Search NASA⌕ Search

SEARCH · Search NASA

Results for “Probabilistic learning”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Transient anisotropic kernel for probabilistic learning on manifolds

PLoM (Probabilistic Learning on Manifolds) is a method introduced in 2016 for handling small training datasets by projecting an Itô equation from a stochastic dissipative Hamiltonian dynamical system, acting as the MCMC generator, for which the KDE-estimated probability measure with the training dataset is the invariant measure. PLoM performs a projection on a reduced-order vector basis related to the training dataset, using the diffusion maps (DMAPS) basis constructed with a time-independent isotropic kernel. In this paper, we propose a new ISDE projection vector basis built from a transient anisotropic kernel, providing an alternative to the DMAPS basis to improve statistical surrogates for stochastic manifolds with heterogeneous data. The construction ensures that for times near the initial time, the DMAPS basis coincides with the transient basis. For larger times, the differences between the two bases are characterized by the angle of their spanned vector subspaces. The optimal instant yielding the optimal transient basis is determined using an estimation of mutual information from Information Theory, which is normalized by the entropy estimation to account for the effects of the number of realizations used in the estimations. Consequently, this new vector basis better represents statistical dependencies in the learned probability measure for any dimension. Three applications with varying levels of statistical complexity and data heterogeneity validate the proposed theory, showing that the transient anisotropic kernel improves the learned probability measure.

Diffusion maps↗
DOE OSTI2026

Enabling probabilistic learning on manifolds through double diffusion maps

Here, we present a generative learning framework for probabilistic sampling that extends Probabilistic Learning on Manifolds (PLoM), which is designed to generate statistically consistent realizations of a random vector in a finite-dimensional Euclidean space, informed by a (representative) set of observations. In its original form, PLoM constructs a reduced-order probabilistic model by combining three main components: (a) kernel density estimation to approximate the underlying probability measure, (b) Diffusion Maps to characterize the manifold of the data, and (c) a reduced-order Itô Stochastic Differential Equation (ISDE) to sample from the learned distribution. However, its sampling dynamics are posed in the ambient space and the retained number of reduced coordinates is chosen by projection-reconstruction error. In practice, this often (i) requires more coordinates than the data’s intrinsic dimension to achieve stable sampling and (ii) lacks a smooth, basis-independent lifting back to the data domain; moreover, standard Diffusion Maps emphasize harmonic eigenfunctions and can miss non-harmonic latent structure. We address these limitations by decoupling geometry learning from sampling: a first Diffusion Maps pass identifies non-harmonic coordinates on which we formulate a full-order ISDE directly in the latent space, while Double Diffusion Maps captures multiscale geometric features and Geometric Harmonics (GH) learns a smooth lifting map to the ambient variables that is independent of the particular diffusion basis. This hybrid design preserves the system’s dynamical richness with a compact geometric representation and enables principled out-of-sample inference. The effectiveness and robustness of the proposed method are illustrated through two numerical studies: one based on data generated from two-dimensional Hermite polynomial functions and another based on high-fidelity simulations of a detonation wave in a reactive flow.

Double diffusion maps↗
NASA NTRS2015

A High Performance Computing Approach to Tree Cover Delineation in 1-m NAIP Imagery Using a Probabilistic Learning Framework

