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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.

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DOE OSTI2025

Position Papers for Inverse Methods for Complex Systems under Uncertainty Workshop

The ability to solve inverse problems – inferring unknown parameters, structures, or states of a system from observed data – is essential for advancing scientific discovery and innovation capabilities for the DOE mission. Basic research needs and challenges are particularly acute in emerging areas such as the interactive, data-driven, modeling and simulation of digital twins; decision support for experiments at DOE scientific user facilities; and for other complex systems and workflows. Inverse problems are at the heart of understanding and controlling complex systems due to factors such as observational data with varying modalities and fidelities, inherent uncertainties in physical measurements and numerical models, and the computational demands of rapid and high-fidelity simulations. The convergence of recent scientific computing trends – scientific machine learning, artificial intelligence, and computing advances such as exascale computing – is creating unprecedented opportunities. These advancements offer the potential to revolutionize how we approach inverse problems to extract actionable insights with the required level of accuracy and computational efficiency. This workshop and the Call for Position Papers are vital steps in bringing together experts to collectively explore and identify the new computational and mathematical directions needed in inverse methods for complex systems under uncertainty.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

High-throughput spin-bath characterization of spin defects in semiconductors

Detailed knowledge of the local environments of spin defects in semiconductors, such as nitrogenvacancy (NV) centers in diamond or divacancies in silicon carbide, is crucial for optimizing control and entanglement protocols in quantum sensing and information applications. However, at present a direct experimental characterization of individual defect environments is not scalable, as conventional spin-bath measurements are time consuming and difficult to automate. Achieving high-throughput characterization requires short experiments to probe the spin bath. However, with fewer and noisier measurements, the inverse problem of recovering spin-bath properties from measured data becomes ill posed, with multiple spin baths having a high likelihood of yielding the same data. In this work, we present a set of computational tools to resolve the ill-posed inverse problem of recovering the atomic positions and hyperfine couplings of random nuclei surrounding spin defects from sparse, noisy experimental coherence data, which can be obtained in hours. Here, we use a trans-dimensional Bayesian approach that incorporates ab initio data to yield full posterior distributions over nuclear spin environments, enabling robust recovery from limited data. We also provide practical tools and guidelines to determine the limits of detectability for hyperfine couplings under specific dynamical decoupling sequences and sampling conditions. In addition, we demonstrate how the tools developed here, in combination with ab initio simulations of spin baths, can guide the design of efficient experimental protocols for application-specific high-throughput screening. To showcase the utility of our approach, we apply it to design fast dynamical decoupling experiments to characterize the spin baths often individual NV centers in diamond. While the primary focus is on accelerating spin-bath characterization of spin defects, this Bayesian approach also lays the foundation for digital-twin studies of spin defects, where a virtual model of the spin-defect system evolves in real time with ongoing experimental measurements. Together, the set of tools we designed and applied paves the way for scalable deployment of spin defects in semiconductors for quantum sensing and information applications.

Bayesian methods↗
DOE OSTI2024

Statistical modelling and Bayesian inversion for a Compton imaging system: application to radioactive source localization

Abstract This paper presents a statistical forward model for a Compton imaging system, called Compton imager. This system, under development at the University of Illinois Urbana Champaign, is a variant of Compton cameras with a single type of sensors which can simultaneously act as scatterers and absorbers. This imager is convenient for imaging situations requiring a wide field of view. The proposed statistical forward model is then used to solve the inverse problem of estimating the location and energy of point-like sources from observed data. This inverse problem is formulated and solved in a Bayesian framework by using a Metropolis within Gibbs algorithm for the estimation of the location, and an expectation-maximization algorithm for the estimation of the energy. This approach leads to more accurate estimation when compared with the deterministic standard back-projection approach, with the additional benefit of uncertainty quantification in the low photon imaging setting.

