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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

A fast two-stage algorithm for non-negative matrix factorization in smoothly varying data

This article reports the study of algorithms for non-negative matrix factorization (NMF) in various applications involving smoothly varying data such as time or temperature series diffraction data on a dense grid of points. Utilizing the continual nature of the data, a fast two-stage algorithm is developed for highly efficient and accurate NMF. In the first stage, an alternating non-negative least-squares framework is used in combination with the active set method with a warm-start strategy for the solution of subproblems. In the second stage, an interior point method is adopted to accelerate the local convergence. The convergence of the proposed algorithm is proved. The new algorithm is compared with some existing algorithms in benchmark tests using both real-world data and synthetic data. Furthermore, the results demonstrate the advantage of the algorithm in finding high-precision solutions.

interior point method↗
DOE OSTI2026

Synthetic data-driven deep learning for label-free autonomous atomic force microscopy

Atomic force microscopy (AFM) is a widely used tool for nanoscale characterization across materials science, energy research, and biology. However, its adoption in high-throughput materials discovery and statistically driven studies remains limited by a strong dependence on expert operator input and by the scarcity of annotated experimental AFM datasets needed to enable data-driven automation. Here, we introduce SimuScan, a synthetic-data–driven framework that enables reliable AFM feature identification, segmentation, and targeted imaging without requiring large manually labeled experimental datasets. SimuScan generates tunable, high-fidelity synthetic AFM images of defined morphologies while incorporating realistic experimental artifacts, including tip–sample convolution, noise, flattening distortions, and surface debris. These datasets are shown to support scalable, label-free training of modern deep learning models for AFM analysis. When integrated into data-driven AFM workflows, SimuScan-trained models can locate and analyze nanoscale structures across large datasets and guide targeted follow-up imaging. We validate this approach on nanostructured surfaces, DNA assemblies, and bacterial cells, demonstrating robust generalization across diverse sample types with minimal operator intervention. More broadly, this work establishes a general strategy for generating explicitly conditioned, task-relevant synthetic data to improve the reliability of downstream models in autonomous microscopy.

Millan-Solsona, Ruben [Oak Ridge National Laborato↗
DOE OSTI2025

Validation of the DESI 2024 Lyman alpha forest BAL masking strategy

Broad absorption line quasars (BALs) exhibit blueshifted absorption relative to a number of their prominent broad emission features. These absorption features can contribute to quasar redshift errors and add absorption to the Lyman-α (Lyα) forest that is unrelated to large-scale structure. We present a detailed analysis of the impact of BALs on the Baryon Acoustic Oscillation (BAO) results with the Lyα forest from the first year of data from the Dark Energy Spectroscopic Instrument (DESI). The baseline strategy for the first year analysis is to mask all pixels associated with all BAL absorption features that fall within the wavelength region used to measure the forest. We explore a range of alternate masking strategies and demonstrate that these changes have minimal impact on the BAO measurements with both DESI data and synthetic data. This includes when we mask the BAL features associated with emission lines outside of the forest region to minimize their contribution to redshift errors. We identify differences in the properties of BALs in the synthetic datasets relative to the observational data, as well as use the synthetic observations to characterize the completeness of the BAL identification algorithm, and demonstrate that incompleteness and differences in the BALs between real and synthetic data also do not impact the BAO results for the Lyα forest.

Lyman alpha forest↗
DOE OSTI2026

Generalizing synthetic data-trained acoustic predictive models to real-world measurements

Acoustic Resonance Spectroscopy (ARS) is highly sensitive to structural properties such as material, geometry, and environmental conditions; as a consequence, it can noninvasively measure internal properties that are unobservable by most other methods. Because of its sensing capabilities and low implementation cost and complexity, ARS has potential as a paradigm shift in noninvasive sensing, characterization, and monitoring applications. However, extracting specific properties from ARS measurements, comprising the vibration spectrum of a test object, is challenging due to the sensitivity of the spectra to other structural changes not being measured, e.g. manufacturing tolerances, component coupling, environmental variation, etc. Neural Networks are promising tools for identifying trends in ARS measurements, but their training typically requires large datasets, which are often impractical to obtain for real-world systems. Synthetic data can be simulated efficiently, but discrepancies between synthetic and real-world data frequently lead to poor generalization when testing on the real-world data. We propose a novel ARS model training framework that enables networks trained exclusively on synthetic ARS data to generalize effectively to real-world measurements. Our approach leverages the Correlation Alignment (CORAL) technique to enforce the extraction of features common to both synthetic and real-world domains. As a case study, we demonstrate noninvasive ARS-based pressure measurements in sealed systems. Finite element method (FEM) simulations were used to generate synthetic training data across diverse vessel configurations and pressure conditions, and model performance was then tested on real-world measurements. We demonstrate that robust machine learning models for ARS can be developed without large real-world datasets, significantly broadening the applicability of ARS for noninvasive sensing. Moreover, the approach is extensible to other sensing modalities where synthetic data are abundant but real-world data are limited.

