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DOE OSTI2025

Online Bayesian State Estimation for Real-Time Monitoring of Growth Kinetics in Thin Film Synthesis

Rapid validation of newly predicted materials through autonomous synthesis requires real-time adaptive control methods that exploit physics knowledge, a capability that is lacking in most systems. Here, in this study, we demonstrate an approach to enable real-time control of thin film synthesis by combining in situ optical diagnostics with a Bayesian state estimation method. We developed a physical model for film growth and applied the direct filter (DF) method for real-time estimation of nucleation and growth rates during pulsed laser deposition (PLD). We validated the approach using simulated and experimental reflectivity data for WSe 2 growth and ultimately deployed the algorithm on an autonomous PLD system during the growth of 1T'-MoTe 2 . The DF robustly estimates growth parameters in real time at early stages of growth, down to 15% monolayer area coverage. This fusion of in situ diagnostics, data assimilation, and physical modeling opens new opportunities in adaptive control of synthesis trajectories toward desired material states.

36 MATERIALS SCIENCE↗

DOE OSTI2025

BEACON—automated aberration correction for scanning transmission electron microscopy using Bayesian optimization

Aberration correction is an important aspect of modern high-resolution scanning transmission electron microscopy. Most methods of aligning aberration correctors require specialized sample regions and are unsuitable for fine-tuning aberrations without interrupting on-going experiments. Here, we present an automated method of correcting first- and second-order aberrations called BEACON, which uses Bayesian optimization of the normalized image variance to efficiently determine the optimal corrector settings. We demonstrate its use on gold nanoparticles and a hafnium dioxide thin film showing its versatility in nano- and atomic-scale experiments. BEACON can correct all first- and second-order aberrations simultaneously to achieve an initial alignment and first- and second-order aberrations independently for fine alignment. Ptychographic reconstructions are used to demonstrate an improvement in probe shape and a reduction in the target aberration.

techniques and instrumentation↗

DOE OSTI2022

Inverse Modeling of Hydrologic Parameters in CLM4 via Generalized Polynomial Chaos in the Bayesian Framework

In this work, generalized polynomial chaos (gPC) expansion for land surface model parameter estimation is evaluated. We perform inverse modeling and compute the posterior distribution of the critical hydrological parameters that are subject to great uncertainty in the Community Land Model (CLM) for a given value of the output LH. The unknown parameters include those that have been identified as the most influential factors on the simulations of surface and subsurface runoff, latent and sensible heat fluxes, and soil moisture in CLM4.0. We set up the inversion problem in the Bayesian framework in two steps: (i) building a surrogate model expressing the input–output mapping, and (ii) performing inverse modeling and computing the posterior distributions of the input parameters using observation data for a given value of the output LH. The development of the surrogate model is carried out with a Bayesian procedure based on the variable selection methods that use gPC expansions. Our approach accounts for bases selection uncertainty and quantifies the importance of the gPC terms, and, hence, all of the input parameters, via the associated posterior probabilities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

A Comparison of Three Ways to Measure Time-Dependent Densities With Quantum Simulators

Quantum algorithms are touted as a way around some classically intractable problems such as the simulation of quantum mechanics. At the end of all quantum algorithms is a quantum measurement whereby classical data is extracted and utilized. In fact, many of the modern hybrid-classical approaches are essentially quantum measurements of states with short quantum circuit descriptions. Here, we compare and examine three methods of extracting the time-dependent one-particle probability density from a quantum simulation: direct Z -measurement, Bayesian phase estimation, and harmonic inversion. We have tested these methods in the context of the potential inversion problem of time-dependent density functional theory. Our test results suggest that direct measurement is the preferable method. We also highlight areas where the other two methods may be useful and report on tests using Rigetti's quantum virtual device. This study provides a starting point for imminent applications of quantum computing.

Yang, Jun↗

DOE OSTI2025

Nuclear Data Adjustment for Nonlinear Applications in the OECD/NEA WPNCS SG14 Benchmark -- A Bayesian Inverse UQ-based Approach for Data Assimilation

The Organization for Economic Cooperation and Development (OECD) Working Party on Nuclear Criticality Safety (WPNCS) proposed a benchmark exercise to assess the performance of current nuclear data adjustment techniques applied to nonlinear applications and experiments with low correlation to applications. This work introduces Bayesian Inverse Uncertainty Quantification (IUQ) as a method for nuclear data adjustments in this benchmark, and compares IUQ to the more traditional methods of Generalized Linear Least Squares (GLLS) and Monte Carlo Bayes (MOCABA). Posterior predictions from IUQ showed agreement with GLLS and MOCABA for linear applications. When comparing GLLS, MOCABA, and IUQ posterior predictions to computed model responses using adjusted parameters, we observe that GLLS predictions fail to replicate computed response distributions for nonlinear applications, while MOCABA shows near agreement, and IUQ uses computed model responses directly. We also discuss observations on why experiments with low correlation to applications can be informative to nuclear data adjustments and identify some properties useful in selecting experiments for inclusion in nuclear data adjustment. Performance in this benchmark indicates potential for Bayesian IUQ in nuclear data adjustments.

