Search NASA⌕ Search

SEARCH · Search NASA

Results for “inverse optimization”

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 91 records · Page 5
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

ARM-IRL: Adaptive Resilience Metric Quantification Using Inverse Reinforcement Learning

The resilience of safety-critical systems is gaining importance due to the rise in cyber and physical threats, especially within critical infrastructure. Traditional static resilience metrics may not capture dynamic system states, leading to inaccurate assessments and ineffective responses to cyber threats. This work aims to develop a data-driven, adaptive method for resilience metric learning. We propose a data-driven approach using inverse reinforcement learning (IRL) to learn a single, adaptive resilience metric. The method infers a reward function from expert control actions. Unlike previous approaches using static weights or fuzzy logic, this work applies adversarial inverse reinforcement learning (AIRL), training a generator and discriminator in parallel to learn the reward structure and derive an optimal policy. The proposed approach is evaluated on multiple scenarios: optimal communication network rerouting, power distribution network reconfiguration, and cyber–physical restoration of critical loads using the IEEE 123-bus system. The adaptive, learned resilience metric enables faster critical load restoration in comparison to conventional RL approaches.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

First-Principles Studies on Sc 2 RuZ (Z = Si, Ge, Sn) Inverse Heusler Alloys: Structural, Electronic, and Transport Properties

The continuous demand for efficient, nontoxic, and thermally stable materials for room-temperature energy conversion motivates the exploration of novel thermoelectric systems beyond the traditional magnetic Heusler alloys. While full and half-Heusler compounds, especially Co-, Ni-, and Mn-based systems, have demonstrated promising thermoelectric properties, their typically high operating temperatures and magnetic complexities limit their applicability in ambient thermal management. In this context, we investigate whether Sc-based inverse Heusler alloys can offer a viable nonmagnetic alternative with competitive thermoelectric performance. In this work, we perform a systematic first-principles study of the inverse Heusler compounds Sc 2 RuZ (Z = Si, Ge, Sn), focusing on their structural, electronic, mechanical, and thermodynamic-thermoelectric properties. Density Functional Theory (DFT) was employed to compute optimized lattice structures and band dispersion, while dynamical stability was assessed via phonon calculations. Thermoelectric transport coefficients, including Seebeck coefficient, electrical conductivity, and thermal conductivity, were estimated using the semiclassical Boltzmann transport theory within the constant relaxation time approximation. Our results show that all Sc 2 RuZ compounds are thermodynamically stable semiconductors with indirect band gaps of 0.12–0.16 eV and exhibit high elastic moduli, especially Sc 2 RuSn, which demonstrates superior stiffness and incompressibility. Importantly, all compounds display promising room-temperature thermoelectric characteristics, including high Seebeck coefficients and power factors. These findings reveal that Sc 2 RuZ alloys represent a rare class of stable, nonmagnetic inverse Heusler semiconductors with intrinsic thermoelectric potential at room temperature, unlike many existing Heusler systems optimized for spintronics or high-temperature operation. This work expands the known design space for Heusler-based thermoelectrics and offers a theoretical basis for experimental realization of efficient, low-temperature, nonmagnetic thermoelectric materials.

alloys↗
DOE OSTI2025

Electron density profile and associated fluctuation measurements using a microwave reflectometry diagnostic on Helically Symmetric eXperiment (HSX)

Abstract A dual-band frequency-modulated reflectometry is employed on the Helically Symmetric eXperiment (HSX) stellarator. This system equips a fast PIN switch to alternate the frequency source between two voltage-controlled oscillators, providing an operational frequency range from 14.5 GHz to 25.5 GHz. A monostatic antenna geometry and an ellipsoidal mirror are implemented in the vessel of HSX, where the polarization of the transmitted microwave can be switched between O- and X-mode to accommodate the magnetic field and plasma density. Although the original system was designed for density fluctuation measurement, significant efforts have been undertaken to improve the system performance and to realize the density profile inversion. Recent improvements of the system reported here include calibration of the dispersion in the transmission line, optimization of the waveform, and implementation of the Choi-Williams time–frequency distribution for spectral analysis. In this paper, we present the optimization of the reflectometry system along with first experimental measurements of the density profile and observations of fluctuations during gas puffing experiments.