Tarpau, Cécilia (ORCID:0000000286539490)↗
DOE OSTI2026

Regularizing INR with Diffusion Prior for Self-Supervised 3D Reconstruction OF Neutron Computed Tomography Data

Recently, generative diffusion priors have made huge strides as inverse problem solvers, including the ability to be adapted for inference on out-of-distribution data. Concurrently, implicit neural representations (INRs) have emerged as fast and lightweight inverse imaging solvers that are amenable to hybrid approaches that combine learned priors with traditional inverse problem formulations. In this paper, we present a diffusive computed tomography (CT) inversion framework for regularizing INRs called Diffusive INR (DINR), designed to enable high-quality reconstruction from sparse-view neutron CT. Pretrained purely on synthetic data, DINR is evaluated on simulated and experimentally obtained observations of concrete microstructures, where traditional reconstruction methods suffer substantial degradation when the number of views is reduced. Our approach delivers superior performance, reduces reconstruction artifacts, and achieves gains in PSNR and SSIM, enabling accurate micro-structural characterization even under extreme data limitations compared to state-of-the-art sparse-view reconstruction techniques.

Hossain, Maliha [ORNL]↗
DOE OSTI2026

New approaches to Bayesian uncertainty quantification for Nuclear Science (Final Technical Report)

Inverse problems play a central role in experimentation and theory/data comparisons for many areas of modern Nuclear Physics (NP) and High-Energy Physics (HEP). Bayes’s Theorem is a powerful tool for solving Inverse Problems, providing conceptually transparent and unbiased constraints on theoretical parameters and their uncertainties (“Bayesian Inference”) and enabling the quantification of agreement or tension between models and data. However, analyses based on Bayesian Inference are often challenging for NP and HEP applications, either because of the large number of parameters in the problem, the high computational cost, or both. We propose a multi-institutional collaboration to develop and deploy novel Bayesian analysis tools that advance the scientific scope of a broad range of current and future NP experiments. This project brings together NP domain scientists working on several high-profile NP projects for which new, high-performance Bayesian Uncertainty Quantification (“Bayesian UQ”) methods are essential to carry out the science, and data scientists who are developing state-of-the-art methods applicable to these problems. The NP projects in this proposal comprise measurements of the mass and fundamental nature of the neutrino; study of the Quark-Gluon Plasma that filled the early universe; and mapping of natural and anthropogenic radiation environments. While these NP projects have very different scientific goals, with datasets and analysis approaches that differ significantly, they share common requirements for improving computationally intensive Bayesian analyses using advanced Machine Learning algorithms and will benefit strongly from a coherent effort to develop general solutions. This proposal brings together these projects and forefront ML-based data science algorithms to develop such general solutions. The methods developed in this project will also be more widely applicable, thereby advancing science in the larger Nuclear Physics portfolio.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Conditional diffusion machine-learning framework for mapping valence electron distribution from convergent beam electron diffraction

Quantitative convergent beam electron diffraction (CBED) enables determination of aspherical valence electron distributions through refinement of low-order structure factors, which are highly sensitive to chemical bonding and charge density variations. However, conventional quantitative CBED (QCBED) requires solving a highly nonlinear inverse problem with many coupled parameters, and computationally intensive dynamical diffraction calculations, making it time-consuming and difficult to apply to complex systems. More broadly, reconstructing charge density and orbital electron distribution from diffraction data has long been a central challenge in both x-ray and electron crystallography. Here, in this study, we introduce an artificial-intelligence (AI)-based framework that replaces traditional refinement with a data-driven inverse solver. Using a large synthetic CBED dataset generated by Bloch-wave simulations, we train a conditional diffusion model to directly infer crystal structural parameters and multipole density formalism parameters, and hence valence electron distributions, from CBED patterns alone. By learning from forward simulations across realistic parameter space, the model effectively solves the inverse problem. Compared with direct regression approaches, the diffusion-based framework provides posterior parameter distributions for rigorous uncertainty quantification while preserving quantitative fidelity and reducing analysis time by orders of magnitude. By eliminating the need for external single-crystal x-ray diffraction data and complex nonlinear refinement, this approach enables practical, high-throughput, and in situ quantitative CBED, enabling real-time mapping of valence electron distributions and their correlation with functional responses in quantum and energy materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Toward an event-level analysis of hadron structure using differential programming