FOS: Computer and information sciences↗

NASA NTRS2016

Uncertainty Estimates of Psychoacoustic Thresholds Obtained from Group Tests

Adaptive psychoacoustic test methods, in which the next signal level depends on the response to the previous signal, are the most efficient for determining psychoacoustic thresholds of individual subjects. In many tests conducted in the NASA psychoacoustic labs, the goal is to determine thresholds representative of the general population. To do this economically, non-adaptive testing methods are used in which three or four subjects are tested at the same time with predetermined signal levels. This approach requires us to identify techniques for assessing the uncertainty in resulting group-average psychoacoustic thresholds. In this presentation we examine the Delta Method of frequentist statistics, the Generalized Linear Model (GLM), the Nonparametric Bootstrap, a frequentist method, and Markov Chain Monte Carlo Posterior Estimation and a Bayesian approach. Each technique is exercised on a manufactured, theoretical dataset and then on datasets from two psychoacoustics facilities at NASA. The Delta Method is the simplest to implement and accurate for the cases studied. The GLM is found to be the least robust, and the Bootstrap takes the longest to calculate. The Bayesian Posterior Estimate is the most versatile technique examined because it allows the inclusion of prior information.

Rathsam, Jonathan↗

DOE OSTI2026

Opportunities in AI/ML for the Rubin LSST Dark Energy Science Collaboration

The Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST) will produce unprecedented volumes of heterogeneous astronomical data (images, catalogs, and alerts) that challenge traditional analysis pipelines. The LSST Dark Energy Science Collaboration (DESC) aims to derive robust constraints on dark energy and dark matter from these data, requiring methods that are statistically powerful, scalable, and operationally reliable. Artificial intelligence and machine learning (AI/ML) are already embedded across DESC science workflows, from photometric redshifts and transient classification to weak lensing inference and cosmological simulations. Yet their utility for precision cosmology hinges on trustworthy uncertainty quantification, robustness to covariate shift and model misspecification, and reproducible integration within scientific pipelines. This white paper surveys the current landscape of AI/ML across DESC's primary cosmological probes and cross-cutting analyses, revealing that the same core methodologies and fundamental challenges recur across disparate science cases. Since progress on these cross-cutting challenges would benefit multiple probes simultaneously, we identify key methodological research priorities, including Bayesian inference at scale, physics-informed methods, validation frameworks, and active learning for discovery. With an eye on emerging techniques, we also explore the potential of the latest foundation model methodologies and LLM-driven agentic AI systems to reshape DESC workflows, provided their deployment is coupled with rigorous evaluation and governance. Finally, we discuss critical software, computing, data infrastructure, and human capital requirements for the successful deployment of these new methodologies, and consider associated risks and opportunities for broader coordination with external actors.

Aubourg, Eric [APC, Paris] (ORCID:000000025592023X↗

DOE OSTI2026

Desmearing Bonse–Hart USANS data using Bayesian Gaussian process regression

Ultra-small-angle neutron scattering (USANS) enables access to micrometer-scale structures but is intrinsically affected by strong, anisotropic resolution smearing arising from slit-geometry optics. As a result, recovery of the intrinsic scattering intensity constitutes an ill-posed inverse problem, and commonly used iterative desmearing methods lack rigorous uncertainty quantification. We present a Bayesian desmearing framework for slit-geometry USANS based on Gaussian process regression. In this approach, the scattering intensity is modeled as a smooth random function, and the instrumental point spread function is incorporated explicitly as a forward operator. The resulting formulation yields a closed-form maximum a posteriori solution with well-defined credibility intervals. Computational benchmarks and experimental validation using combined USANS and small-angle neutron scattering (SANS) measurements demonstrate that the framework enables stable desmearing, suppresses experimental noise, and preserves physically meaningful structural features under realistic conditions.