Tree cover delineation is a useful instrument in deriving Above Ground Biomass (AGB) density estimates from Very High Resolution (VHR) airborne imagery data. Numerous algorithms have been designed to address this problem, but most of them do not scale to these datasets, which are of the order of terabytes. In this paper, we present a semi-automated probabilistic framework for the segmentation and classification of 1-m National Agriculture Imagery Program (NAIP) for tree-cover delineation for the whole of Continental United States, using a High Performance Computing Architecture. Classification is performed using a multi-layer Feedforward Backpropagation Neural Network and segmentation is performed using a Statistical Region Merging algorithm. The results from the classification and segmentation algorithms are then consolidated into a structured prediction framework using a discriminative undirected probabilistic graphical model based on Conditional Random Field, which helps in capturing the higher order contextual dependencies between neighboring pixels. Once the final probability maps are generated, the framework is updated and re-trained by relabeling misclassified image patches. This leads to a significant improvement in the true positive rates and reduction in false positive rates. The tree cover maps were generated for the whole state of California, spanning a total of 11,095 NAIP tiles covering a total geographical area of 163,696 sq. miles. The framework produced true positive rates of around 88% for fragmented forests and 74% for urban tree cover areas, with false positive rates lower than 2% for both landscapes. Comparative studies with the National Land Cover Data (NLCD) algorithm and the LiDAR canopy height model (CHM) showed the effectiveness of our framework for generating accurate high-resolution tree-cover maps.

Segments↗
NASA NTRS1970

Learning with a probabilistic teacher

Learning scheme for solving unsupervised learning problems with correct estimate convergence and for state estimates of Gauss-Markov sequences with additive and multiplicative observed noise

Agrawala, A. K.↗
DOE OSTI2024

Impurity gas detection for SNF canisters using probabilistic deep learning and acoustic sensing *

Abstract Monitoring impurity gases in spent nuclear fuel (SNF) canisters is a novel structural health monitoring approach for SNF in dry storage. The SNF canisters are sealed containers that do not facilitate visual access to the inside. Acoustic sensing can be deployed by taking advantage of the pathways unobstructed by internal hardware. Although the ultrasonic time-of-flight measurement can provide valuable information, it is limited in its ability to discern the concentration of only one impurity gas. As such, deep learning algorithms, particularly convolutional neural networks (CNNs), offer a promising solution. In this study, CNN-based probabilistic deep learning models were implemented to detect and quantify multiple impurity gases in helium. An experimental platform was established to simulate canister conditions, and ultrasonic test data were collected. The presence of argon and air in helium at concentrations ranging from 0% to 1.2% at increments of 0.05% was considered. The multi-layer perceptron, decision tree, and logistic regression classifiers achieved high accuracies when distinguishing pure helium from helium with impurities. CNN with dropout layers and CNN using maximum likelihood estimation showed a similar performance, indicating their ability to capture uncertainties. The ensemble CNN model exhibited improved predictions and the ability to balance individual gas concentration by integrating 1D- and 2D-CNN models. These findings contribute probabilistic deep learning solutions for impurity gas detection and analysis within SNF canisters, thus ensuring safe storage and management of SNFs.

47 OTHER INSTRUMENTATION↗
DOE OSTI2025

MOOSE ProbML: Parallelized probabilistic machine learning and uncertainty quantification for computational energy applications

Here, this paper presents the development and demonstration of massively parallel probabilistic machine learning (ML) and uncertainty quantification (UQ) capabilities within the Multiphysics Object-Oriented Simulation Environment (MOOSE), an open-source computational platform for parallel finite element and finite volume analyses. In addressing the computational expense and uncertainties inherent in complex multiphysics simulations, this paper integrates Gaussian process (GP) variants, active learning, Bayesian inverse UQ, adaptive forward UQ, Bayesian optimization, evolutionary optimization, and Markov chain Monte Carlo (MCMC) within MOOSE. It also elaborates on the interaction among key MOOSE systems — Sampler, MultiApp, Reporter, and Surrogate — in enabling these capabilities. The modularity offered by these systems enables development of a multitude of probabilistic ML and UQ algorithms in MOOSE. Example code demonstrations include parallel active learning and parallel Bayesian inference via active learning. The impact of these developments is illustrated through five applications relevant to computational energy applications: UQ of nuclear fuel fission product release, using parallel active learning Bayesian inference; very rare events analysis in nuclear microreactors using active learning; advanced manufacturing process modeling using multi-output GPs (MOGPs) and dimensionality reduction; fluid flow using deep GPs (DGPs); and tritium transport model parameter optimization for fusion energy, using batch Bayesian optimization. These capabilities are part of the MOOSE framework.

