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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

High-Dimensional Bayesian Optimization via Semi-Supervised Learning with Optimized Unlabeled Data Sampling

We introduce a novel semi-supervised learning approach, named Teacher-Student Bayesian Optimization (TSBO ), integrating the teacher-student paradigm into BO to minimize expensive labeled data queries for the first time. TSBO incorporates a teacher model, an unlabeled data sampler, and a student model. The student is trained on unlabeled data locations generated by the sampler, with pseudo labels predicted by the teacher. The interplay between these three components implements a unique selective regularization to the teacher in the form of student feedback. This scheme enables the teacher to predict high-quality pseudo labels, enhancing the generalization of the GP surrogate model in the search space. To fully exploit TSBO , we propose two optimized unlabeled data samplers to construct effective student feedback that well aligns with the objective of Bayesian optimization. Furthermore, we quantify and leverage the uncertainty of the teacher-student model for the provision of reliable feedback to the teacher in the presence of risky pseudo-label predictions. TSBO demonstrates significantly improved sample-efficiency in several global optimization tasks under tight labeled data budgets. The implementation is available at https://github.com/reminiscenty/TSBO-Official.

Yin, Yuxuan↗
DOE OSTI2024

Forward variable selection enables fast and accurate dynamic system identification with Karhunen-Loève decomposed Gaussian processes

A promising approach for scalable Gaussian processes (GPs) is the Karhunen-Loève (KL) decomposition, in which the GP kernel is represented by a set of basis functions which are the eigenfunctions of the kernel operator. Such decomposed kernels have the potential to be very fast, and do not depend on the selection of a reduced set of inducing points. However KL decompositions lead to high dimensionality, and variable selection thus becomes paramount. This paper reports a new method of forward variable selection, enabled by the ordered nature of the basis functions in the KL expansion of the Bayesian Smoothing Spline ANOVA kernel (BSS-ANOVA), coupled with fast Gibbs sampling in a fully Bayesian approach. It quickly and effectively limits the number of terms, yielding a method with competitive accuracies, training and inference times for tabular datasets of low feature set dimensionality. Theoretical computational complexities are O ( N P 2 ) in training and O ( P ) per point in inference, where N is the number of instances and P the number of expansion terms. The inference speed and accuracy makes the method especially useful for dynamic systems identification, by modeling the dynamics in the tangent space as a static problem, then integrating the learned dynamics using a high-order scheme. The methods are demonstrated on two dynamic datasets: a ‘Susceptible, Infected, Recovered’ (SIR) toy problem, along with the experimental ‘Cascaded Tanks’ benchmark dataset. Comparisons on the static prediction of time derivatives are made with a random forest (RF), a residual neural network (ResNet), and the Orthogonal Additive Kernel (OAK) inducing points scalable GP, while for the timeseries prediction comparisons are made with LSTM and GRU recurrent neural networks (RNNs) along with the SINDy package.

Hayes, Kyle↗
NASA NTRSDate not supplied

Countermeasures for Mitigation of Sensorimotor Decrements Following Head-Down Bed Rest