36 MATERIALS SCIENCE↗
DOE OSTI2024

3D radiated power analysis of JET SPI discharges using the Emis3D forward modeling tool

Abstract Precise values for radiated energy in tokamak disruption experiments are needed to validate disruption mitigation techniques for burning plasma tokamaks like ITER and SPARC. Control room analysis of radiated power ( P rad ) on JET assumes axisymmetry, since fitting 3D radiation structures with limited bolometry coverage is an under-determined problem. In mitigated disruptions, radiation is toroidally asymmetric and 3D, due to fast-growing 3D MHD modes and localized impurity sources. To address this problem, Emis3D adopts a physics motivated forward modeling (‘guess and check’) approach, comparing experimental bolometry data to synthetic data from user-defined radiation structures. Synthetic structures are observed with the Cherab modeling framework and a best fit chosen using a reduced χ 2 statistic. 2D tomographic inversion models are tested, as well as helical flux tubes and 3D MHD simulated structures from JOREK. Two nominally identical pure neon shattered pellet injection (SPI) mitigated discharges in JET are analyzed. 2D tomographic inversions with added toroidal freedom are the best fits in the thermal quench (TQ) and current quench (CQ). In the pre-TQ, 2D reconstructions are statistically the best fits, but are likely over-optimized and do not capture the 3D radiation structure seen in fast camera images. The next-best pre-TQ fits are helical structures that extend towards the high-field side, consistent with an impurity flow under the magnetic nozzle effect also observed in JOREK simulations. Whole-disruption radiated fractions of 0.98 + 0.03 / − 0.29 and 1.01 + 0.02 / − 0.17 are found, suggesting that the stored energy may have been fully mitigated by each SPI, although mitigation efficiencies well below ITER and SPARC requirements for high energy pulses are still within the large uncertainties. Emis3D is also used to validate JOREK SPI simulations, and confirms improvements in matching experiment from changes to impurity modeling. Time-dependent toroidal peaking factors are calculated and discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Improved Earthquake Source Parameters with 3D Wavespeed Models in California and Nevada

Seismic tomography harnesses earthquake data to explore the inaccessible structure of the Earth. Adjoint waveform tomography (AWT), a method of seismic tomography, updates the tomographic model by optimizing the fit between observed earthquake data and synthetic waveforms. The synthetic data are calculated by solving the wave equation through a given 3D model. An important requirement to calculating synthetics is the source information (location, centroid time, depth, and moment tensor). Errors in source information affect the quality of the synthetics produced, which in turn can limit how structure can be inferred in the AWT workflow. Here, to test the effect of updating source information, we used MTTime (Chiang, 2020), a time-domain full-waveform moment tensor inversion code, to calculate the moment tensors and depths of 118 earthquakes that occurred in California and Nevada over a 20-yr period. We calculated 3D Green’s functions using a 3D seismic wavespeed model of California and Nevada (Doody et al., 2023b). We show that the inverted solutions provide better waveform fits than the Global Centroid Moment Tensor catalog and increase usable, well-correlated data by up to 7%. Therefore, we argue that recalculating source parameters should be considered in AWT workflows, particularly for smaller magnitude events (⁠M w > 5.0).

58 GEOSCIENCES↗
DOE OSTI2021

SoDa: An Irradiance-Based Synthetic Solar Data Generation Tool (SoDa) v0.1

SoDa is an irradiance-based synthetic Solar Data generation tool to generate realistic sub-minute solar photovoltaic (PV) power time series, that emulate the weather pattern for a certain geographical location. Our tool relies on the National Solar Radiation Database (NSRDB) to obtain irradiance and weather data patterns for the site. Irradiance is mapped onto a PV model estimate of a solar plant's 30-min power output, based on the configuration of the panel. We use a stochastic model with a switching behavior due to different weather regimes as provided by the cloud type label in the NSRDB, with parameters for the cloudy states trained on the high-resolution solar power measurements from a Phasor Measurement Unit (PMU).