Han, X. (ORCID:0000000184986433)↗
DOE OSTI2026

Constrained variational optimization of counting-time allocation in sequential scattering measurements: Application to Bonse–Hart USANS

Sequential scattering measurements are often performed under a fixed experimental-time budget, even though the expected count rate varies strongly across the measured coordinate. When the dwell time at each measurement position can be controlled independently, this variation creates a general resource-allocation problem: how should the available time be distributed to minimize the uncertainty of the reconstructed profile? We formulate this problem as a constrained variational optimization for measurements governed by Poisson counting statistics. When each measurement is treated independently, minimizing the averaged squared relative uncertainty yields an inverse-square-root intensity allocation. The formulation is then generalized to include correlations between neighboring measurements and an instrumental resolution operator, leading to an allocation criterion that equalizes the marginal reduction in posterior uncertainty per unit measurement time. Bonse–Hart ultra-small-angle neutron scattering (USANS), in which reciprocal space is sampled sequentially through analyzer-angle stepping, provides an experimentally grounded application. Computational benchmarking shows that the optimized allocation outperforms uniform-time and constant-relative-error strategies, while application to an experimentally measured graphite USANS profile from the Spallation Neutron Source, using Poisson resampling under alternative schedules, demonstrates how counting time should be redistributed toward weak-intensity regions under an identical total duration. The resulting framework applies to sequential scattering and related scanning measurements whenever local dwell times are adjustable and directly determine the measurement uncertainties, and when the relevant correlation and instrumental-response models are available.

Tung, Chi-Huan [ORNL] (ORCID:0000000221972074)↗
DOE OSTI2025

Identification Uncertainty in Inverse Material Model Parameter Determination: A Sensitivity‐Based Decision Process for Load Path Selection

This research proposes a sensitivity-based framework for selecting the optimal prescribed loading path for a biaxial cruciform specimen. Optimality here is determined by the direction and magnitude of the prescribed displacement that minimizes the influence of random noise on the material model parameter identification. Using simulated experimental data based on finite element simulation, in this work, we identify the material model parameters of a Ludwik hardening model and plane stress implementation of the Hill-48 yield criterion using finite element model updating (FEMU). Our analysis reveals that the identification (or estimator) uncertainty of model parameters depends on the displacement boundary conditions (i.e., loading sequence) and the ground-truth value of the individual parameters. Optimal experimental design (OED) criteria based on the Fisher information matrix were investigated to mitigate indecision in the choice of optimal load path when the identification uncertainty of different material model parameters optimized at different load paths. The determinant of the Fisher information matrix was chosen here as the more useful metric due to its ability to capture uncertainty of the most influential material model parameters. The proposed framework demonstrates potential for real-time automated load step selection using scalar criteria derived prior to mechanical loading. The framework can be generalized to other geometries, boundary conditions and material models, allowing this procedure to be utilized for different experimental configurations and materials.

Fayad, Samuel S. [University of Illinois at Urbana↗
DOE OSTI2026

KTaO 3 -Based Supercurrent Diode

The supercurrent diode effect (SDE), characterized by nonreciprocal critical currents, represents a promising building block for future dissipationless electronics and quantum circuits. Realizing SDE requires breaking both time-reversal and inversion symmetry in the device. Here we use conductive atomic force microscope (c-AFM) lithography to pattern reconfigurable superconducting weak links (WLs) at the LaAlO 3 /KTaO 3 (LAO/KTO) interface. By deliberately engineering the WL geometry at the nanoscale, we realize SDE in these devices in the presence of modest out-of-plane magnetic fields. The SDE polarity can be reversed by simply changing the WL position, and the rectification efficiency reaches up to 13% under optimal magnetic field conditions. Time-dependent Ginzburg–Landau simulations reveal that the observed SDE originates from asymmetric vortex motion in the inversion-symmetry-breaking device geometry. This demonstration of SDE in the LAO/KTO system establishes a versatile platform for investigating and engineering vortex dynamics, forming the basis for engineered quantum circuit elements.