BACKGROUND Astronauts experience postflight disturbances in postural and locomotor control due to sensorimotor adaptations during spaceflight. These alterations may have adverse consequences if a rapid egress is required after landing. Although exercise is partially effective for mitigating cardiovascular and muscular deconditioning, additional countermeasures are needed to further preserve sensorimotor function for exploration missions. We have identified proprioceptive training and electrical muscle stimulation (EMS) as promising in-flight countermeasures. Since prolonged head down bed rest (HDBR) is a spaceflight analog for body unloading and causes postural and locomotor control decrements that parallel those observed after spaceflight, it can be used to accelerate the development of these countermeasures. METHODS This study will determine the effects of proprioceptive training and EMS on functional task performance and sensorimotor function following 60 days of 6° HDBR. Subjects will be randomly assigned to one of four groups: 1) an EMS arm, 2) a proprioceptive training arm, 3) an exercise plus proprioceptive training arm, and 4) a control arm. The EMS countermeasure will include daily bilateral stimulation of the quadriceps femoris muscle (30 minutes per session). Proprioceptive training will be performed three days per week (20 minutes per session) consisting of body-loaded postural tasks in the horizontal position on an air bearing sled. Exercise training will mimic current protocols used on the International Space Station, but treadmill aerobic exercise will be replaced with additional cycling aerobic exercise. Primary outcome measures will include pre and post HDBR functional tests that are representative of high priority exploration mission tasks and require high demand for dynamic control of postural stability. Additional measures will be used to identify the key physiological factors contributing to countermeasure benefits. Given the constrained samples size, a Bayesian modelling approach will be used to quantify the probability that there is an effect of a given magnitude. COUNTERMEASURE UPDATES Proprioceptive countermeasure design enhancements and human in the loop pilot testing continued through the Crew Health Countermeasures (CHC) Systems Capability Leadership Team (SCLT). The primary goals of this work were to enhance the visual feedback system’s capabilities and develop a proprioceptive training program for 60 days of HDBR. Six healthy non-astronaut volunteers participated in four pilot training sessions to systematically examine how each training variable (e.g., axial load, foot placement, and software profile) affects the overall proprioceptive challenge. The resulting training program will maintain an appropriate challenge during 60 days of HDBR by progressively decreasing the subject’s base of support, increasing tilt board target distances, and increasing axial loads using both subjective verbal feedback and objective performance data. RELEVANCE The deliverable from this project will be proof-of-concept sensorimotor countermeasure designs for functional task performance with full assessment of efficacy in a spaceflight analog. If the countermeasures are effective, they will be translated for validation with the suite of operationally implemented in-flight countermeasures.

T R Macaulay↗
NASA NTRSDate not supplied

Countermeasures for Mitigation of Sensorimotor Decrements Following Head-Down Bed Rest

BACKGROUND Astronauts experience postflight disturbances in postural and locomotor control due to sensorimotor adaptations during spaceflight. These alterations may have adverse consequences if a rapid egress is required after landing. Although exercise is partially effective for mitigating cardiovascular and muscular deconditioning, additional countermeasures are needed to further preserve sensorimotor function for exploration missions. We have identified proprioceptive training and electrical muscle stimulation (EMS) as promising in-flight countermeasures. Since prolonged head down bed rest (HDBR) is a spaceflight analog for body unloading and causes postural and locomotor control decrements that parallel those observed after spaceflight, it can be used to facilitate the development of these countermeasures. METHODS This study will determine the effects of proprioceptive training and EMS on functional task performance and sensorimotor function following 60 days of 6° HDBR. Subjects will be randomly assigned to one of four groups: 1)an EMS arm, 2) a proprioceptive training arm, 3) an exercise plus proprioceptive training arm, and 4) a control arm. The EMS countermeasure will include daily bilateral stimulation of selected bilateral lower extremity muscles (30 minutes per session). Proprioceptive training will be performed three days per week (20 minutes per session) consisting of body-loaded postural tasks in the horizontal position on an air bearing sled. Exercise training will mimic current protocols used on the International Space Station, but treadmill aerobic exercise will be replaced with additional cycling aerobic exercise. Primary outcome measures will include pre and post HDBR functional tests that are representative of high priority exploration mission tasks and require high demand for dynamic control of postural stability. Additional measures will be used to identify the key physiological factors contributing to countermeasure benefits. Given the constrained samples size, a Bayesian modelling approach will be used to quantify the probability that there is an effect of a given magnitude. HARDWARE AND PROTOCOL DEVELOPMENT Proprioceptive countermeasure design enhancements continued as part of the Mars Campaign Office (MCO) Crew Health and Performance (CHP) Crew Health Countermeasures (CHC). The primary goals of this work were to assemble a portable version of the countermeasure system that can be used at the :envihab facility, expand the software feedback system’s capabilities, and develop an actuator loading system that mimics what could be used on the International Space Station. In addition, one major piece of exercise hardware used in previous HDBR studies, the Horizontal Squat Device, was reassembled and restored to full functionality. Human-in-the-loop pilot testing is ongoing, prior to shipping both devices to the :envihab HDBR facility. Evaluations are also underway for the best EMS device technologies and specific methods. Finally, assessment techniques are being translated for administration in the horizontal position (e.g., leg dexterity and foot sole skin sensitivity). Our current goals are to refine the countermeasure training and assessment techniques and integrate protocols across multiple modalities. RELEVANCE The deliverable from this project will be proof-of-concept sensorimotor countermeasure designs for functional task performance with full assessment of efficacy in a spaceflight analog. If one or more countermeasures are effective, they will be translated for validation with the suite of operationally implemented in-flight countermeasures. ACKNOWLEDGEMENT This work is supported by NASA’s Human Research Program Human Health Countermeasures Element and by the Canadian Space Agency (L. Bent).