Tung, Chi-Huan [Oak Ridge National Laboratory (ORN↗

NASA NTRS2020

Bayesian retrieval of optically relevant properties from hyperspectral water-leaving reflectances

Current methods to retrieve optically relevant properties from ocean color observations do not explicitly make use of prior knowledge about property distributions. Here we implement a simplified Bayesian approach that takes into account prior probability distributions on two sets of five optically relevant parameters, and conduct a retrieval of these parameters using hyperspectral simulated water-leaving reflectances. We focus specifically on the ability of the model to distinguish between two optically similar phytoplankton taxa, diatoms and Noctiluca scintillans. The inversion retrieval gives most-likely concentrations and uncertainty estimates, and we find that the model is able to probabilistically predict the occurrence of Noctiluca scintillans blooms using these metrics. We discuss how this method can be expanded to include a priori covariances between different parameters, and show the effect of varying measurement uncertainty and spectral resolution on Noctiluca scintillans bloom predictions.

Zachary K Erickson↗

DOE OSTI2024

Localization of infrasonic sources via Bayesian back projection

SUMMARY A Bayesian framework is investigated for event-specific localization of infrasonic sources using back projection ray tracing. Direction-of-arrival information from array-based detection analysis is used to initialize a back projection ray path originating from the detecting array location and quantifying propagation characteristics from hypothetical source locations. The Fisher statistic, computed from the array’s beam coherence, is mapped into uncertainty in the launch angles of the ray path. Auxiliary parameters previously introduced for solving the Transport equation to compute geometric spreading along ray paths are used to map uncertainty in the ray launch angles into spatial and temporal uncertainties in the ray path. An atmospheric ensemble approach is applied to account for atmospheric uncertainty, and the relation between uncertainties in the atmospheric state and confidence in estimated localization are evaluated using several ensembles with specified variances. The method is evaluated using a synthetic event in the western United States constructed via forward propagation simulations as well as a single-station, multi-arrival detection from a surface explosion in the western United States. Localization results using this event-specific approach are more accurate and exhibit improved precision than existing Bayesian localization methods that leverage generalized, pre-computed propagation statistics.

58 GEOSCIENCES↗

NASA NTRS1973

Analytical study to define a helicopter stability derivative extraction method, volume 1

A method is developed for extracting six degree-of-freedom stability and control derivatives from helicopter flight data. Different combinations of filtering and derivative estimate are investigated and used with a Bayesian approach for derivative identification. The combination of filtering and estimate found to yield the most accurate time response match to flight test data is determined and applied to CH-53A and CH-54B flight data. The method found to be most accurate consists of (1) filtering flight test data with a digital filter, followed by an extended Kalman filter (2) identifying a derivative estimate with a least square estimator, and (3) obtaining derivatives with the Bayesian derivative extraction method.

Molusis, J. A.↗

DOE OSTI2020

Probabilistic Solar Power Forecasting Using Bayesian Model Averaging

There is rising interest in probabilistic forecasting to mitigate risks from solar power uncertainty, but the numerical weather prediction (NWP) ensembles readily available to system operators are often biased and underdispersed. We propose a Bayesian model averaging (BMA) post-processing method suitable for forecasting power from utility-scale photovoltaic (PV) plants at multiple time horizons up to at least the day-ahead timescale. BMA is a kernel dressing technique for NWP ensembles in which the forecast is a weighted sum of member-specific probability density functions. We tailor BMA for utility-scale PV forecasting by modeling power clipping at the AC inverter rating and advance the theory of BMA with a new beta kernel parameterization that accommodates theoretical constraints not previously addressed. BMA is demonstrated for a case study of 11 utility-scale PV plants in Texas, forecasting at hourly resolution for the complete year 2018. BMA's mixture-model approach mitigates underdispersion of the raw ensemble to significantly improve forecast calibration, while consistently outperforming an ensemble model output statistics (EMOS) parametric approach from the literature. At 4-hour lead time, the BMA post-processing achieves continuous ranked probability skill scores of 2--36% over the raw ensemble, with consistent performance at multiple lead times suitable for power system operations.