C-AFM lithography↗
DOE OSTI2025

Basic Research Needs for Inverse Methods for Complex Systems under Uncertainty

Inverse problems, which aim to infer unknown properties of a system using experimental and observational data, are central to addressing many of the U.S. Department of Energy’s (DOE) most critical scientific and engineering challenges. Accurate, computationally efficient, and data-efficient solutions to inverse problems are essential for advancing DOE mission-critical science drivers, including analyzing data from large-scale experimental facilities, optimizing fusion reactor performance, accelerating materials discovery, enhancing geophysical imaging, improving wildfire predictions, and enabling autonomous systems and digital twins. However, these problems are becoming increasingly complex, often involving nonlinear, highdimensional, and interconnected systems and models that span multiple physics and scales, while relying on data with varying quantity, quality, and information content. Compounding these challenges is the uncertainty inherent in DOE-relevant systems, where errors in inputs, noise in data, incompleteness of data, and discrepancies between models and reality constrain the accuracy and precision of solutions. At the same time, the convergence of recent scientific computing trends—scientific machine learning, artificial intelligence, and computing advances such as exascale computing—is creating unprecedented opportunities for tackling these challenges. The cross-cutting nature of inverse problems, combined with their growing complexity and rapidly evolving data and algorithmic demands, strongly motivates the formulation of a prioritized research agenda to maximize their capabilities and impact. In response to this need, DOE’s Advanced Scientific Computing Research (ASCR) program in the Office of Science convened the Workshop on Basic Research Needs for Inverse Problems for Complex Systems Under Uncertainty in June 2025. This workshop brought together experts across disciplines to identify grand challenges and major opportunities in the field. Through collaborative discussions, the workshop defined transformative research directions aimed at addressing the mathematical, statistical, and computational challenges posed by inverse problems under uncertainty. As a result of these efforts, four priority research directions (PRDs) were identified to guide future research and development in this area. These PRDs, summarized below, represent a roadmap for advancing the foundational science and mathematics of inverse problems, enabling robust, scalable, and uncertainty-aware solutions that are critical for DOE applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

MOOSE ProbML: Parallelizable Probabilistic Machine Learning and Uncertainty Quantification Capabilities

The Multiphysics Object Oriented Simulation Environment (MOOSE) is a widely used open- source finite element software for performing multiphysics multiscale simulations in a massively parallel fashion. Recently, the computational team at Idaho National Laboratory (INL) has implemented Probabilistic Machine Learning (ProbML) capabilities in MOOSE—in a parallelized fashion—and enable active learning with large-scale computational models for tasks such as surrogate model development, scale bridging, forward/inverse uncertainty quantification (UQ), Bayesian optimization, etc. This presentation summarizes these developments in MOOSE along with demonstrations on several real applications relevant to nuclear energy. At the fundamental level, samplers like Monte Carlo/Latin Hypercube, variance reduction, parallelized Markov Chain Monte Carlo (MCMC) support uncertainty propagation in both forward and inverse settings. These samplers can be integrated with the Gaussian processes (GP) suite in MOOSE, which offer several variants like scalar GPs, multi-output GPs, and deep GPs, to enable active learning. These GPs can be tuned using gradient-based optimization methods like Adam and its variants or gradient-free methods like the elliptical slice sampler (a variant of MCMC adept under Gaussian settings) for more complex covariance kernels or likelihoods whose gradient computations can be cumbersome. A variety of batch acquisition functions permit parallelized evaluation of the computational model and support different learning objectives with high efficiency like Bayesian inference, global surrogate development, optimization, etc. Furthermore, libtorch integration supports training, evaluation, and re-training of neural networks and other complex machine learning models in active learning settings. The impacts of these developments are shown on several real applications: (1) nuclear fuel inverse UQ and model inadequacy assessment using the Kennedy O’Hagan framework; (2) uncertainty aware surrogate modeling for additive manufacturing to predict field quantities; (3) nuclear reactor rare events analysis; and (4) complex fluid flow prediction using a global surrogate with quantified prediction uncertainty. Finally, the outlook of MOOSE ProbML is discussed for both outer-loop and inner-loop computations in the broad view to accelerate fuels and materials qualification, address gaps in knowledge and data, and assess new reactor/fuel systems.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

Distributed Stochastic Optimization of a Neural Representation Network for Time-Space Tomography Reconstruction

