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DOE OSTI2024

A Diffusion‐Based Uncertainty Quantification Method to Advance E3SM Land Model Calibration

Abstract Calibrating land surface models and accurately quantifying their uncertainty are crucial for improving the reliability of simulations of complex environmental processes. This, in turn, advances our predictive understanding of ecosystems and supports climate‐resilient decision‐making. Traditional calibration methods, however, face challenges of high computational costs and difficulties in accurately quantifying parameter uncertainties. To address these issues, we develop a diffusion‐based uncertainty quantification (DBUQ) method. Unlike conventional generative diffusion methods, which are computationally expensive and memory‐intensive, DBUQ innovates by formulating a parameterized generative model and approximates this model through supervised learning, which enables quick generation of parameter posterior samples to quantify its uncertainty. DBUQ is effective, efficient, and general‐purpose, making it suitable for site‐specific ecosystem model calibration and broadly applicable for parameter uncertainty quantification across various earth system models. In this study, we applied DBUQ to calibrate the Energy Exascale Earth System Model land model at the Missouri Ozark AmeriFlux forest site. Results indicated that DBUQ produced accurate parameter posterior distributions similar to those from Markov Chain Monte Carlo sampling but with 30 times less computing time. This significant improvement in efficiency suggests that DBUQ can enable rapid, site‐level model calibration at a global scale, enhancing our predictive understanding of climate impacts on terrestrial ecosystems.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Uncertainty quantification for neural network potential foundation models

Abstract For neural network potentials (NNPs) to gain widespread use, researchers must be able to trust model outputs. However, the blackbox nature of neural networks and their inherent stochasticity are often deterrents, especially for foundation models trained over broad swaths of chemical space. Uncertainty information provided at the time of prediction can help reduce aversion to NNPs. In this work, we detail two uncertainty quantification (UQ) methods. Readout ensembling, by finetuning the readout layers of an ensemble of foundation models, provides information about model uncertainty, while quantile regression, by replacing point predictions with distributional predictions, provides information about uncertainty within the underlying training data. We demonstrate our approach with the MACE-MP-0 model, applying UQ to the foundation model and a series of finetuned models. The uncertainties produced by the readout ensemble and quantile methods are demonstrated to be distinct measures by which the quality of the NNP output can be judged.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Enhancing generative molecular design via uncertainty-guided fine-tuning of variational autoencoders

In recent years, deep generative models have been successfully applied to various molecular design tasks, particularly in the life and materials sciences. One critical challenge for pre-trained generative molecular design (GMD) models is to fine-tune them to be better suited for downstream design tasks that aim at optimizing specific molecular properties. However, redesigning and training an existing effective generative model from scratch for each new design task are impractical. Furthermore, the black-box nature of typical downstream tasks that involve property prediction makes it nontrivial to optimize the generative model in a task-specific manner. In this work, we propose an uncertainty-guided fine-tuning strategy that can effectively enhance a pre-trained variational autoencoder (VAE) for GMD through performance feedback in an active learning setting. The strategy begins by quantifying the model uncertainty of the generative model using an efficient active subspace-based UQ (uncertainty quantification) scheme. Next, the decoder diversity within the characterized model uncertainty class is explored to expand the viable space of molecular generation. The low-dimensionality of the active subspace makes this exploration tractable using a black-box optimization scheme, which in turn enables us to identify and leverage a diverse set of high-performing models to generate enhanced molecules. Empirical results across six target molecular properties using multiple VAE-based generative models demonstrate that our uncertainty-guided fine-tuning strategy consistently leads to improved models that outperform the original pre-trained models.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Quantification and visualization of uncertainties in reconstructed penumbral images of implosions at Omega

Penumbral imaging is a technique used in plasma diagnostics in which a radiation source shines through one or more large apertures onto a detector. To interpret a penumbral image, one must reconstruct it to recover the original source. The inferred source always has some error due to noise in the image and uncertainty in the instrument geometry. Interpreting the inferred source thus requires quantification of that inference’s uncertainty. Markov chain Monte Carlo algorithms have been used to quantify uncertainty for similar problems but have never been used for the inference of the shape of an image. Because of this, there are no commonly accepted ways of visualizing uncertainty in two-dimensional data. This paper demonstrates the application of the Hamiltonian Monte Carlo algorithm to the reconstruction of penumbral images of fusion implosions and presents ways to visualize the uncertainty in the reconstructed source. This methodology enables more rigorous analysis of penumbral images than has been done in the past.