T R Macaulay↗
NASA NTRS2025

Countermeasures for Mitigation of Sensorimotor Decrements Following Head-Down Tilt Bed Rest

BACKGROUND Astronauts experience postflight disturbances in postural and locomotor control due to sensorimotor adaptations during spaceflight. These alterations may have adverse consequences if a rapid egress is required after landing. Although exercise is partially effective for mitigating cardiovascular and muscular deconditioning, additional countermeasures are needed to further preserve sensorimotor function. Proprioception training and electrical muscle stimulation (EMS) are two promising in-flight countermeasures. Since prolonged head down tilt bed rest (HDTBR) is a spaceflight analog for body unloading and causes postural and locomotor control decrements that parallel those observed after spaceflight, it can be used to facilitate the development of these countermeasures. METHODS This study will determine the effects of proprioception training and EMS on functional task performance and sensorimotor function following 60 days of 6° HDTBR. Subjects will be randomly assigned to one of four groups: 1) an EMS arm, 2) a proprioception training arm, 3) an exercise plus proprioceptive training arm, and 4) a control arm. The EMS countermeasure will include daily bilateral stimulation of selected bilateral lower extremity muscles (30 minutes per session). Proprioception training will be performed three days per week (25 minutes per session) consisting of body-loaded postural tasks in the horizontal position on an air bearing sled. Exercise training will mimic current protocols used on the International Space Station, but treadmill aerobic exercise will be replaced with additional cycling aerobic exercise. Primary outcome measures will include pre- and post- HDTBR functional tests that require high demand for dynamic control of postural stability. Secondary measures will be used to explore key physiological changes that underlie countermeasure benefits. All HDTBR and data collection activities will be completed by the German Aerospace Center (DLR) at the :envihab facility. Given the constrained samples size, a Bayesian modelling approach will be used to quantify the probability that there is an effect of a given magnitude. HARDWARE AND PROTOCOL DEVELOPMENT Final hardware modifications and protocol developments were completed in preparation for Campaign 1, which began in September 2024. These included shipment, setup, and operator training for the transportable gravity bed, horizontal squat device, foam obstacle course, EMS devices, leg dexterity system, foot sole skin sensitivity system, and Radiofrequency Echographic Multi Spectrometry (REMS) ultrasound device. In addition, specialized protocols were developed for data collection using DLR’s equipment, including muscle morphology magnetic resonance imaging (MRI), optical coherence tomography, venous blood flow MRI and ultrasound, muscle ultrasound and impedance, and skin blood flow ultrasound. We will present early data from the first campaign, which concluded in November, 2024. These will be compared with previous data from the recent 30-day HDTBR campaigns (Spaceflight associated neuro-ocular syndrome countermeasures (SANS-CM)) conducted at DLR. RELEVANCE The deliverable from this project will be proof-of-concept sensorimotor countermeasure designs for functional task performance with full assessment of efficacy in a spaceflight analog. If one or more countermeasures are effective, they will be translated for validation with the suite of operationally implemented in-flight countermeasures.