4D time-space reconstruction of dynamic events or deforming objects using X-ray computed tomography (CT) is an important inverse problem in non-destructive evaluation. Conventional back-projection based reconstruction methods assume that the object remains static for the duration of several tens or hundreds of X-ray projection measurement images (reconstruction of consecutive limited-angle CT scans). However, this is an unrealistic assumption for many in-situ experiments that causes spurious artifacts and inaccurate morphological reconstructions of the object. To solve this problem, we propose to perform a 4D time-space reconstruction using a distributed implicit neural representation (DINR) network that is trained using a novel distributed stochastic training algorithm. Our DINR network learns to reconstruct the object at its output by iterative optimization of its network parameters such that the measured projection images best match the output of the CT forward measurement model. Here, we use a forward measurement model that is a function of the DINR outputs at a sparsely sampled set of continuous valued 4D object coordinates. Unlike previous neural representation architectures that forward and back propagate through dense voxel grids that sample the object's entire time-space coordinates, we only propagate through the DINR at a small subset of object coordinates in each iteration resulting in an order-of-magnitude reduction in memory and compute for training. DINR leverages distributed computation across several compute nodes and GPUs to produce high-fidelity 4D time-space reconstructions. We use both simulated parallel-beam and experimental cone-beam X-ray CT datasets to demonstrate the superior performance of our approach.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Semi-Analytical Hierarchical Bayesian Inference of Nonlinear Model Structure in Stochastic Dynamics: Applied to Compartmental Models of Infectious Diseases

A Bayesian computational framework for parsimonious inference in stochastic nonlinear dynamical systems is presented. This framework enables the concurrent estimation of system states, time-varying parameters, time-invariant parameters, and the optimal sparsity structure of the model parameters. Because differential equation-based models are often simplified mechanistic or phenomenological representations, robust inference from noisy measurement data requires explicit treatment of model error and uncertainty. Model error and time-varying parameters can be represented as random processes, enabling inference while making minimal assumptions about the underlying sources of discrepancy and variability. Adopting stochastic differential equation representations affords the model significant flexibility, but can also render it susceptible to overfitting during statistical inversion, where the inferred model may track noise rather than the underlying signal. To alleviate the effects of overfitting and to enable the discovery of the optimal sparse representation of the time-invariant parameters, a Bayesian sparse learning algorithm is embedded within the framework. This sparse learning framework adopts an approximate hierarchical Bayesian setting defined by a series of semi-analytical expressions. The model structure inference framework is validated using a stochastic compartmental model for tracking and forecasting active cases of an infectious disease. Compartmental models describe population-level infectious disease dynamics through interactions among population fractions grouped by disease state. Mathematically, such models consist of a system of coupled ordinary differential equations. This example adopts an expressive compartmental model that includes multiple possible interactions between disease states, motivated by early uncertainty surrounding COVID-19 reinfection dynamics and their implications for long-term epidemic forecasting. The sparse learning exercise permits the inference of a priori unknown epidemiological dynamics from simulated public health data, discovering the nested compartmental model that optimizes the trade-off between average data-fit and model complexity. It is shown that inducing sparsity among the model parameters eliminates redundant interactions between compartments, equivalently revealing the optimal coupling structure between differential equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A deep learning and finite element approach for exploration of inverse structure–property designs of lightweight hybrid composites

Hybrid composites have important applications, such as high-performance and lightweight materials in aerospace and automotive industries. Hybrid composites utilize the synergy of diverse fillers to achieve desired material properties, but usually have more complicated microstructures. While topology optimization can optimize a particular property, designing hybrid composites for customized mechanical performances, e.g. full-range stress–strain curve, remains challenging. Here, a computational framework that integrated finite element analysis (FEA) and artificial intelligence (AI) methods of Conditional Generative Adversarial Networks (cGAN) deep learning and transfer learning was developed to establish inverse structure–property relationships and design tailor-made hybrid composites. Based on FEA-generated datasets of hybrid fiber-particle–matrix microstructures and their corresponding full-range stress–strain curves, a cGAN architecture was trained to generate tailored microstructures and establish structure–property relationships. Similarity in microstructural features and well-matched stress–strain curves based on the AI-generated composites were achieved. In conclusion, transfer learning was used to expand the pre-trained model for designing different materials systems.

Hybrid composites↗
DOE OSTI2024

Analyzing Potential Failures and Effects in a Pilot-Scale Biomass Preprocessing Facility for Improved Reliability

This study demonstrates a failure identification methodology applied to a preprocessing facility generating conversion-ready feedstocks from biomass meeting conversion process critical quality attribute (CQA) specifications. Failure Modes and Effects Analysis (FMEA) was used as an industrially relevant risk analysis approach to evaluate a logging residue preprocessing system to prepare feedstock for pyrolysis conversion. Risk evaluations considered both system-level and operation unit-level assessments considering process efficiency, product quality, cost, sustainability, and safety. Key outputs included estimations of semi-quantitative risk scores for each failure, identification of the failure impacts, identification of failure causes associated with material attributes and process parameters, ranking success rates of failure detection methods, and speculation of potential mitigation strategies for decreasing failure risk scores. Results showed that deviations from moisture specifications had cascading consequences for other CQAs along with process safety implications. Failures linked to fixed carbon specifications carried the highest risk scores for product quality and process efficiency impacts. As increased throughput can be inversely related to meeting product quality specifications; achieving throughput and other material-based CQAs simultaneously will likely require system optimization or prioritization based on system economics. Ultimately, this work successfully demonstrates FMEA as a risk analysis approach for other bioenergy process systems.