Carreno, IgnacioLosada↗
DOE OSTI2025

CAFE AU LAIT: Compute-Aware Federated Augmented Low-Rank AI Training

Federated finetuning is crucial for unlocking the knowledge embedded in pretrained Large Language Models (LLMs) when data are geographically distributed across clients. Unlike finetuning with data from a single institution, federated finetuning allows collaboration across multiple institutions, enabling the utilization of diverse and decentralized datasets while preserving data privacy. Given the high computing costs of LLM training and the emphasis on energy efficiency in Federated Learning (FL), Low-Rank Adaptation (LoRA) has emerged as a widely adopted algorithm due to its significantly reduced number of trainable parameters. However, this assumes that all data silos have the necessary computing resources to compute local updates of LLMs. Nevertheless, in practice, the computing resources across clients are highly heterogeneous: while some may have access to hundreds of GPUs, others might have limited or no GPU access. Recently, federated finetuning using synthetic data has been proposed, allowing clients to participate in a collaborative training run without training LLMs locally. However, our experimental results reveal a performance gap between models trained using synthetic data and those trained using local updates. Motivated by the observed heterogeneity in computing resources and the performance gap, we propose a novel two-stage algorithm that leverages the storage and computing capabilities of a strong server. In the first stage, under the coordination of the strong server, clients with limited computing resources collaborate to generate synthetic data, which is transferred to and stored on the strong server. In the second stage, the strong server uses this synthetic data on behalf of the resource-constrained clients to perform federated LoRA finetuning alongside clients with sufficient computing resources. This approach ensures that all clients can participate in the finetuning process. Experimental results demonstrate that incorporating local updates from even a small fraction of clients improves performance compared to using synthetic data for all clients. Furthermore, we incorporate the Gaussian mechanism in both stages to guarantee client-level differential privacy.

Wang, Jiayi [ORNL]↗
DOE OSTI2022

Training a Quantum Annealing Based Restricted Boltzmann Machine on Cybersecurity Data

A restricted Boltzmann machine (RBM) is a generative model that could be used in effectively balancing a cybersecurity dataset because the synthetic data a RBM generates follows the probability distribution of the training data. RBM training can be performed using contrastive divergence (CD) and quantum annealing (QA). QA-based RBM training is fundamentally different from CD and requires samples from a quantum computer. We present a real-world application that uses a quantum computer. Specifically, we train a RBM using QA for cybersecurity applications. The D-Wave 2000Q has been used to implement QA. RBMs are trained on the ISCX data, which is a benchmark dataset for cybersecurity. For comparison, RBMs are also trained using CD. CD is a commonly used method for RBM training. Our analysis of the ISCX data shows that the dataset is imbalanced. We present two different schemes to balance the training dataset before feeding it to a classifier. The first scheme is based on the undersampling of benign instances. The imbalanced training dataset is divided into five sub-datasets that are trained separately. A majority voting is then performed to get the result. Our results show the majority vote increases the classification accuracy up from 90.24% to 95.68%, in the case of CD. For the case of QA, the classification accuracy increases from 74.14% to 80.04%. In the second scheme, a RBM is used to generate synthetic data to balance the training dataset. We show that both QA and CD-trained RBM can be used to generate useful synthetic data. Balanced training data is used to evaluate several classifiers. Among the classifiers investigated, K-Nearest Neighbor (KNN) and Neural Network (NN) perform better than other classifiers. They both show an accuracy of 93%. Our results show a proof-of-concept that a QA-based RBM can be trained on a 64-bit binary dataset. The illustrative example suggests the possibility to migrate many practical classification problems to QA-based techniques. Further, we show that synthetic data generated from a RBM can be used to balance the original dataset.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Data efficiency assessment of generative adversarial networks in energy applications