T R Macaulay↗
DOE OSTI2025

Scalable Algorithms for Inverse Problems With High-Dimensional Parameter Spaces

Inverse problems, which involve inferring unknown parameters from observed data, present significant computational challenges, especially in large-scale settings with high-dimensional unknown parameters and nonlinear relationships between the unknowns and observations. Bayesian inference provides an approach for addressing these problems, often relying on sequential sampling methods like Markov chain Monte Carlo (MCMC) to approximate the posterior distribution of the parameters. However, MCMC methods become computationally demanding as the dimensionality of the problem increases, particularly in large-scale systems where likelihood evaluations rely on solving partial differential equations (PDEs) on large spatial domains with finely resolved meshes. To overcome these limitations, recent advancements have focused on designing scalable computa tional techniques – for both PDE simulations and sampling strategies – to make Bayesian methods feasible for high-dimensional problems.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2016

Probabilistic Prognosis of Non-Planar Fatigue Crack Growth

Quantifying the uncertainty in model parameters for the purpose of damage prognosis can be accomplished utilizing Bayesian inference and damage diagnosis data from sources such as non-destructive evaluation or structural health monitoring. The number of samples required to solve the Bayesian inverse problem through common sampling techniques (e.g., Markov chain Monte Carlo) renders high-fidelity finite element-based damage growth models unusable due to prohibitive computation times. However, these types of models are often the only option when attempting to model complex damage growth in real-world structures. Here, a recently developed high-fidelity crack growth model is used which, when compared to finite element-based modeling, has demonstrated reductions in computation times of three orders of magnitude through the use of surrogate models and machine learning. The model is flexible in that only the expensive computation of the crack driving forces is replaced by the surrogate models, leaving the remaining parameters accessible for uncertainty quantification. A probabilistic prognosis framework incorporating this model is developed and demonstrated for non-planar crack growth in a modified, edge-notched, aluminum tensile specimen. Predictions of remaining useful life are made over time for five updates of the damage diagnosis data, and prognostic metrics are utilized to evaluate the performance of the prognostic framework. Challenges specific to the probabilistic prognosis of non-planar fatigue crack growth are highlighted and discussed in the context of the experimental results.

Leser, Patrick E.↗
NASA NTRS1991

Data analysis using scale-space filtering and Bayesian probabilistic reasoning

This paper describes a program for analysis of output curves from Differential Thermal Analyzer (DTA). The program first extracts probabilistic qualitative features from a DTA curve of a soil sample, and then uses Bayesian probabilistic reasoning to infer the mineral in the soil. The qualifier module employs a simple and efficient extension of scale-space filtering suitable for handling DTA data. We have observed that points can vanish from contours in the scale-space image when filtering operations are not highly accurate. To handle the problem of vanishing points, perceptual organizations heuristics are used to group the points into lines. Next, these lines are grouped into contours by using additional heuristics. Probabilities are associated with these contours using domain-specific correlations. A Bayes tree classifier processes probabilistic features to infer the presence of different minerals in the soil. Experiments show that the algorithm that uses domain-specific correlation to infer qualitative features outperforms a domain-independent algorithm that does not.

Kulkarni, Deepak↗
DOE OSTI2026

Statistical inference of anomalous thermal transport with uncertainty quantification for interpretive 2D SOL models

The critical task of inferring anomalous cross-field transport coefficients is addressed in simulations of boundary plasmas with fluid models. A workflow for parameter inference in the UEDGE fluid code is developed using Bayesian optimization with parallelized sampling and integrated uncertainty quantification. In this workflow, transport coefficients are inferred by maximizing their posterior probability distribution, which is generally multidimensional and non-Gaussian. Uncertainty quantification is integrated throughout the optimization within the Bayesian framework that combines diagnostic uncertainties and model limitations. As a concrete example, we infer the anomalous electron thermal diffusivity $\chi_\perp$ from an interpretive 2D model describing electron heat transport in the conduction-limited region with radiative power loss. The workflow is first benchmarked against synthetic data and then tested on H-, L-, and I-mode discharges to match their midplane temperature and divertor heat flux profiles. We demonstrate that the workflow efficiently infers diffusivity and its associated uncertainty, generating 2D profiles that match 1D measurements. Future efforts will focus on incorporating more complicated fluid models and analyzing transport coefficients inferred from a large database of experimental results.