09 BIOMASS FUELS↗
DOE OSTI2024

(Doublon) Benchmarking of Different Inverse Point Kinetics Implementations for an Autocorrected Reactimeter Algorithm

In November 2017, the Transient Reactor Test Facility returned to operation. Since that time, many transient test series have been completed, such as the Transient Heatsink Overpower Response capsule (THOR), the Transient Water Irradiation System for TREAT (TWIST), and Sirius. Each has provided valuable data for materials performance and reactor safety that can be applied in future designs. During each experimental series, detector count rates provided important information on the core behavior during transients. However, a limitation of these data is that variations in the neutron distribution during experiments can cause errors when attempting to infer reactivity evolution from detector signals. Neutron physics codes can be used to compute the flux shape variations. However, this is a poor solution when the experimental data is used for code verification, validation and uncertainty quantification. Indeed, if the output of the code is used both as a reference and to correct what the reference is compared to, the circular dependency limits the quality of the verification, validation and uncertainty quantification approach. To overcome this problem, the autocorrected reactimeter algorithm (ACRA) has been developed. This approach infers a time-dependent reactivity evolution by testing different spatial corrections and selecting the one that minimizes reactivity variations when the core is in a frozen configuration (i.e., when there is no variation in parameters affecting reactivity). However, the scope of this method was limited to transients where there were negligible thermal feedback. Indeed, the core is never in a frozen configuration when the fuel temperature varies during the whole transient. This is our motivation for developing an improved version of the ACRA that does not require frozen configurations. To develop this new algorithm, we need a precise and unbiased implementation of the inverse point kinetic equations (IPKEs) as any error in the reactivity evaluation will be propagated into the choice of the optimal spatial correction. Indeed, the previous reactimeter algorithm would use approximations, such as a negligible flux amplitude derivative, to focus on rapidity. For the numerical validation of ACRA, we aim at absolute error under for reactivity derived from signals similar to the one of this study. In this summary, we test eight different IPKE implementations. Each will process a mockup signal built for this study, similar to those that the future ACRA will process. Each reactivity output will be compared to the reference reactivity that has been used to generate the mockup signal. The implementation minimizing the difference with the reference reactivity will be used in the development of a new ACRA formulation.

73 - NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Improving the Quasi‐Biennial Oscillation via a Surrogate‐Accelerated Multi‐Objective Optimization

Accurate simulation of the quasi-biennial oscillation (QBO) is challenging due to uncertainties in representing convectively generated gravity waves. We develop an end-to-end uncertainty quantification workflow that calibrates these gravity wave processes in E3SM for a realistic QBO. Central to our approach is a domain knowledge-informed, compressed representation of high-dimensional spatio-temporal wind fields. By employing a parsimonious statistical model that learns the fundamental frequency from complex observations, we extract interpretable and physically meaningful quantities capturing key attributes. Building on this, we train a probabilistic surrogate model that approximates the fundamental characteristics of the QBO as functions of critical physics parameters governing gravity wave generation. Leveraging the Karhunen–Loève decomposition, our surrogate efficiently represents these characteristics as a set of orthogonal features, capturing cross-correlations among multiple physics quantities evaluated at different pressure levels and enabling rapid surrogate-based inference at a fraction of the computational cost of full-scale simulations. Finally, we analyze the inverse problem using a multi-objective approach. Our study reveals a tension between amplitude and period that constrains the QBO representation, precluding a single optimal solution. To navigate this, we quantify the bi-criteria trade-off and generate a set of Pareto optimal parameter values that balance the conflicting objectives. This integrated workflow improves the fidelity of QBO simulations and offers a versatile template for uncertainty quantification in complex geophysical models.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Investigation of acoustic waves under subsurface conditions to improve the predictions of rock mechanical properties and natural fracture characteristics