97 - MATHEMATICS AND COMPUTING↗
NASA NTRS2021

Probabilistic Machine Learning Estimation of Ocean Mixed Layer Depth from Dense Satellite and Sparse In-Situ Observations

The ocean mixed layer plays an important role in the coupling between the upper ocean and atmosphere across a wide range of time scales. Estimation of the variability of the ocean mixed layer is therefore important for atmosphere-ocean prediction and analysis. The increasing coverage of in situ Argo profile data allows for an increasingly accurate analysis of the mixed layer depth (MLD) variability associated with deviations from the seasonal climatology. However, sampling rates are not sufficient to fully resolve subseasonal (<90 day) MLD variability. Yet, many multivariate observations-based analyses include implicit modeled subseasonal MLD variability. One analysis method is optimal interpolation of in situ data, but the interior analysis can be improved by leveraging surface data with regression or variational approaches. Here, we demonstrate how machine learning methods and satellite sea surface temperature, salinity, and height facilitate MLD estimation in a pilot study of two regions: the mid-latitude southern Indian and the eastern equatorial Pacific Oceans. We construct multiple machine learning architectures to produce weekly 1/2° gridded MLD anomaly fields (relative to a monthly climatology) with uncertainty estimates. We test multiple traditional and probabilistic machine learning techniques to compare both accuracy and probabilistic calibration. We validate our methodology by applying it to ocean model simulations. We find that incorporating sea surface data through a machine learning model improves the performance of spatiotemporal MLD variability estimation compared to optimal interpolation of Argo observations alone. These preliminary results are a promising first step for the application of machine learning to MLD prediction.

Machine Learning↗
DOE OSTI2024

Probabilistic machine learning for battery health diagnostics and prognostics—review and perspectives

Abstract Diagnosing lithium-ion battery health and predicting future degradation is essential for driving design improvements in the laboratory and ensuring safe and reliable operation over a product’s expected lifetime. However, accurate battery health diagnostics and prognostics is challenging due to the unavoidable influence of cell-to-cell manufacturing variability and time-varying operating circumstances experienced in the field. Machine learning approaches informed by simulation, experiment, and field data show enormous promise to predict the evolution of battery health with use; however, until recently, the research community has focused on deterministic modeling methods, largely ignoring the cell-to-cell performance and aging variability inherent to all batteries. To truly make informed decisions regarding battery design in the lab or control strategies for the field, it is critical to characterize the uncertainty in a model’s predictions. After providing an overview of lithium-ion battery degradation, this paper reviews the current state-of-the-art probabilistic machine learning models for health diagnostics and prognostics. Details of the various methods, their advantages, and limitations are discussed in detail with a primary focus on probabilistic machine learning and uncertainty quantification. Last, future trends and opportunities for research and development are discussed.

25 ENERGY STORAGE↗
DOE OSTI2024

Error mitigation in variational quantum eigensolvers using tailored probabilistic machine learning

Quantum computing technology has the potential to revolutionize the simulation of materials and molecules in the near future. A primary challenge in achieving near-term quantum advantage is effectively mitigating the noise effects inherent in current quantum processing units (QPUs). This challenge is also decisive in the context of quantum-classical hybrid schemes employing variational quantum eigensolvers (VQEs) that have attracted significant interest in recent years. In this paper, we present a method that employs parametric Gaussian process regression (GPR) within an active learning framework to mitigate noise in quantum computations, focusing on VQEs. Our approach, grounded in probabilistic machine learning, exploits a custom prior based on the VQE ansatz to capture the underlying correlations between VQE outputs for different variational parameters, thereby enhancing both accuracy and efficiency. We demonstrate the effectiveness of our method on a two-site Anderson impurity model and a eight-site Heisenberg model, using the IBM open-source quantum computing framework, Qiskit, showcasing substantial improvements in the accuracy of VQE outputs while reducing the number of direct QPU energy evaluations. This paper contributes to the ongoing efforts in quantum-error mitigation and optimization, bringing us a step closer to realizing the potential of quantum computing in quantum matter simulations. Published by the American Physical Society 2024