Reconstructing the internal properties of hadrons in terms of fundamental quark and gluon de- grees of freedom is a central goal in nuclear and particle physics. This effort lies at the core of major experimental programs, such as the Jefferson Lab 12 GeV program and the upcoming Electron-Ion Collider. A primary challenge is the inherent inverse problem: converting large-scale observational data from collision events into the fundamental QCD-defined densities that characterize the micro- scopic structure of hadronic systems. Recent advances in AI and machine learning have opened new avenues for addressing this challenge using deep learning techniques. A particularly promising direction is the integration of complex theoretical calculations and experimental simulations into a unified framework capable of reconstructing these densities directly from event-level information. In this document, we introduce a key algorithm called LOITS, which enables differentiable program- ming within such a framework, facilitating the use of AI/ML techniques to solve the inverse problem of QCF reconstruction at the event level.

Braga, Kevin [College of William and Mary, William↗
DOE OSTI2026

Machine learning for seismic low-frequency extrapolation

The cycle-skipping problem that plagues full waveform inversion (FWI) can be at least partially mitigated if low frequencies (which encode the kinematics of wave propagation in seismic data) are recorded. However, seismic sources and receivers are band-limited, so seismic data does not generally include signals down to 0 Hz. To improve our ability to solve the seismic inverse problem, one can synthesize this missing low-frequency (LF) content from the recorded high-frequency (HF) data using machine learning (ML) models. Deep learning models such as convolutional neural networks (CNNs) demonstrate impressive ability to perform low frequency extrapolation. However, such models require powerful hardware (GPU machines) and careful training. We assess the extrapolation capabilities of three different ML models that do not require GPU machines, namely, random forest, Gaussian process regression and gradient boosting, on both synthetic and real data. Experimental results on two synthetic data sets (generated from a low velocity lens embedded in a homogeneous medium, and the Marmousi model) demonstrate that FWI applied to the extrapolated data consistently improves inversion accuracy relative to FWI applied to the original data sets that do not contain low frequencies. Application of low-frequency extrapolation to real data from the Northwest Shelf of Australia demonstrates that tree-based ML models such as gradient boosting can outperform CNNs in terms of both accuracy and computational cost on non-GPU architectures.

58 GEOSCIENCES↗
DOE OSTI2024

Scientific machine learning for closure models in multiscale problems: A review

Here, closure problems are omnipresent when simulating multiscale systems, where some quantities and processes cannot be fully prescribed despite their effects on the simulation's accuracy. Recently, scientific machine learning approaches have been proposed as a way to tackle the closure problem, combining traditional (physics-based) modeling with data-driven (machine-learned) techniques, typically through enriching differential equations with neural networks. This paper reviews the different reduced model forms, distinguished by the degree to which they include known physics, and the different objectives of a priori and a posteriori learning. The importance of adhering to physical laws (such as symmetries and conservation laws) in choosing the reduced model form and choosing the learning method is discussed. The effect of spatial and temporal discretization and recent trends toward discretization-invariant models are reviewed. In addition, we make the connections between closure problems and several other research disciplines: inverse problems, Mori-Zwanzig theory, and multi-fidelity methods. In conclusion, much progress has been made with scientific machine learning approaches for solving closure problems, but many challenges remain. In particular, the generalizability and interpretability of learned models is a major issue that needs to be addressed further.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Efficient Neural Network Approaches for Conditional Optimal Transport with Applications in Bayesian Inference

In this work, we present two neural network approaches that approximate the solutions of static and dynamic conditional optimal transport (COT) problems. Both approaches enable conditional sampling and conditional density estimation, which are core tasks in Bayesian inference—particularly in the simulation-based (“likelihood-free”) setting. Our methods represent the target conditional distribution as a transformation of a tractable reference distribution. Obtaining such a transformation, chosen here to be an approximation of the COT map, is computationally challenging even in moderate dimensions. To improve scalability, our numerical algorithms use neural networks to parameterize candidate maps and further exploit the structure of the COT problem. Our static approach approximates the map as the gradient of a partially input convex neural network. It uses a novel numerical implementation to increase computational efficiency compared to state-of-the-art alternatives. Our dynamic approach approximates the conditional optimal transport via the flow map of a regularized neural ODE; compared to the static approach, it is slower to train but offers more modeling choices and can lead to faster sampling. We demonstrate both algorithms numerically, comparing them with competing state-of-the-art approaches, using benchmark datasets and simulation-based Bayesian inverse problems.