Bayesian optimization↗
DOE OSTI2025

Bayesian Entropy Neural Networks for physics-aware prediction

This article addresses the need for deep learning models to integrate well-defined constraints into their outputs, driven by their application in surrogate models, learning with limited data and partial information, and scenarios requiring flexible model behavior to incorporate non-data sample information. We introduce Bayesian Entropy Neural Networks (BENN), a framework grounded in Maximum Entropy (MaxEnt) principles, designed to impose constraints on Bayesian Neural Network (BNN) predictions. BENN is capable of constraining not only the predicted values but also their derivatives and variances, ensuring a more robust and reliable model output. To achieve simultaneous uncertainty quantification and constraint satisfaction, we employ the method of multipliers approach. This allows for the concurrent estimation of neural network parameters and the Lagrangian multipliers associated with the constraints. Our experiments, spanning diverse applications such as beam deflection modeling and microstructure generation, demonstrate the effectiveness of BENN. The results highlight significant improvements over traditional BNNs and showcase competitive performance relative to contemporary constrained deep learning methods.

14 SOLAR ENERGY↗
DOE OSTI2024

Multivariate Testing of Sampling Techniques to Address Class Imbalance in Building Use Type Classification

This study addresses the challenges inherent in building use type classification, particularly focusing on the issue of class imbalance in the training datasets for machine learning classifiers. We comprehensively analyze the efficacy of various class-balancing sampling techniques. Employing Monte Carlo simulations and Bayesian optimization, we evaluated the performance of multiple sampling methods, including Random Oversampling, Random Undersampling, SMOTE, Borderline-SMOTE, and ADASYN, across a dataset encompassing nine southeastern coastal states of the United States. Our findings reveal that simple random over- and undersampling techniques outperform more sophisticated methods. Additionally, we show inherent value in creating an imbalance in training data to effectively train a machine learning classifier for distinguishing between residential and nonresidential buildings. This study provides valuable guidance for future research on building use type classification research and lays essential groundwork for developing attribute-rich building stock datasets.

Adams, Daniel↗
NASA NTRS2004

Bayesian Approach to the Joint Inversion of Gravity and Magnetic Data, with Application to the Ismenius Area of Mars

This viewgraph presentation reviews a Bayesian approach to the inversion of gravity and magnetic data with specific application to the Ismenius Area of Mars. Many inverse problems encountered in geophysics and planetary science are well known to be non-unique (i.e. inversion of gravity the density structure of a body). In hopes of reducing the non-uniqueness of solutions, there has been interest in the joint analysis of data. An example is the joint inversion of gravity and magnetic data, with the assumption that the same physical anomalies generate both the observed magnetic and gravitational anomalies. In this talk, we formulate the joint analysis of different types of data in a Bayesian framework and apply the formalism to the inference of the density and remanent magnetization structure for a local region in the Ismenius area of Mars. The Bayesian approach allows prior information or constraints in the solutions to be incorporated in the inversion, with the "best" solutions those whose forward predictions most closely match the data while remaining consistent with assumed constraints. The application of this framework to the inversion of gravity and magnetic data on Mars reveals two typical challenges - the forward predictions of the data have a linear dependence on some of the quantities of interest, and non-linear dependence on others (termed the "linear" and "non-linear" variables, respectively). For observations with Gaussian noise, a Bayesian approach to inversion for "linear" variables reduces to a linear filtering problem, with an explicitly computable "error" matrix. However, for models whose forward predictions have non-linear dependencies, inference is no longer given by such a simple linear problem, and moreover, the uncertainty in the solution is no longer completely specified by a computable "error matrix". It is therefore important to develop methods for sampling from the full Bayesian posterior to provide a complete and statistically consistent picture of model uncertainty, and what has been learned from observations. We will discuss advanced numerical techniques, including Monte Carlo Markov

data analysis↗
DOE OSTI2025

eDNAjoint: An R package for interpreting paired or semi‐paired environmental DNA and traditional survey data in a Bayesian framework