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

MOOSE ProbML: Parallelizable Probabilistic Machine Learning and Uncertainty Quantification Capabilities

The Multiphysics Object Oriented Simulation Environment (MOOSE) is a widely used open- source finite element software for performing multiphysics multiscale simulations in a massively parallel fashion. Recently, the computational team at Idaho National Laboratory (INL) has implemented Probabilistic Machine Learning (ProbML) capabilities in MOOSE—in a parallelized fashion—and enable active learning with large-scale computational models for tasks such as surrogate model development, scale bridging, forward/inverse uncertainty quantification (UQ), Bayesian optimization, etc. This presentation summarizes these developments in MOOSE along with demonstrations on several real applications relevant to nuclear energy. At the fundamental level, samplers like Monte Carlo/Latin Hypercube, variance reduction, parallelized Markov Chain Monte Carlo (MCMC) support uncertainty propagation in both forward and inverse settings. These samplers can be integrated with the Gaussian processes (GP) suite in MOOSE, which offer several variants like scalar GPs, multi-output GPs, and deep GPs, to enable active learning. These GPs can be tuned using gradient-based optimization methods like Adam and its variants or gradient-free methods like the elliptical slice sampler (a variant of MCMC adept under Gaussian settings) for more complex covariance kernels or likelihoods whose gradient computations can be cumbersome. A variety of batch acquisition functions permit parallelized evaluation of the computational model and support different learning objectives with high efficiency like Bayesian inference, global surrogate development, optimization, etc. Furthermore, libtorch integration supports training, evaluation, and re-training of neural networks and other complex machine learning models in active learning settings. The impacts of these developments are shown on several real applications: (1) nuclear fuel inverse UQ and model inadequacy assessment using the Kennedy O’Hagan framework; (2) uncertainty aware surrogate modeling for additive manufacturing to predict field quantities; (3) nuclear reactor rare events analysis; and (4) complex fluid flow prediction using a global surrogate with quantified prediction uncertainty. Finally, the outlook of MOOSE ProbML is discussed for both outer-loop and inner-loop computations in the broad view to accelerate fuels and materials qualification, address gaps in knowledge and data, and assess new reactor/fuel systems.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Transfer learning for probabilistic localization of hidden cracks in concrete structures

Abstract The utility of discriminative supervised learning models built using multiple training-data sources is investigated for hidden crack localization in concrete. Feed-forward neural network (FFNN) is chosen as the model architecture, and transfer learning is used to assimilate the information obtained from different sources (computational physics simulations and laboratory experiments). The labeled training data consists of values of a damage index and the known locations of hidden cracks. The classification models need to learn how the presence of damage (hidden cracks) affects the damage index at different sensors for different test conditions. To this end, diagnostic FFNN models are built by sequentially adding and training new hidden layers to assimilate labeled information from computer models (different model geometries, test conditions, crack lengths, crack locations) and laboratory experiments on a plain cement slab. These transfer learning-based models are then used to localize damage in concrete specimens that reflect real-world conditions (i.e., specimens with steel reinforcement and randomly distributed aggregate). The actual damage state in these specimens is determined by extracting cores and performing petrographic studies on the extracted cores. The damage probability estimated by transfer learning-based models is compared with the petrographic damage rating index (DRI) to identify the most suitable approach to train the diagnostic models. The transfer learning-based diagnostic methodology shows promise and could be used in various structural health monitoring applications, where sufficient labeled data are typically not available from a single data source.

