaches the retrieval of target accuracy requirements for nuclear data, as the inverse problem of uncertainty quantification. The preliminary results obtained in a previous work are here refined by explicitly taking into account the total contribution due to correlations among variables in the optimization constraint, while its various components are evaluated individually. Moreover, three different sets of cost parameters are considered to introduce a bias in the solution in order to take in due account the relative difficulties in the execution of new differential experiments as needed for achieving the proposed target accuracies. By this, the obtained results are deemed usefully informative, and proposed for the update of a High Priority List which identifies the isotopes-reaction couples of most interest for future refinement experiments, especially when integrated with further analogous information collected on other advanced nuclear systems. Among the cross-sections whose refinement contributes the most to the reduction of the multiplication factor, the fission of Pu{sup 239} was found, which needs to be fixed below 1% in the range of interest for ALFRED (2 keV-4 MeV). Another contribution for the amelioration of the multiplication factor calculation accuracy, is due to the capture channel of Pu{sup 239}, for which the initial high uncertainty (around 15%) can be significantly reduced resorting to easily practicable experiments. The same occurs for the inelastic of Pb{sup 207}, for which the initial uncertainty value of around 50% can be drastically reduced up to target values between 4% and 7%.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2020

Far-field thermal imaging below diffraction limit

Non-uniform self-heating and temperature hotspots are major concerns compromising the performance and reliability of submicron electronic and optoelectronic devices. At deep submicron scales where effects such as contact-related artifacts and diffraction limits accurate measurements of temperature hotspots, non-contact thermal characterization can be extremely valuable. In this work, we use a Bayesian optimization framework with generalized Gaussian Markov random field (GGMRF) prior model to obtain accurate full-field temperature distribution of self-heated metal interconnects from their thermoreflectance thermal images (TRI) with spatial resolution 2.5 times below Rayleigh limit for 530nm illumination. Finite element simulations along with TRI experimental data were used to characterize the point spread function of the optical imaging system. In addition, unlike iterative reconstruction algorithms that use ad hoc regularization parameters in their prior models to obtain the best quality image, we used numerical experiments and finite element modeling to estimate the regularization parameter for solving a real experimental inverse problem.

42 ENGINEERING↗
DOE OSTI2021

Neural-adjoint method for the inverse design of all-dielectric metasurfaces

All-dielectric metasurfaces exhibit exotic electromagnetic responses, similar to those obtained with metal-based metamaterials. Research in all-dielectric metasurfaces currently uses relatively simple unit-cell designs, but increased geometrical complexity may yield even greater scattering states. Although machine learning has recently been applied to the design of metasurfaces with impressive results, the much more challenging task of finding a geometry that yields a desired spectra remains largely unsolved. We propose and demonstrate a method capable of finding accurate solutions to ill-posed inverse problems, where the conditions of existence and uniqueness are violated. A specific example of finding the metasurface geometry which yields a radiant exitance matching the external quantum efficiency of gallium antimonide is demonstrated. We also show how the neural-adjoint method can intelligently grow the design search space to include designs that increasingly and accurately approximate the desired scattering response. The neural-adjoint method is not restricted to the case demonstrated and may be applied to plasmonics, photonic crystal, and other artificial electromagnetic materials.

42 ENGINEERING↗
DOE OSTI2022

Physics-assisted generative adversarial network for X-ray tomography

X-ray tomography is capable of imaging the interior of objects in three dimensions non-invasively, with applications in biomedical imaging, materials science, electronic inspection, and other fields. The reconstruction process can be an ill-conditioned inverse problem, requiring regularization to obtain satisfactory results. Recently, deep learning has been adopted for tomographic reconstruction. Unlike iterative algorithms which require a distribution that is known a priori , deep reconstruction networks can learn a prior distribution through sampling the training distributions. In this work, we develop a Physics-assisted Generative Adversarial Network (PGAN), a two-step algorithm for tomographic reconstruction. In contrast to previous efforts, our PGAN utilizes maximum-likelihood estimates derived from the measurements to regularize the reconstruction with both known physics and the learned prior. Compared with methods with less physics assisting in training, PGAN can reduce the photon requirement with limited projection angles to achieve a given error rate. The advantages of using a physics-assisted learned prior in X-ray tomography may further enable low-photon nanoscale imaging.