97 MATHEMATICS AND COMPUTING↗
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↗
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 OSTI2025

Karhunen–Loève deep learning method for surrogate modeling and approximate Bayesian parameter estimation

We evaluate the performance of the Karhunen-Loève Deep Neural Network (KL-DNN) framework for surrogate modeling and approximate Bayesian parameter estimation in partial differential equation models. In the surrogate model, the Karhunen-Loève (KL) expansions are used for the dimensionality reduction of the number of unknown parameters and variables, and a deep neural network is employed to relate the reduced space of parameters to that of the state variables. The KL-DNN surrogate model is used to formulate a maximum-a-posteriori-like least-squares problem, which is randomized to draw samples of the posterior distribution of the parameters. We test the proposed framework for a hypothetical unconfined aquifer via comparison with the forward MODFLOW and inverse PEST++ iterative ensemble smoother (IES) solutions as well as the state-of-the-art Fourier neural operator (FNO) and deep operator networks (DeepONets) operator learning surrogate models. Our results show that the KL-DNN surrogate model outperforms FNO and DeepONet for forward predictions. For solving inverse problems, the randomized algorithm provides the same or more accurate Bayesian predictions of the parameters than IES as evidenced by the higher log-predictive probability of both the estimated parameter field and the forecast hydraulic head. The posterior mean obtained from the randomized algorithm is closer to the reference parameter field than that obtained with FNO as the maximum a posteriori estimate.

Approximate Bayesian inference↗
DOE OSTI2026

Overview of IMPACT Data Acquisition System and Data Reduction Process

This report documents the development of the data acquisition system (DAS) and data reduction methodologies for the Irradiated Material Property Accelerated Characterization Test (IMPACT) experiment at the Advanced Test Reactor (ATR). The IMPACT experiment is designed to enable in-pile measurement of thermal conductivity in metallic nuclear fuels, specifically U-10Zr, using an instrumented thermal conductivity probe. The DAS supports both passive temperature monitoring and active thermal interrogation of the probe through controlled AC and DC excitation. Significant modifications to laboratory-scale systems were required to accommodate the higher resistance paths associated with the in-pile application. Custom electronics and relay-controlled measurement sequencing were developed to enable the measurement and sufficient power delivery to the sensing region. A reduced-order, axisymmetric thermal model based on the thermal quadrupoles method is presented to support data interpretation. This model enables efficient evaluation of transient heat transfer behavior and facilitates solution of the inverse problem required to extract thermal properties from measured signals. Multiple boundary condition formulations are discussed to address varying experimental time scales and geometries. Additionally, machine learning techniques are introduced to support data reduction and improve confidence in inverse solutions. Convolutional neural networks are applied to identify the presence of gas gaps and other evolving geometric features that significantly impact thermal response during irradiation. These efforts contribute to the broader integration of digital twin frameworks and real-time modeling capabilities within the Advanced Fuels Campaign.