Abstract Environmental DNA (eDNA) sampling is increasingly used in surveys of species distribution as a potentially sensitive and efficient monitoring method. Yet access to modelling tools designed specifically for interpreting this new data type lags behind its ubiquity. While occupancy modelling software has dominated the analytical landscape for eDNA data analysis of single species, this type of model may not always be the most appropriate. The rate of eDNA detection often corresponds to species density, rather than just occupancy, and researchers often have access to observations from non‐genetic sampling methods at the same sites. To provide users access to a modelling framework designed to maximize the use of all available data, we developed an R package, eDNAjoint . The package provides an easy‐to‐use interface for fitting a ‘joint’ model that integrates data from paired or semi‐paired eDNA and traditional surveys in a Bayesian framework. The model can be used to estimate parameters like the probability of a false positive eDNA detection and mean catch rate at a site, and the package allows access to multiple model variations and Bayesian prior customization. Additional functionality can be used for model selection, summarising posteriors and comparing the relative sensitivities of the two survey methods. We demonstrate the use of eDNAjoint by fitting a variation of the model with site‐level covariates that scale the sensitivity of eDNA sampling relative to traditional sampling. The example workflow uses binary eDNA and seine count data for the endangered tidewater goby ( Eucyclogobius newberryi ) from a study by Schmelzle and Kinziger (2016). This use case includes a prior sensitivity analysis and an evaluation of the relationship between detection rates and environmental variables. eDNAjoint has the potential to greatly increase the range of users who will be able to rigorously analyse eDNA and traditional survey data in a Bayesian framework, understand if and how eDNA can improve monitoring practices, and gain confidence in the interpretability of eDNA data.

Keller, Abigail G. [Department of Environment Scie↗
DOE OSTI2026

Improvement of Drop‐Hammer Impact Testing for Safety Assessment of High Explosives Using 10‐mg Samples

Here, in this study, we established an improved method for drop-hammer impact testing of small quantities of high explosives (10 mg). We performed about seven hundred impact tests under various experimental conditions (e.g., sandpaper vs bare anvil, different sample masses, drop-weights, and striker diameters) to determine an optimal set of conditions and reaction detection methods (e.g., gas analysis, video, and sound recordings) that give the most statistically reliable results with 10 mg samples. We used both Frequentist and Bayesian statistical approaches to compare estimates of the drop height (DH50) that initiates a reaction 50% of the time, and to quantify the associated uncertainty. Gas analysis proved to be the most reliable reaction detection method, showing unambiguous rises in HE decomposition products (e.g., CO 2 ) even when the other indicators (e.g., sound, video) were inconclusive. The impact tests performed with a bare anvil showed much better reproducibility than those conducted with sandpaper, reducing the largest uncertainty observed in the data sets by a factor of 1.7. The DH 50 values obtained from three different sample masses (10, 20, and 35 mg) fell within the uncertainties of the measurements. We demonstrated the improved procedure (i.e., 10-mg samples, gas analysis, bare anvil, and Bayesian approach) on a variety of PETN samples having different surface areas and thermal histories.

PETN↗
DOE OSTI2025

Multimodality in the Search for New Physics in Pulsar Timing Data and the Case of Kination-amplified Gravitational-wave Background from Inflation

We investigate the kination-amplified inflationary gravitational-wave background (GWB) interpretation of the signal recently reported by various pulsar timing array (PTA) experiments. Kination is a post-inflationary phase in the expansion history dominated by the kinetic energy of some scalar field, characterized by a stiff equation of state w = 1. Within the inflationary GWB model, we identify two modes that can fit the current data sets (NANOGrav and EPTA) with equal likelihood: the kination-amplification (KA) mode and the ordinary, no-kination-amplification (no-KA) mode. The multimodality of the likelihood motivates a Bayesian analysis with nested sampling. We analyze the free spectra of current PTA data and mock free spectra constructed with higher signal-to-noise ratios using nested sampling. The analysis of the mock spectrum designed to be consistent with the best fit to the NANOGrav 15 yr (NG15) data successfully reveals the expected bimodal posterior for the first time while excluding the reheating mode that appears in the fit to the current NG15 data, making a case for our correct and comprehensive treatment of potential multimodal posteriors arising from future PTA data sets. The resultant Bayes factor is $\mathcal{B}$ $\equiv$ Z no–KA /Z KA = 2.9 ± 1.9, indicating comparable statistical significance between the two modes. Given the theoretical model-building challenges of producing highly blue-tilted primordial tensor spectra, the KA mode has the advantage of requiring less blue primordial spectra, compared with the no-KA mode. The synergy between future cosmic microwave background polarization, pulsar timing, and laser interferometer measurements of gravitational waves will help resolve the ambiguity implied by the multimodal posterior in PTA-only searches.