This study investigates the data requirements of generative artificial intelligence (AI), particularly generative adversarial networks (GANs), for reliable data augmentation in energy applications. Generative AI, though seen as a solution to data limitations, requires substantial data to learn meaningful distributions—a challenge often overlooked. This study addresses the challenge through synthetic data generation for critical heat flux (CHF) and power grid demand, focusing on renewable and nuclear energy. Two variants of GAN employed are conditional GAN (cGAN) and Wasserstein GAN (wGAN). Our findings include the strong dependency of GAN on data size, with performance declining on smaller datasets and varying performance when generalizing to unseen experiments. Mass flux and heated length significantly influence CHF predictions. wGAN is more robust to feature exclusion, making it suitable for constrained synthetic data generation. In energy demand forecasting, wGAN performed well for solar, wind, and load predictions. Longer lookback hours and larger datasets improved predictions, especially for load power. Seasonal variations posed challenges, with wGAN achieving a relatively high error of Root Mean Squared Error (RMSE) of 0.32 for load power prediction, compared to RMSE of 0.07 under same-season conditions. Feature exclusions impacted cGAN the most, while wGAN showed greater robustness. This study concludes that, while generative AI is effective for data augmentation, it requires substantial data and careful training to generate realistic synthetic data and generalize to new experiments in engineering applications.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

SSTDR and FDR Detection of Un-Energized and Energized Cable Anomalies Including Thermal Degradation Using Machine Learning

Historically, cables are initially qualified for nuclear power plant use for 40 years. As plants extend their operating license to 60 and 80 years, continued use of these cables must shift to a performance-based approach since it is cost prohibitive to completely replace cables that are likely still capable of performing their design function. A variety of cable tests are available and are commonly applied during outages when the cables can be taken out of service. Frequency domain reflectometry (FDR) is one of these test methods that is being more broadly accepted and used because it not only detects anomalies along the cable with a low-voltage signal that does not stress the cable insulation, but the technique also locates the anomalies. This supports follow-up local inspection and local repair or partial replacement of a damaged cable segment. Currently, FDR testing is only applied to cables that are taken out of service since the test instrument would be damaged by operational voltages. A related technology that has found some acceptance in the aircraft and rail industry is spread spectrum time domain reflectometry (SSTDR). This technology has been implemented with a custom commercial instrument by LiveWire Innovation that is designed to operate on live cables up to 1000 volts and with a bandwidth of 48 MHz. Initial evaluation by the Pacific Northwest National Laboratory (PNNL) of the Live Wire system indicated that a broader bandwidth (BW) SSTDR may be better for many kinds of flaws. This led PNNL to develop an SSTDR laboratory instrument suitable for tests up to 500 MHz bandwidth. Testing on energized cables is also desirable for online monitoring systems so an inductive clamshell coupler was developed that allows energized cables to be tested up to at least 5 kV and likely higher voltage levels. Dielectric spectroscopy and tan delta testing plus various laboratory destructive tests were included in this data acquisition campaign directed to feed a machine learning (ML) study. With these kinds of developments, online energized cable tests may be possible with industrial adoption of such hardware advances but it will be completely impractical to have highly skilled data analysts continually examine these complex signals for indications of damage or compromised conditions. If online testing is to be implemented in new test hardware, it must be accompanied by software that can interpret the signals and alert plant operators of changing or degraded conditions. The thermally aged, shielded cable investigated here was separately treated for ML analysis. Visual analysis of electrical data showed generally increasing peaks where the cable entered and exited the oven. These peaks were not exactly aligned with expected locations, but these differences were attributed to velocity of propagation calibration errors. Only supervised ML was applied to the thermally aged data as this data was only available shortly before the committed publication date of this report. The supervised ML was structured to divide the 0 to 70-day responses as ‘normal’ from 0 to 35 days or ‘anomalous’ from 36 to 70 days, based on cable tensile elongation at break (EAB) insulation characterization. Using 80% of the data for training and 20% for testing, the supervised ML predicted normal versus anomalous was 70% accurate. Important conclusions include: • Accuracy to predict the presence of cable damage is improved from the 2023 effort by more training data. Weighted accuracies for comparisons among the instruments ranged from 67 to 89 % for unsupervised ML and 71 to 99% for supervised ML. • Based on the synthetic data tests, the unsupervised models are more generalizable to unseen anomalies. The Multi-Layer Perceptron classifier (MLP) model reported as high as 99.7% accuracy on the test data, but this dropped to 58.3% when tested on the synthetic data. In contrast, the unsupervised Pointwise model only achieved 89.7% accuracy on the experimental data but reported 78.3% accuracy on the synthetic data. • The best anomaly indicators are higher frequency (400 MHz BW) FDR data. Other tests may be interesting but for this study, this was the best predicter.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2023