47 OTHER INSTRUMENTATION↗
DOE OSTI2025

Self-supervised physics-informed generative networks for phase retrieval from a single X-ray hologram

X-ray phase contrast imaging significantly improves the visualization of structures with weak or uniform absorption, broadening its applications across a wide range of scientific disciplines. Propagation-based phase contrast is particularly suitable for time- or dose-critical in vivo/in situ/operando (tomography) experiments because it requires only a single intensity measurement. However, the phase information of the wave field is lost during the measurement and must be recovered. Conventional algebraic and iterative methods often rely on specific approximations or boundary conditions that may not be met by many samples or experimental setups. In addition, they require manual tuning of reconstruction parameters by experts, making them less adaptable for complex or variable conditions. Here we present a self-learning approach for solving the inverse problem of phase retrieval in the near-field regime of Fresnel theory using a single intensity measurement (hologram). A physics-informed generative adversarial network is employed to reconstruct both the phase and absorbance of the unpropagated wave field in the sample plane from a single hologram. Unlike most state-of-the-art deep learning approaches for phase retrieval, our approach does not require paired, unpaired, or simulated training data. This significantly broadens the applicability of our approach, as acquiring or generating suitable training data remains a major challenge due to the wide variability in sample types and experimental configurations. The algorithm demonstrates robust and consistent performance across diverse imaging conditions and sample types, delivering quantitative, high-quality reconstructions for both simulated data and experimental datasets acquired at beamline P05 at PETRA III (DESY, Hamburg), operated by Helmholtz-Zentrum Hereon. Furthermore, it enables the simultaneous retrieval of both phase and absorption information.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Quantitative Nonlinear Optical Polarimetry with High Spatial Resolution

Nonlinear optical microscopy such as in the optical second-harmonic generation (SHG) modality has become a popular tool today for probing materials in the physical and biological sciences. While imaging and spectroscopy are widely used in the microscopy mode, nonlinear polarimetry, which can shed light on materials’ symmetry and microstructure, is relatively underdeveloped. This is partly because quantitative analytical modeling of the optical SHG response for anisotropic crystals and films largely assumes low-numerical aperture (NA) focusing of light, where the plane-wave approximation is sufficient. Tight focusing provides unique benefits in revealing out-of-plane polarization responses, which cannot be detected by near-plane-wave illumination at normal incidence. Here, we outline a method for quantitatively analyzing SHG polarimetry measurements obtained under high-NA focusing within a microscope geometry. Experiments and simulations of a variety of standard samples, from single crystals to thin films, are in good agreement, including measured and simulated spatial SHG maps of ferroelectric domains. A solution to the inverse problem is demonstrated, where the spatial distribution of an SHG tensor with unknown tensor coefficient magnitudes is determined by experimentally measured polarimetry. The ability to extract the out-of-plane component of the nonlinear polarization in normal incidence is demonstrated, which can be valuable for high-resolution polarimetry of 2D materials, thin films, heterostructures, and uniaxial crystals with a strong out-of-plane response.

36 MATERIALS SCIENCE↗
DOE OSTI2026

A scalable variational method for estimating the latent infection-rate field of an outbreak

In this paper, we explore whether the infection-rate of a disease can serve as a robust monitoring variable in epidemiological surveillance algorithms. The infection-rate is dependent on population mixing patterns that do not vary erratically day-to-day; in contrast, daily case-counts used in contemporary surveillance algorithms are corrupted by reporting errors. The technical challenge lies in estimating the latent infection-rate from case-counts. Here we devise a Bayesian method to estimate the infection-rate across multiple adjoining areal units, and then use it, via an anomaly detector, to discern a change in epidemiological dynamics. We extend an existing model for estimating the infection-rate in an areal unit by incorporating a Markov random field model, so that we may estimate infection-rates across multiple areal units, while preserving spatial correlations observed in the epidemiological dynamics. To carry out the high-dimensional Bayesian inverse problem, we develop an implementation of mean-field variational inference specific to the infection model and integrate it with the random field model to incorporate correlations across counties. The method is tested on estimating the COVID-19 infection-rates across all 33 counties in New Mexico using data from the summer of 2020, and then employing them to detect the arrival of the Fall 2020 COVID-19 wave. We perform the detection using a temporal algorithm that is applied county-by-county. We also show how the infection-rate field can be used to cluster counties with similar epidemiological dynamics.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