Cosmology↗
NASA NTRS2021

Computational Inference of Vibratory System with Incomplete Modal Information Using Parallel, Interactive and Adaptive Markov Chains

Inverse analysis of vibratory system is an important subject in fault identification, model updating, and robust design and control. It is challenging subject because 1) the problem is oftentimes underdetermined while the measurements are limited and/or incomplete; 2) many combinations of parameters may yield results that are similar with respect to actual response measurements; and 3) uncertainties inevitably exist. The aim of this research is to leverage upon computational intelligence through statistical inference to facilitate an enhanced, probabilistic framework using incomplete modal response measurement. This new framework is built upon efficient inverse identification through optimization, whereas Bayesian inference is employed to account for the effect of uncertainties. To overcome the computational cost barrier, we adopt Markov chain Monte Carlo (MCMC) to characterize the target function/distribution. Instead of using single Markov chain in conventional Bayesian approach, we develop a new sampling theory with multiple parallel, interactive and adaptive Markov chains and incorporate it into Bayesian inference. This can harness the collective power of these Markov chains to realize the concurrent search of multiple local optima. The number of required Markov chains and their respective initial model parameters are automatically determined via Monte Carlo simulation-based sample pre-screening followed by K-means clustering analysis. These enhancements can effectively address the aforementioned challenges in finite element inverse analysis. The validity of this framework is systematically demonstrated through case studies.

K Zhou↗
DOE OSTI2025

Accelerating Hamiltonian Monte Carlo for Bayesian inference in neural networks and neural operators

Hamiltonian Monte Carlo (HMC) is a powerful and accurate method to sample from the posterior distribution in Bayesian inference. However, HMC techniques are computationally demanding for Bayesian neural networks due to the high dimensionality of the network’s parameter space and the non-convexity of their posterior distributions. Therefore, various approximation techniques, such as variational inference (VI) or stochastic gradient MCMC, are often employed to infer the posterior distribution of the network parameters. Such approximations introduce inaccuracies in the inferred distributions, resulting in unreliable uncertainty estimates. In this work, we propose a hybrid approach that combines inexpensive VI and accurate HMC methods to efficiently and accurately quantify uncertainties in neural networks and neural operators. The proposed approach leverages an initial VI training on the full network. We examine the influence of individual parameters on the prediction uncertainty, which shows that a large proportion of the parameters do not contribute substantially to uncertainty in the network predictions. This information is then used to significantly reduce the dimension of the parameter space, and HMC is performed only for the subset of network parameters that strongly influence prediction uncertainties. This yields a framework for accelerating the full batch HMC for posterior inference in neural networks. We demonstrate the efficiency and accuracy of the proposed framework on deep neural networks and operator networks, showing that inference can be performed for large networks with tens to hundreds of thousands of parameters. Finally, we show that this method can effectively learn surrogates for complex physical systems by modeling the operator that maps from upstream conditions to wall-pressure data on a cone in hypersonic flow.

Bayesian inference↗
DOE OSTI2024

Cluster expansion by transfer learning for phase stability predictions

Recent progress towards universal machine-learned interatomic potentials holds considerable promise for materials discovery. Yet the accuracy of these potentials for predicting phase stability may still be limited. In contrast, cluster expansions provide accurate phase stability predictions but are computationally demanding to parameterize from first principles, especially for structures of low dimension or with a large number of components, such as interfaces or multimetal catalysts. We overcome this trade-off via transfer learning. Using Bayesian inference, we incorporate prior statistical knowledge from machine-learned and physics-based potentials, enabling us to sample the most informative configurations and to efficiently fit first-principles cluster expansions. Furthermore, this algorithm is tested on Pt:Ni, showing robust convergence of the mixing energies as a function of sample size with reduced statistical fluctuations.

36 MATERIALS SCIENCE↗