Mechanical properties and natural fracture characteristics are critical to investigate for subsurface engineering applications, including carbon storage, well drilling, and stimulation, as they govern rock stability, fluid flow, and mechanical behavior under stress. This dissertation integrates experimental and machine learning approaches to enhance the prediction and understanding of these properties by analyzing acoustic wave behavior under varied subsurface conditions. First, the influence of temperature, pore pressure, and supercritical CO2 (scCO2) saturation on poroelastic properties is examined using Gray Berea sandstone samples. The results show that temperature and pore pressure significantly affect the bulk modulus and Biot’s coefficient, while scCO2 saturation impacts rock compressibility, informing strategies for effective geological carbon storage. The study extends this understanding by experimentally evaluating the impact of reservoir depletion on the dynamic mechanical properties of the emerging Caney shale in South Oklahoma with the employment of unsupervised machine learning to predict static mechanical properties across the Caney shale. Integrating petrophysical data and chemostratigraphy, the workflow—featuring K-means clustering, principal component analysis (PCA), and inverse distance weighting (IDW)—improves stratigraphic characterization and the estimation of static-to-dynamic modulus ratios, which is vital for optimizing drilling and stimulation strategies. Finally, the work explores how natural fracture characteristics in shale influence acoustic waveforms and shear wave splitting (SWS) analysis. Experimental data on fractured samples under different stress and temperature conditions, combined with machine learning models such as K-nearest neighbors (KNN) and extreme gradient boosting (XGBoost), reveal key fracture properties impacting SWS and wave propagation. Together, these studies provide a comprehensive framework for linking acoustic wave behavior with rock properties, advancing the methods for monitoring and predicting geomechanical changes. The insights offered valuable implications for safer, more efficient CO2 injection, hydrocarbon extraction, and subsurface management.

Elkholy, Sherif↗
DOE OSTI2025

Efficient shallow Ritz method for 1D diffusion problems

This paper studies the shallow Ritz method for solving the one-dimensional diffusion problem. It is shown that the shallow Ritz method improves the order of approximation dramatically for non-smooth problems. To realize this optimal or nearly optimal order of the shallow Ritz approximation, we develop a damped block Newton (dBN) method that alternates between updates of the linear and non-linear parameters. Per each iteration, the linear and the non-linear parameters are updated by exact inversion and one step of a modified, damped Newton method applied to a reduced non-linear system, respectively. The computational cost of each dBN iteration is $\mathcal{O}$(n). Starting with the non-linear parameters as a uniform partition of the interval, numerical experiments show that the dBN is capable of efficiently moving mesh points to nearly optimal locations. In conclusion, to improve the efficiency of the dBN further, we propose an adaptive damped block Newton (AdBN) method by combining the dBN with the adaptive neuron enhancement (ANE) method [28].

Diffusion problems↗
DOE OSTI2025

Nondestructive Evaluation of Concrete: Elastic Property Imaging Through Full Waveform Inversion

Concrete is a major construction material worldwide and plays a crucial role in the nuclear industry. The elastic properties of concrete are prone to change and degrade while in service, as it is often subjected to extreme operational and environmental conditions. An accurate evaluation of concrete's elastic properties is thus essential to ensure structural integrity and safety. This is especially true for concrete in nuclear power plants, where irradiation effects significantly impact concrete mechanical properties. There are various methods to assess these properties, with ultrasound-based techniques showing high potential due to their nondestructive nature, cost-effectiveness, and safety. While several nondestructive evaluation methods exist, most rely on idealizations such as assuming homogeneous material and plane wavefronts. In this work, we address these issues by introducing an ultrasound-based nondestructive method aimed at reconstructing spatially varying images of concrete mechanical properties. By accurately modeling wave physics, including scattering and reflection, we overcome several of the aforementioned idealizations and aim to utilize the full waveform for imaging material properties through depth, resulting in more reliable images. Full waveform inversion (FWI) was first introduced by geophysicists to reconstruct subsurface elastic property images. The goal is to minimize the difference between simulated and recorded wavefield signals, often through gradient-based optimization algorithms. While FWI is primarily conducted using the acoustic approximation of the wave equation, few works focus on elastic FWI, where the goal is to reconstruct images of not only the pressure wave speed but also the shear wave speed and density (or their equivalents). This work explores the potential of using elastic FWI to predict concrete mechanical properties as an initial effort for a more accurate monitoring of concrete conditions in service. Reconstructing images of different elastic parameters enables more specificity and accurate condition diagnosis. This paper will detail this approach and provide examples demonstrating the effectiveness of elastic FWI in reconstructing comprehensive maps of concrete mechanical properties.

42 - ENGINEERING↗