Instruments & Instrumentation↗

DOE OSTI2024

ETHOS: An automated framework to generate multi-fidelity constitutive data tables and propagate uncertainties to hydrodynamic simulations

Accurate constitutive data, such as equations of state and plasma transport coefficients, are necessary for reliable hydrodynamic simulations of plasma systems such as fusion targets, planets, and stars. Here, we develop a framework for automatically generating transport-coefficient tables using a parameterized model that incorporates data from both high-fidelity sources (e.g., density functional theory calculations and reference experiments) and lower-fidelity sources (e.g., average-atom and analytic models). The framework incorporates uncertainties from these multi-fidelity sources, generating ensembles of optimally diverse tables that are suitable for uncertainty quantification of hydrodynamic simulations. We illustrate the utility of the framework with magnetohydrodynamic simulations of magnetically launched flyer plates, which are used to measure material properties in pulsed-power experiments. We explore how changes in the uncertainties assigned to the multi-fidelity data sources propagate to changes in simulation outputs and find that our simulations are most sensitive to uncertainties near the melting transition. The presented framework enables computationally efficient uncertainty quantification that readily incorporates new high-fidelity measurements or calculations and identifies plasma regimes where additional data will have high impact.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Parameter uncertainties for imperfect surrogate models in the low-noise regime

Abstract Bayesian regression determines model parameters by minimizing the expected loss, an upper bound to the true generalization error. However, this loss ignores model form error, or misspecification, meaning parameter uncertainties are significantly underestimated and vanish in the large data limit. As misspecification is the main source of uncertainty for surrogate models of low-noise calculations, such as those arising in atomistic simulation, predictive uncertainties are systematically underestimated. We analyze the true generalization error of misspecified, near-deterministic surrogate models, a regime of broad relevance in science and engineering. We show that posterior parameter distributions must cover every training point to avoid a divergence in the generalization error and design a compatible ansatz which incurs minimal overhead for linear models. The approach is demonstrated on model problems before application to thousand-dimensional datasets in atomistic machine learning. Our efficient misspecification-aware scheme gives accurate prediction and bounding of test errors in terms of parameter uncertainties, allowing this important source of uncertainty to be incorporated in multi-scale computational workflows.

Swinburne, Thomas D. (ORCID:0000000232554257)↗

DOE OSTI2026

Information-theoretic astrophysical uncertainties in the effective theory of dark matter direct detection

The impact of astrophysical uncertainties in direct detection searches can vary significantly across particle dark matter models and detector targets, due to the different velocity and momentum dependencies of the scattering cross section. We address these uncertainties for all operators of the nonrelativistic effective field theory of dark-matter/nucleon interactions, making use of the Kullback-Leibler (KL) information divergence to measure the deviation of the true dark matter velocity distribution from the Maxwell-Boltzmann form. This approach quantifies how astrophysical uncertainties affect each operator in the effective theory, without assuming any specific functional form for the velocity distribution. While for some operators the uncertainties are smaller than 1 order of magnitude for entropically motivated deviations from the Maxwell-Boltzmann form, for other operators, these uncertainties can be as large as three orders of magnitude near threshold. Furthermore, we identify the dependence of the scattering rate for various operators of the effective theory with different velocity-weighted moments of the velocity distribution, functionally analogous to the mean, variance, or skewness. This provides new analytic insight into which features of the velocity distribution are most relevant to detect a given particle dark matter model. Our technique is general and could be applied to a broader class of physics problems where a physical observable depends on the statistical moments of an uncertain theoretical distribution.

Herrera, Gonzalo [MIT, MKI; Harvard U.; Virginia T↗

DOE OSTI2025

Quantifying uncertainty in machine learning for nuclear binding energy

Techniques from artificial intelligence and machine learning are increasingly employed in nuclear theory; however, the uncertainties that arise from the complex parameter manifold encoded by the neural networks are often overlooked. Epistemic uncertainties arising from training the same network multiple times for an ensemble of initial weight sets offer a first insight into the confidence of machine learning predictions, but they often come with a high computational cost. Instead, we apply a single-model uncertainty quantification method called Δ-UQ that gives epistemic uncertainties with one-time training. Here, we demonstrate our approach on a two-feature model of nuclear binding energies per nucleon with proton and neutron number pairs as inputs. We show that Δ-UQ can produce reliable and self-consistent epistemic uncertainty estimates and can be used to assess the degree of confidence in predictions made with deep neural networks.