Spurious regulatory connections dictate the expression-fitness landscape of translation factors

During steady-state cell growth, individual enzymatic fluxes can be directly inferred from growth rate by mass conservation, but the inverse problem remains unsolved. Perturbing the flux and expression of a single enzyme could have pleiotropic effects that may or may not dominate the impact on cell fitness. Here, we quantitatively dissect the molecular and global responses to varied expression of translation termination factors (peptide release factors, RFs) in the bacterium Bacillus subtilis. While endogenous RF expression maximizes proliferation, deviations in expression lead to unexpected distal regulatory responses that dictate fitness reduction. Molecularly, RF depletion causes expression imbalance at specific operons, which activates master regulators and detrimentally overrides the transcriptome. Through these spurious connections, RF abundances are thus entrenched by focal points within the regulatory network, in one case located at a single stop codon. Such regulatory entrenchment suggests that predictive bottom-up models of expression-fitness landscapes will require near-exhaustive characterization of parts.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Anomaly Attribution with Likelihood Compensation

This paper addresses the task of explaining anomalous predictions of a black-box regression model. When using a black-box model, such as one to predict building energy consumption from many sensor measurements, we often have a situation where some observed samples may significantly deviate from their prediction. It may be due to a sub-optimal black-box model, or simply because those samples are outliers. In either case, one would ideally want to compute a responsibility score indicative of the extent to which an input variable is responsible for the anomalous output. In this work, we formalize this task as a statistical inverse problem: Given model deviation from the expected value, infer the responsibility score of each of the input variables. We propose a new method called likelihood compensation (LC), which is founded on the likelihood principle and computes a correction to each input variable. To the best of our knowledge, this is the first principled framework that computes a responsibility score for real valued anomalous model deviations. We apply our approach to a real-world building energy prediction task and confirm its utility based on expert feedback.

Idé, Tsuyoshi↗
DOE OSTI2025

Conditional Pseudo-Reversible Normalizing Flow for Surrogate Modeling in Quantifying Uncertainty Propagation

We introduce a conditional pseudo-reversible normalizing flow (PR-NF) that directly learns conditional probability distributions from noisy physical models to efficiently quantify both forward and inverse uncertainty propagation. Traditional surrogate modeling approaches approximate only the deterministic component of physical models, requiring separate noise characterization and computationally expensive sampling methods for inverse problems. Here, in this work, we develop the conditional PR-NF model to directly learn and efficiently generate samples from the conditional probability density functions (PDFs). The training process utilizes dataset consisting of input-output pairs without requiring prior knowledge about the noise and the function. Once trained, our model efficiently generates samples from conditional PDFs for any input within the training domain. Moreover, the pseudo-reversibility feature allows for the use of fully connected neural network architectures, which simplifies the implementation and enables theoretical analysis. We provide a rigorous convergence analysis of the conditional PR-NF model, showing its ability to converge to the target conditional PDF using the Kullback−Leibler divergence. To demonstrate the effectiveness of our method, we apply it to several benchmark tests and a real-world geologic carbon storage problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

High-dimensional maximum-entropy phase space tomography

Reconstructing 4D or 6D phase space distributions from 1D or 2D measurements is a challenging inverse problem encountered in particle accelerators. Entropy maximization is an established method to incorporate prior information in the reconstruction, but it is typically infeasible in high-dimensional spaces. In this paper, I review two recent approaches to high-dimensional entropy maximization. The first approach utilizes differentiable simulations and a class of generative models known as normalizing flows, whereas the second approach employs the method of Lagrange multipliers and Markov Chain Monte Carlo (MCMC) sampling. My aim is to provide a short explanation of each method using a common notation. I conclude by mentioning several unsolved problems in phase space tomography.

Hoover, Austin [ORNL] (ORCID:0000000153136962)↗