Machine learning-based inversion for acoustic impedance with large synthetic training data: Workflow and data characterization

Where wells are sparse or training data are difficult to label with high-quality wireline-derived impedance logs, machine learning (ML)-based inversion of acoustic impedance typically depends on small training data sets, leading to biased prediction. We have advanced a novel workflow that applies large synthetic seismic training data to reduce facies-related bias. Using a geologically realistic model as the truth model, we randomly select sparse seed wells to perform sequential Gaussian simulation (SGS) for impedance models of the same geometry and simulate facies variability. We implement random forest regression on 30 features extracted from the synthetic volume. We observe that more seed wells tend to reduce facies-induced bias by sampling more types of facies, resulting in a better prediction. We then focus on the responses of SGS models to facies changes, the number of seed wells necessary for a useful synthetic model, and how much a synthetic model can help ML-based inversion. Here, we observe that the SGS synthetic training model outperforms well-direct training in general. For modeled clastic shore-zone systems in Miocene Gulf of Mexico, two or more seed wells are necessary for a significant reduction of root-mean-square error and outliners, and improvement of facies imaging. In a field-data test, we apply a similar workflow to quantitatively predict acoustic impedance, which is then converted to a sand-volume map at a high-frequency sequence (10–100 m), revealing detailed facies and sandstone patterns. Such results are valuable in many geologic and engineering applications, such as hydrocarbon and CO 2 reservoir prospecting, reserve estimation, simulation, etc.

3D seismic↗
DOE OSTI2022

A machine learning approach to water quality forecasts and sensor network expansion: Case study in the Wabash River Basin, United States

Abstract Midwestern cities require forecasts of surface nitrate loads to bring additional treatment processes online or activate alternative water supplies. Concurrently, networks of nitrate monitoring stations are being deployed in river basins, co‐locating water quality observations with established stream gauges. However, tools to evaluate the future value of expanded networks to improve water quality forecasts remains challenging. Here, we construct a synthetic data set of stream discharge and nitrate for the Wabash River Basin—one of the United States’ most nutrient polluted basins—using the established Agro‐IBIS and THMB models. Synthetic data enables rapid, unbiased and low‐cost assessment of potential sensor placements to support management objectives, such as near‐term forecasting. Using the synthetic data, we established baseline 1‐day forecasts for surface water nitrate at 12 cities in the basin using support vector machine regression (SVMR; RMSE 0.48–3.3 ppm). Next, we used the SVMRs to evaluate the improvement in forecast performance associated with deployment of additional nitrate sensors. We identified the optimal sensor placement to improve forecasts at each city, and the relative value of sensors at each candidate location. Finally, we assessed the co‐benefit realized by other cities when a sensor is deployed to optimize a forecast at one city, finding significant positive externalities in all cases. Ultimately, our study explores the potential for machine learning to make near‐term predictions and critically evaluate the improvement realized by expanding a monitoring network. While we use nitrate pollution in the Wabash River Basin as a case study, this approach could be readily applied to any problem where the future value of sensors and network design are being evaluated.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Developing Data-Driven Synthetic Infrastructure Models for Resilience Analysis

Research on infrastructure resilience has produced promising methods to simulate and optimize complex networks to improve performance. However, restrictions on sharing infrastructure models and the steep cost of developing and maintaining infrastructure models presents a roadblock to adoption. To overcome this limitation, this research focuses on methods to create data-driven infrastructure models that will help improve infrastructure resilience and security. The analysis couples incomplete utility data, geospatial data, machine learning, and synthetic network generation methods to rapidly develop and update infrastructure models. The methods are validated using realistic utility models and site-specific data, with a focus on Puerto Rico due to its unique infrastructure challenges and available data. This research highlights promising opportunities for the use of synthetic network generation and machine learning to create infrastructure models when very little data is available. Results demonstrate that hybrid methods, which combine sparse utility data with synthetic models, can enhance model accuracy, and machine learning can predict model attributes using training data from other models. However, the complexity of infrastructure systems means that even minor changes in network connectivity can significantly impact simulation results. Resilience analysis using synthetic infrastructure models shows that while some system behaviors are preserved, the magnitude of disruptions may not be accurately represented, indicating the need for more research and validation before using synthetic models for critical infrastructure investment decisions. The framework outlined in this report represents a significant advance to infrastructure model development and could be applied to additional domains and sites. Future research will continue to streamline and validate methods to help reduce roadblocks to resilience analysis.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2026