Huang, Mengyao [Lawrence Livermore National Labora↗

DOE OSTI2026

REV-INR: Regularized Evidential Implicit Neural Representation for Uncertainty-Aware Volume Visualization

Applications of Implicit Neural Representations (INRs) have emerged as a promising deep learning approach for compactly representing large volumetric datasets. These models can act as surrogates for volume data, enabling efficient storage and on-demand reconstruction via model predictions. However, conventional deterministic INRs only provide value predictions without insights into the model’s prediction uncertainty or the impact of inherent noisiness in the data. This limitation can lead to unreliable data interpretation and visualization due to prediction inaccuracies in the reconstructed volume. Identifying erroneous results extracted from model-predicted data may be infeasible, as raw data may be unavailable due to its large size. To address this challenge, we introduce REV-INR, Regularized Evidential Implicit Neural Representation, which learns to predict data values accurately along with the associated coordinate-level data uncertainty and model uncertainty using only a single forward pass of the trained REV-INR during inference. By comprehensively comparing and contrasting REV-INR with existing well-established deep uncertainty estimation methods, we show that REV-INR achieves the best volume reconstruction quality with robust data (aleatoric) and model (epistemic) uncertainty estimates using the fastest inference time. Consequently, we demonstrate that REV-INR facilitates assessment of the reliability and trustworthiness of the extracted isosurfaces and volume visualization results, enabling analyses to be solely driven by model-predicted data.

Saklani, Shanu [Indian Institute of Technology, Ka↗

DOE OSTI2026

3D Deep Learning Joint Inversion of Active Seismic Full Waveform and Passive Seismic Traveltime Data for Reservoir Imaging and Uncertainty Quantification

Here, we present deep learning (DL) networks for three-dimensional (3D) joint inversion of active seismic full waveform and passive seismic traveltime data to image reservoirs and their properties and quantify imaging uncertainties. Active seismic full-waveform data can provide high-resolution monitoring images but are collected only intermittently because of their high acquisition cost. In contrast, passive seismic data can be gathered at relatively low cost between regular active surveys, although their imaging quality can be compromised by factors such as low signal-to-noise ratios and limited ray coverage of the target. Although these datasets are routinely acquired together at CO 2 storage sites, their combined inversion within a 3D DL framework has not been previously demonstrated. To our knowledge, this is the first study to address this gap, combining the strength of both data types. For efficient data storage and DL training with large 3D seismic datasets, we use a 3D data matrix in which a random number of passive seismic traveltime data are stored as parabolic envelopes using one-hot encoding and a 3D full-waveform data matrix in which multiple shot gathers are summed. Two network architectures are evaluated: a single-encoder U-Net for single-data type inversion and a dual-encoder U-Net for joint inversion of active and passive seismic data. We also evaluate the single-encoder U-Net for joint inversion by concatenating full-waveform data and traveltime data. We propose a systematic approach for selecting an optimal dropout rate that balances regularization during training and Monte Carlo dropout-based uncertainty quantification during prediction by examining the correlation coefficient between standard deviation and prediction error, along with the training misfit, across a range of dropout rates. 3D DL inversion experiments include five different network configurations, with evaluations under ideal, noisy and dropout-enabled conditions. Both model and data uncertainties are assessed, as well as their combined effects. Across all conditions, the networks consistently predict accurate CO 2 saturation models with low prediction errors, such as a structural similarity index of 0.993 and CO 2 difference of 1.1%. Uncertainty estimates show strong spatial correlation with prediction errors, confirming the effectiveness of the proposed dropout selection approach. The results demonstrate that our DL approach, utilizing compact data representations and appropriate uncertainty quantification, yields accurate subsurface images under various inversion conditions and provides valuable insights into the reliability of predictions.