46 - INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AN↗
DOE OSTI2025

Feedforward equilibrium trajectory optimization with GSPulse

One of the common tasks required for designing new plasma scenarios or evaluating capabilities of a tokamak is to design the desired equilibria using a Grad-Shafranov (GS) equilibrium solver. However, most standard equilibrium solvers are time-independent and do not include dynamic effects such as plasma current flux consumption, induced vessel currents, or voltage constraints. Another class of tools, plasma equilibrium evolution simulators, do include time-dependent effects. These are generally structured to solve the forward problem of evolving the plasma equilibrium given feedback-controlled voltages. In this work, we introduce GSPulse, a novel algorithm for equilibrium trajectory optimization, that is more akin to a pulse planner than a pulse simulator. GSPulse includes time-dependent effects and solves the inverse problem: given a user-specified set of target equilibrium shapes, as well as limits on the coil currents and voltages, the optimizer returns trajectories of the voltages, currents, and achievable equilibria. This task is useful for scoping performance of a tokamak and exploring the space of achievable pulses. The computed equilibria satisfy both Grad-Shafranov force balance and axisymmetric circuit dynamics. The optimization is performed by restructuring the free-boundary equilibrium evolution equations into a form where it is computationally efficient to optimize the entire dynamic sequence. GSPulse can solve for hundreds of equilibria simultaneously within a few minutes. GSPulse has been validated against NSTX-U and MAST-U experiments and against SPARC feedback control simulations, and is being used to perform scenario design for SPARC. The computed trajectories can be used as feedforward inputs that are connected to the feedback controller to inform and improve feedback performance. The code for GSPulse is available open-source at github.com/jwai-cfs/GSPulse_public.

equilibrium↗
DOE OSTI2024

NeuroSEM: A hybrid framework for simulating multiphysics problems by coupling PINNs and spectral elements

Multiphysics problems that are characterized by complex interactions among fluid dynamics, heat transfer, structural mechanics, and electromagnetics, are inherently challenging due to their coupled nature. While experimental data on certain state variables may be available, integrating these data with numerical solvers remains a significant challenge. Physics-informed neural networks (PINNs) have shown promising results in various engineering disciplines, particularly in handling noisy data and solving inverse problems in partial differential equations (PDEs). However, their effectiveness in forecasting nonlinear phenomena in multiphysics regimes, particularly involving turbulence, is yet to be fully established. Here, this study introduces NeuroSEM, a hybrid framework integrating PINNs with the highfidelity Spectral Element Method (SEM) solver, Nektar++. NeuroSEM leverages the strengths of both PINNs and SEM, providing robust solutions for multiphysics problems. PINNs are trained to assimilate data and model physical phenomena in specific subdomains, which are then integrated into the Nektar++ solver. We demonstrate the efficiency and accuracy of NeuroSEM for thermal convection in cavity flow and flow past a cylinder. The framework effectively handles data assimilation by addressing those subdomains and state variables where the data is available. We applied NeuroSEM to the Rayleigh-B´enard convection system, including cases with missing thermal boundary conditions and noisy datasets. Finally, we applied the proposed NeuroSEM framework to real particle image velocimetry (PIV) data to capture flow patterns characterized by horseshoe vortical structures. Our results indicate that NeuroSEM accurately models the physical phenomena and assimilates the data within the specified subdomains. The framework’s plug-and-play nature facilitates its extension to other multiphysics or multiscale problems. Furthermore, NeuroSEM is optimized for efficient execution on emerging integrated GPU-CPU architectures. This hybrid approach enhances the accuracy and efficiency of simulations, making it a powerful tool for tackling complex engineering challenges in various scientific domains.

42 ENGINEERING↗
DOE OSTI2026

Learning neural representations for X-ray ptychography reconstruction with unknown probes

X-ray ptychography provides exceptional nanoscale resolution and is widely applied in materials science, biology, and nanotechnology. However, its full potential is constrained by the critical challenge of accurately reconstructing images when the illuminating probe is unknown. Conventional iterative methods and deep learning approaches are often suboptimal, particularly under the low-signal conditions inherent to low-dose and high-speed experiments. These limitations compromise reconstruction fidelity and restrict the broader adoption of the technique. In this work, we introduce the Ptychographic Implicit Neural Representation (PtyINR), a self-supervised framework that simultaneously addresses the object- and probe-recovery problem. By parameterizing both as continuous neural representations, PtyINR performs end-to-end reconstruction directly from raw diffraction patterns without requiring any pre-characterization of the probe. Extensive evaluations demonstrate that PtyINR achieves superior reconstruction quality on both simulated and experimental data, with remarkable robustness under challenging low-signal conditions. Furthermore, PtyINR offers a generalizable, physics-informed framework for addressing probe-dependent inverse problems, making it applicable to a wide range of computational microscopy problems.

36 MATERIALS SCIENCE↗