14 SOLAR ENERGY↗

NASA NTRSDate not supplied

Probabilistic Calibration of Expensive Models using Efficiently Trained Surrogates

Calibration of computational models in the presence of uncertainty is often cast as a Bayesian inference problem and solved via sampling methods, e.g., Markov chain Monte Carlo. When the computational model is expensive, this task becomes intractable due to the large number of samples required to accurately estimate the posterior distribution of the calibration parameters. A popular solution to this problem is to use machine learning to develop a faster-to-evaluate, lower-fidelity substitute for the original model to serve as a surrogate while solving the inference problem. Although considered an offline cost, generating training data to construct this surrogate model can still be an expensive task in practice. An active learning algorithm is presented that focuses training on improving surrogate accuracy specifically in and around the bulk of the posterior distribution, as this is where the model is exercised during calibration. Candidate samples are drawn from families of distributions related to an approximation of the posterior. The sample maximizing predictive variance is then selected for evaluation by the original computational model, yielding a label for the training point. Iterating this approach increases efficiency relative to space filling designs (e.g., Latin hypercube sampling) by avoiding low probability points. Practical considerations are discussed, including the benefits of using a sequential Monte Carlo sampling approach, convergence heuristics, and the importance of both exploration and exploitation given that the true posterior is unknown a priori.

uncertainty quantification↗

DOE OSTI2024

AEOLUS: Advances in Experimental Design, Optimal Control, and Learning for Uncertain Complex Systems

Sustained advances in the mathematics of modeling and simulation have resulted in the capability today for routine simulation of a number of large scale complex DOE-relevant systems. As remarkable as this capability for solving the so-called forward problem is, it is typically only the first step-an inner loop within an outer loop that explores the simulation model's parameter space and decision space to characterize uncertainty in the model's predictions, learn unknown model parameters from data, design the most informative experiments, determine optimal control strategies, and create optimal designs. Broadly, what unifies all of these outer loop problems is that they are, in one form or another, optimization problems over parameter/control/design space that are constrained by complex uncertain models. To fully realize the power of scientific simulation as a basis for scientific discovery, technological innovation, and rational decision-making, it is imperative to move beyond simulation to tackle the outer loop of optimization for learning from data, experimental design, and control with complex uncertain models. When the models under consideration are large-scale and complex, and when the optimization variable and uncertain parameter spaces are high (or infinite) dimensional, this constitutes a grand challenge of the highest order, and is intractable with conventional methods. To overcome these challenges, the AEOLUS Center was established to develop a unified mathematical, computational, and statistical framework for (1) Learning predictive models from complex data via Bayesian inference and optimization, and (2) Optimizing experiments, processes, and designs using the resulting uncertain models. These problems are intractable with conventional methods, for several reasons: (1) The simulation problems that govern the inner loops of the optimization problems are expensive to execute (due to severe nonlinearity, heterogeneity, multiphysics/multiscale coupling); (2) The optimization variable and uncertain parameter spaces are high dimensional, often stemming from discretizations of infinite dimensional fields such as initial conditions, sources, or material properties. We argue that the key to overcoming these challenges is to develop new mathematical, computational, and statistical methods that exploit the structure of the Bayesian inference and optimization problems mediated by their underlying complex uncertain models. This structure includes the regularity, sparsity, geometry, low intrinsic dimensionality, and multifidelity nature of the maps from uncertain parameter/optimization variable spaces to the specific objectives targeted: Bayesian inference, optimal experimental design, and optimal control design. Black box methods developed as generic tools are incapable of exploiting this structure. To be successful, we must create, integrate, and cross-fertilize ideas across multiple areas of applied math--including approximation theory, Bayesian inference, data science, experimental design, information theory, machine learning, model reduction, optimal control theory, parallel algorithms, PDE-constrained optimization, randomized algorithms, stochastic optimization, and uncertainty quantification--all while exploiting the structure of the problems at hand. With this goal in mind, we have marshaled a team of leading authorities in these areas. While the methods we develop will be broadly applicable across a wide spectrum of DOE problems in which experiments inform models and the systems those models describe must be optimized under uncertainty, we have chosen a specific area, advanced manufacturing and materials, to drive our work. AMM is characterized by complex models across multiple scales, and is a rich source of challenging problems in inference, experimental design, and optimal control, requiring multifaceted and integrated advances in applied mathematics. As such, AMM serves as an excellent vehicle to motivate and demonstrate the advances in applied mathematics developed by our center.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Multimodal Bayesian registration of noisy functions using Hamiltonian Monte Carlo

Functional data registration is a necessary processing step for many applications. The observed data can be inherently noisy, often due to measurement error or natural process uncertainty; which most functional alignment methods cannot handle. A pair of functions can also have multiple optimal alignment solutions, which is not addressed in current literature. In this paper, a flexible Bayesian approach to functional alignment is presented, which appropriately accounts for noise in the data without any pre-smoothing required. Additionally, by running parallel MCMC chains, the method can account for multiple optimal alignments via the multi-modal posterior distribution of the warping functions. To most efficiently sample the warping functions, the approach relies on a modification of the standard Hamiltonian Monte Carlo to be well-defined on the infinite-dimensional Hilbert space. In this work, this flexible Bayesian alignment method is applied to both simulated data and real data sets to show its efficiency in handling noisy functions and successfully accounting for multiple optimal alignments in the posterior; characterizing the uncertainty surrounding the warping functions.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2022