Um, Evan Schankee [Lawrence Berkeley National Labo↗

DOE OSTI2025

Sigma: Uncertainty Propagation for C++

Sigma is a header-only C++-17 library for uncertainty propagation, inspired by uncertainties for Python and Measurements.jl for Julia. The library tracks the functional correlation between dependent and independent variables, ensuring that the uncertainty of the independent variables is properly considered in the calculation of the dependent variables’ uncertainties. It is intended as a near drop-in replacement for the standard floating point types (aside from uncertainty specification), and aims to be easily interoperable with the existing standard types.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Uncertainty Quantification in GADRAS Inverse Modeling

The Gamma Detector Response and Analysis Software (GADRAS) package includes an inverse modeling tool that is helpful in identifying characteristics of unknown radioactive materials. Traditionally, uncertainties in this analysis were derived solely from measurement data quality and the fit of synthetic spectra. This paper aims to rigorously quantify additional sources of uncertainty, focusing on uncertainties arising from measurements being analyzed, Detector Response Function (DRF) characterization, and DRF extrapolation. Applying these findings to the BeRPBall benchmark data set, we demonstrated the impact of these uncertainties on plutonium and polyethylene estimates. The results underscore the importance of incorporating diverse uncertainty sources to enhance the accuracy and reliability of GADRAS’s inverse modeling capabilities.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2025

Uncertainty based Online Ensemble on Non-Stationary Data for Fusion Science

Machine Learning (ML) is poised to play a pivotal role in the development and operation of next-generation fusion devices. Fusion data shows non-stationary behavior due to drifts in the data. The drifts can arise from both experimental evolution and machine wear-and-tear. ML models assume stationary distribution and fail to maintain performance when encountered with non-stationary data streams.Online learning can be used to continuously adapt the models with new data as it is acquired. However, traditional online learning can suffer from short-term performance degradation, as ground truth are not available before making the prediction. To address this challenge, we propose uncertainty aware ensemble approach for online learning. We use Deep Gaussian Process Approximation (DGPA) technique for calibrated uncertainty estimation and use the uncertainty values to guide a meta-algorithm that produces predictions based on ensemble of learners. Moreover, DGPA also provides uncertainty estimation along with the predictions for decision makers. This paper demonstrates that the proposed method outperforms traditional online learning approach, and a naive ensemble without uncertainty guidance by about 7% and 6%, respectively, on B-coil deflection prediction at DIII-D Fusion Facility.

Rajput, Kishansingh [Thomas Jefferson National Acc↗

DOE OSTI2024

Methods for Incorporating Model Uncertainty into Exoplanet Atmospheric Analysis

A key goal of exoplanet spectroscopy is to measure atmospheric properties, such as abundances of chemical species, in order to connect them to our understanding of atmospheric physics and planet formation. In this new era of high-quality JWST data, it is paramount that these measurement methods are robust. When comparing atmospheric models to observations, multiple candidate models may produce reasonable fits to the data. Typically, conclusions are reached by selecting the best-performing model according to some metric. This ignores model uncertainty in favor of specific model assumptions, potentially leading to measured atmospheric properties that are overconfident and/or incorrect. In this paper, we compare three ensemble methods for addressing model uncertainty by combining posterior distributions from multiple analyses: Bayesian model averaging, a variant of Bayesian model averaging using leave-one-out predictive densities, and stacking of predictive distributions. We demonstrate these methods by fitting the Hubble Space Telescope (HST) + Spitzer transmission spectrum of the hot Jupiter HD 209458b using models with different cloud and haze prescriptions. All of our ensemble methods lead to uncertainties on retrieved parameters that are larger but more realistic and consistent with physical and chemical expectations. Since they have not typically accounted for model uncertainty, uncertainties of retrieved parameters from HST spectra have likely been underreported. We recommend stacking as the most robust model combination method. Our methods can be used to combine results from independent retrieval codes and from different models within one code. They are also widely applicable to other exoplanet analysis processes, such as combining results from different data reductions.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

The Dark Energy Survey Supernova Program: Cosmological Analysis and Systematic Uncertainties