Miele, S.↗
DOE OSTI2024

Evidential Deep Learning for Probabilistic Modelling of Extreme Storm Events

Uncertainty quantification (UQ) methods play an important role in reducing errors in weather forecasting. Conventional approaches in UQ for weather forecasting rely on generating an ensemble of forecasts from physics-based simulations to estimate the uncertainty. However, it is computationally expensive to generate many forecasts to predict real-time extreme weather events. Evidential Deep Learning (EDL) is an uncertainty-aware deep learning approach designed to provide confidence about its predictions using only one forecast. It treats learning as an evidence acquisition process where more evidence is interpreted as increased predictive confidence. We apply EDL to storm forecasting using real-world weather datasets and compare its performance with traditional methods. Our findings indicate that EDL not only reduces computational overhead but also enhances predictive uncertainty. This method opens up novel opportunities in research areas such as climate risk assessment, where quantifying the uncertainty about future climate is crucial.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Evaluating Probabilistic Deep Learning Methods for Uncertainty Quantification of Precipitation Bias Correction

Climate models often exhibit biases in their precipitation predictions, particularly underestimating high-intensity events and overestimating low precipitation. Deep learning approaches offer promising solutions, but their epistemic uncertainty associated with a deep learning–based bias correction method has not previously been quantified for reliable downstream climate impact studies. While methods for capturing the epistemic uncertainty in deep learning frameworks exist, there is currently no consensus on the best method. In this work, we compare three uncertainty quantification (UQ) methods—Deep Ensembles (DEns), Monte Carlo Dropout (MCD), and Flipout—by assessing the reliability of their uncertainty estimates using standard measures such as sharpness and calibration. These UQ methods are applied to an existing deep learning precipitation bias correction model known as UFNet: a coupled U-Net and fully connected neural network. The methods utilized to assess the models’ uncertainties are 1) calibration, which ensures that the expected probabilities of the model align with reality and 2) sharpness, which is a measure of the precision of the model’s probabilistic predictions. Of the three UQ methods evaluated, the DEns and MCD methods demonstrated the best-calibrated performance (expected calibration error of 0.36 and 0.35, respectively), compared to Flipout (0.58). In contrast, Flipout had the sharpest predictions and the highest metric performance in bias correcting precipitation—especially for higher-order moments such as kurtosis with a spatial correlation of 72% compared to 32% and 55% spatial correlation for DEns and MCD, respectively. Of the three UQ methods, MCD was found to be the most suitable method for UQ purposes based on its calibration, sharpness, and computational requirements.

Bayesian methods↗
DOE OSTI2025

Evaluating probabilistic deep learning methods for uncertainty quantification of temperature downscaling

Deep learning (DL) has emerged as a promising tool for downscaling coarse-resolution climate data to high-resolution outputs, enabling improved regional climate predictions. A critical aspect of DL-based downscaling is the incorporation of uncertainty quantification (UQ), which enhances the interpretability and reliability of predictions—key factors for climate risk assessment and decision-making. This study develops a DL model to downscale 2 m temperature across the contiguous United States using reanalysis datasets. We systematically evaluate three epistemic UQ methods—deep ensembles (DEns), Monte Carlo dropout (MCD), and Flipout—based on their probabilistic accuracy, downscaling performance, sensitivity to geographical features, and computational efficiency. Results indicate that MCD generally outperforms Flipout and DEns in terms of calibration and downscaling accuracy. However, DEns demonstrate lower calibration errors in coastal regions, indicating its higher confidence within these areas. Flipout, in contrast, is more sensitive to elevation gradients and exhibits higher calibration errors in mountainous regions. Hence, the choice of UQ method for this task depends on the specific requirements of the application. For applications that prioritize overall calibration, downscaling accuracy, and computational efficiency, MCD is a strong candidate. These findings highlight the importance of selecting UQ methods based on application-specific requirements, such as geographical context and computational constraints. By addressing the trade-offs between UQ methods, this study provides actionable insights for improving the reliability, scalability, and utility of DL-based downscaling in climate science.

Environmental sciences↗