Unsupervised domain adaptation for radioisotope identification in gamma spectroscopy

Training machine learning models for radioisotope identification using gamma spectroscopy remains an elusive challenge for many practical applications, largely stemming from the difficulty of acquiring and labeling large, diverse experimental datasets. Simulations can mitigate this challenge, but the accuracy of models trained on simulated data can deteriorate substantially when deployed to an out-of-distribution operational environment. In this study, we demonstrate that unsupervised domain adaptation (UDA) can improve the ability of a model trained on synthetic data to generalize to a new testing domain, provided unlabeled data from the target domain are available. Conventional supervised techniques are unable to utilize this data because the absence of isotope labels precludes defining a supervised classification loss. Instead, we first pretrain a spectral classifier using labeled synthetic data and subsequently leverage unlabeled target data to align the learned feature representations between the source and target domains. We compare a range of different UDA techniques, finding that minimizing the maximum mean discrepancy (MMD) between source and target feature vectors yields the most consistent improvement to testing scores. For instance, using a custom transformer-based neural network, we achieved a testing accuracy of $0.904 \pm 0.022$ on an experimental LaBr test set after performing unsupervised feature alignment via MMD minimization, compared to $0.754 \pm 0.014$ before alignment. Overall, our results highlight the potential of using UDA to adapt a radioisotope classifier trained on synthetic data for real-world deployment.

Lalor, Peter W.↗
DOE OSTI2021

A second order yield-temperature relation for accurate inference of burn-averaged quantities in multi-species plasmas

Measured yields and ion temperatures inferred from the fusion product energy spectra can be used as metrics for the performance of an ICF implosion. This can be used to infer species separation, thermal decoupling, flows, or other effects that can cause the inferred ion temperatures to deviate from the true underlying thermal temperature and the yield ratio to deviate from the expected value. Direct inference of the impact of these effects on observed temperatures and yields can be difficult to uncover due to the underlying dependence on the shape and time evolution of the temperature and density profiles of the fusing plasma. Due to differences in the temperature dependence of the reactivities, different fusion products are emitted from different regions and times within the implosion. In order to properly account for this, a second-order analytical expression relating the apparent temperatures and yield ratios is developed. This expression can be coupled to models of yield and/or temperature altering effects to infer their burn-averaged impact on an implosion. The second-order expression shows significant improvement over lower-order expressions in synthetic data studies. Demonstrations of its applications to synthetic data coupled with models of ion thermal decoupling and radial flows are presented. In the case of thermal decoupling, both first and second-order expressions show reasonable levels of accuracy. To consistently infer the amplitude of radial flow with a <10% error, the second-order equation is required.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

A second order yield-temperature relation for accurate inference of burn-averaged quantities in multi-species plasmas

Measured yields and ion temperatures inferred from the fusion product energy spectra can be used as metrics for the performance of an ICF implosion. This can be to infer species separation, thermal decoupling, flows or other effects that can cause the inferred ion temperatures to deviate from the true underlying thermal temperature and the yield ratio to deviate from the expected value. Direct inference of the impact of these effects on observed temperatures and yields can be difficult to uncover due to underlying dependence on the shape and time evolution of the temperature and density proles of the fusing plasma. Due to differences in the temperature dependence of the reactivities, different fusion products are emitted from different regions and times within the implosion. In order to properly account for this, a second order analytic expression relating the apparent temperatures and yield ratios is developed. This expression can be coupled to models of yield and/or temperature altering effects to infer their burn-averaged impact on an implosion. The second order expression shows significant improvement over lower order expressions in synthetic data studies. Demonstrations of its applications to synthetic data coupled with models of ion thermal decoupling and radial flows are presented. In the case of thermal decoupling both first and second order expressions show reasonable levels of accuracy. To consistently infer the amplitude of radial flow with <10% error the second order equation is required.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