Bayesian Deep Learning for Segmentation for Autonomous Safe Planetary Landing

Hazard detection is critical for enabling autonomous landing on planetary surfaces. Current state-of-the-art methods leverage traditional computer vision approaches to automate the identification of safe terrain from input digital elevation models (DEMs). However, performance for these methods can degrade for input DEMs with increased sensor noise. In the last decade, deep learning techniques have been developed for various applications. Nevertheless, their applicability to safety-critical space missions has often been limited due to concerns regarding their outputs’ reliability. In response to these limitations, this paper proposes an application of the Bayesian deep learning segmentation method for hazard detection. The developed approach enables reliable, safe landing site detection by i) generating simultaneously a safety prediction map and its uncertainty map via Bayesian deep learning and semantic segmentation, and ii) using the uncertainty map to filter out the uncertain pixels in the prediction map so that the safe site identification is performed only based on the certain pixels (i.e., pixels for which the model is certain about its safety prediction). Experiments are presented with simulated data based on a Mars HiRISE digital terrain model by varying uncertainty threshold and noise levels to demonstrate the performance of the proposed approach.

Kento Tomita↗

DOE OSTI2022

The emergence and transmission dynamics of HIV-1 CRF07_BC in Mainland China

A total of 1155 partial pol gene sequences of human immunodeficiency virus (HIV)-1 CRF07_BC were sampled between 1997 and 2015, spanning 13 provinces in Mainland China and risk groups [heterosexual, injecting drug users (IDU), and men who have sex with men (MSM)] to investigate the evolution, adaptation, spatiotemporal and risk group dynamics, migration patterns, and protein structure of HIV-1 CRF07_BC. Due to the unequal distribution of sequences across time, location, and risk group in the complete dataset (‘full1155’), subsampling methods were used. Maximum-likelihood and Bayesian phylogenetic analysis as well as discrete trait analysis of geographical location and risk group were carried out. To study mutations of a cluster of HIV-1 CRF07_BC (CRF07-1), we performed a comparative analysis of this cluster to the other CRF07_BC sequences (‘backbone_295’) and mapped the mutations observed in the respective protein structure. Our findings showed that HIV-1 CRF07_BC most likely originated among IDU in Yunnan Province between October 1992 to July 1993 [95 per cent hightest posterior density (HPD): May 1989–August 1995] and that IDU in Yunnan Province and MSM in Guangdong Province likely served as the viral sources during the early and more recent spread in Mainland China. We also revealed that HIV-1 CRF07-1 has been spreading for roughly 20 years and continues to cause local transmission in Mainland China and worldwide. Overall, our study sheds light on the dynamics of HIV-1 CRF07_BC distribution patterns in Mainland China. Our research may also be useful in formulating public health policies aimed at controlling acquired immune deficiency syndrome in Mainland China and globally.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2025

Deep learning-based spatio-temporal fusion for high-fidelity ultra-high-speed X-ray radiography

Full-field ultra-high-speed (UHS) X-ray imaging experiments have been well established to characterize various processes and phenomena. However, the potential of UHS experiments through the joint acquisition of X-ray videos with distinct configurations has not been fully exploited. In this paper, we investigate the use of a deep learning-based spatio-temporal fusion (STF) framework to fuse two complementary sequences of X-ray images and reconstruct the target image sequence with high spatial resolution, high frame rate and high fidelity. We applied a transfer learning strategy to train the model and compared the peak signal-to-noise ratio (PSNR), average absolute difference (AAD) and structural similarity (SSIM) of the proposed framework on two independent X-ray data sets with those obtained from a baseline deep learning model, a Bayesian fusion framework and the bicubic interpolation method. The proposed framework outperformed the other methods with various configurations of the input frame separations and image noise levels. With three subsequent images from the low-resolution (LR) sequence of a four times lower spatial resolution and another two images from the high-resolution (HR) sequence of a 20 times lower frame rate, the proposed approach achieved average PSNRs of 37.57 dB and 35.15 dB, respectively. When coupled with the appropriate combination of high-speed cameras, the proposed approach will enhance the performance and therefore the scientific value of UHS X-ray imaging experiments.

deep learning↗