We present the full Hubble diagram of photometrically classified Type Ia supernovae (SNe Ia) from the Dark Energy Survey supernova program (DES-SN). DES-SN discovered more than 20,000 SN candidates and obtained spectroscopic redshifts of 7000 host galaxies. Based on the light-curve quality, we select 1635 photometrically identified SNe Ia with spectroscopic redshift 0.10 < z < 1.13, which is the largest sample of supernovae from any single survey and increases the number of known z > 0.5 supernovae by a factor of 5. In a companion paper, we present cosmological results of the DES-SN sample combined with 194 spectroscopically classified SNe Ia at low redshift as an anchor for cosmological fits. Here we present extensive modeling of this combined sample and validate the entire analysis pipeline used to derive distances. We show that the statistical and systematic uncertainties on cosmological parameters are ${\sigma }_{{{\rm{\Omega }}}_{M},\mathrm{stat}+\mathrm{sys}}^{{\rm{\Lambda }}\mathrm{CDM}}=$ 0.017 in a flat ΛCDM model, and $({\sigma }_{{{\rm{\Omega }}}_{M}},{\sigma }_{w}{)}_{\mathrm{stat}+\mathrm{sys}}^{w\mathrm{CDM}}$ = (0.082, 0.152) in a flat wCDM model. Combining the DES SN data with the highly complementary cosmic microwave background measurements by Planck Collaboration reduces by a factor of 4 uncertainties on cosmological parameters. In all cases, statistical uncertainties dominate over systematics. We show that uncertainties due to photometric classification make up less than 10% of the total systematic uncertainty budget. This result sets the stage for the next generation of SN cosmology surveys such as the Vera C. Rubin Observatory's Legacy Survey of Space and Time.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Uncertainty based Online Ensemble on Non-Stationary Data for Fusion Science

Rajput, Kishansingh [Thomas Jefferson National Acc↗

DOE OSTI2026

An uncertainty visualization framework for large-scale cardiovascular flow simulations: A case study on aortic stenosis

We present a generalizable uncertainty quantification (UQ) and visualization framework for lattice Boltzmann method simulations of high Reynolds number vascular flows, demonstrated on a patient-specific stenosed aorta. The framework combines EasyVVUQ for parameter sampling with large-eddy simulation turbulence modeling in HemeLB, and executes ensembles on the Frontier exascale supercomputer. Spatially resolved metrics, including entropy and isosurface-crossing probability, are used to map uncertainty in pressure and wall shear stress fields directly onto vascular geometries. Two sources of model variability are examined: inlet peak velocity and the Smagorinsky constant. Inlet velocity variation produces high uncertainty downstream of the stenosis where turbulence develops, while upstream regions remain stable. Smagorinsky constant variation has little effect on the large-scale pressure field but increases WSS uncertainty in localized high-shear regions. In both cases, the stenotic throat manifests low entropy, indicative of robust identification of elevated WSS. By linking quantitative UQ measures to three-dimensional anatomy, the framework improves interpretability over conventional 1D UQ plots and supports clinically relevant decision-making, with broad applicability to vascular flow problems requiring both accuracy and spatial insight.

Hemodynamics↗

DOE OSTI2025

Decision-Dependent Uncertainty-Aware Distribution System Planning Under Wildfire Risk

The interaction between power systems and wildfires can be dangerous and costly. Distribution grids can be liable for the outbreak of wildfires during extreme weather. In wildfire-prone areas, investment planning should consider the impact of operational actions on wildfire-related uncertainties affecting line failure likelihood. Here, in this case, endogenous-based uncertainty modeling should comprise the backbone of the investment planning model viz-a-viz the inability of standard exogenous-based uncertainty modeling. Therefore, we propose a decision-dependent uncertainty (DDU) aware methodology to optimize investment portfolios for distribution systems, considering that high power-flow levels in high-threat areas can ignite wildfires and increase line failure probability. The methodology identifies the best combination of upgrades (new lines, hardening existing lines, and placing switching devices). Methodologically, we propose a two-stage distributionally robust planning optimization problem with DDU that considers the distribution system's multiperiod operation. The first stage determines optimal switching actions and line investments, and the second stage evaluates the worst-case expected operational cost under a DDU framework designed to account for the endogenous impact of power-flow levels and hardening investment decisions in the line failure probabilities. An iterative method is tailored to handle the problem and numerical experiments demonstrate a more prepared grid to deal with wildfire risk.

Power systems investment planning↗