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DOE OSTI2026

A Data-Driven Method for Modeling Creep-Fatigue Stress- Strain Behavior Using Neural ODEs

In this paper, we introduce a data-driven machine learning approach for modeling one-dimensional stress–strain behavior under cyclic loading, utilizing experimental data from the nickel-based Alloy 617. The study employs uniaxial creep–fatigue test data acquired under various loading histories and compares two distinct neural network-based ODE models. The first model, known as the black-box model, comprehensively describes the strain–stress relationship using a Neural ODE equation. To interpret this black-box model, we apply the Sparse Identification of Nonlinear Dynamical Systems (SINDy) technique, transforming the black-box model into an equation-based model using symbolic regression. The second model, the Neural flow rule model, incorporates Hooke’s Law for the linear elastic component, with the nonlinear part characterized by a Neural ODE. Both models are trained with experimental data to accurately reflect the observed stress–strain behavior. We conduct a detailed comparison with the standard Chaboche model, which includes three back stresses. Our results demonstrate that the neural network-based ODE models precisely capture the experimental creep–fatigue mechanical behavior, exceeding the standard Chaboche model’s accuracy. Furthermore, an interpretable model derived from the black-box neural ODE model through symbolic regression achieves accuracy comparable to the Chaboche model, enhancing its interpretability. The results highlight the potential of neural network-based ODE models to depict complex creep–fatigue behavior, eliminating the necessity for experts to define a specific, material-focused model form.

creep-fatigue↗

DOE OSTI2023

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

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

3D seismic↗

NASA NTRSDate not supplied

Mitigating the Impacts of Measurement Error in the Quesst Mission Community Noise Study

Beginning in 2025, the NASA Quesst mission will conduct a series of community response tests involving flyovers of the X-59 aircraft at select localities across the United States. Several waves of a longitudinal survey will be administered over approximately one month of testing in order to capture perceptual responses to low-amplitude sonic booms, or “sonic thumps”. Simultaneously, noise exposure levels will be estimated by fusing model-based predictions with measurements taken from a sparse network of monitors in the region. As one of the aims of the study is to produce a dose-response curve, a regression model relating perceptual response to noise exposure levels, it is important to acknowledge the potential attenuation bias that results from measurement error in the estimated noise exposure levels. In this presentation we review and compare several methods for dealing with measurement error in generalized linear mixed models. The methods are demonstrated on simulated data and real data collected during past NASA risk reduction studies.

measurement error↗

DOE OSTI2024

Leveraging Multitime Hamilton–Jacobi PDEs for Certain Scientific Machine Learning Problems

Hamilton-Jacobi partial differential equations (HJ PDEs) have deep connections with a wide range of fields, including optimal control, differential games, and imaging sciences. By considering the time variable to be a higher dimensional quantity, HJ PDEs can be extended to the multi-time case. In this paper, we establish a novel theoretical connection between specific optimization problems arising in machine learning and the multi-time Hopf formula, which corresponds to a representation of the solution to certain multi-time HJ PDEs. Through this connection, we increase the interpretability of the training process of certain machine learning applications by showing that when we solve these learning problems, we also solve a multi-time HJ PDE and, by extension, its corresponding optimal control problem. As a first exploration of this connection, we develop the relation between the regularized linear regression problem and the Linear Quadratic Regulator (LQR). We then leverage our theoretical connection to adapt standard LQR solvers (namely, those based on the Riccati ordinary differential equations) to design new training approaches for machine learning. Lastly, we provide some numerical examples that demonstrate the versatility and possible computational advantages of our Riccati-based approach in the context of continual learning, post-training calibration, transfer learning, and sparse dynamics identification.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Machine-Learning of Nonlocal Kernels for Anomalous Subsurface Transport from Breakthrough Curves

Anomalous behavior is ubiquitous in subsurface solute transport due to the presence of high degrees of heterogeneity at different scales in the media. Although fractional models have been extensively used to describe the anomalous transport in various subsurface applications, their application is hindered by computational challenges. Simpler nonlocal models characterized by integrable kernels and finite interaction length represent a computationally feasible alternative to fractional models; yet, the informed choice of their kernel functions still remains an open problem. We propose a general data-driven framework for the discovery of optimal kernels on the basis of very small and sparse data sets in the context of anomalous subsurface transport. Using spatially sparse breakthrough curves recovered from fine-scale particle-density simulations, we learn the best coarse-scale nonlocal model using a nonlocal operator regression technique. Predictions of the breakthrough curves obtained using the optimal nonlocal model show good agreement with fine-scale simulation results even at locations and time intervals different from the ones used to train the kernel, confirming the excellent generalization properties of the proposed algorithm. A comparison with trained classical models and with black-box deep neural networks confirms the superiority of the predictive capability of the proposed model.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Predicting Drug Effects from High-dimensional Asymmetric Drug Data Sets using Graph Neural Networks: A Comprehensive Analysis of Multi-target Drug Effect Prediction

Graph neural networks (GNNs) have emerged as one of the most effective Machine learning (ML) techniques for drug effect prediction from drug molecular graphs. Despite having immense potential, GNN models lack performance when using data sets that contain high dimensional asymmetrically co-occurrent drug effects as targets with complex correlations between them. Training individual learning models for each drug effect and incorporating every prediction result for a wide spectrum of drug effects is beyond practicality. Such an implication provides a testbed to address this challenge as multi-target prediction problems, aiming to predict all drug effects at a time. We develop standard and hybrid graph neural networks (GNNs)to perform two separate tasks that are multi-regression for continuous values and multi-label classification for categorical values contained in our data sets. Since this step makes the target data even more sparse and introduces asymmetric label co-occurrence, the learning of multi-label classification models becomes difficult and heavily impacts the GNN's performance. To address these challenges, we propose a new data oversampling technique to improve multi-label classification performances on all the given imbalanced molecular graph data sets. Using the technique, we improve the data imbalance ratio of the drug effects better than before while protecting the data set's integrity. Finally, we evaluate multi-label classification performance using the best-performant hybrid GNN model on all the oversampled data sets obtained from the proposed oversampling technique. These results outperform those of other ML models including GNN models when they are trained on the original data sets or oversampled data sets using MLSMOTE (a well-known oversampling technique) in all evaluation metrics precision, recall, and F1 score by a significant margin.

Bose, Avishek [ORNL]↗

DOE OSTI2025

Bayesian learning with Gaussian processes for low-dimensional representations of time-dependent nonlinear systems

This work presents a data-driven method for learning low-dimensional time-dependent physics-based surrogate models whose predictions are endowed with uncertainty estimates. We use the operator inference approach to model reduction that poses the problem of learning low-dimensional model terms as a regression of state space data and corresponding time derivatives by minimizing the residual of reduced system equations. Standard operator inference models perform well with accurate training data that are dense in time, but producing stable and accurate models when the state data are noisy and/or sparse in time remains a challenge. Another challenge is the lack of uncertainty estimation for the predictions from the operator inference models. Our approach addresses these challenges by incorporating Gaussian process surrogates into the operator inference framework to (1) probabilistically describe uncertainties in the state predictions and (2) procure analytical time derivative estimates with quantified uncertainties. The formulation leads to a generalized least-squares regression and, ultimately, reduced-order models that are described probabilistically with a closed-form expression for the posterior distribution of the operators. The resulting probabilistic surrogate model propagates uncertainties from the observed state data to reduced-order predictions. Furthermore, we demonstrate the method is effective for constructing low-dimensional models of two nonlinear partial differential equations representing a compressible flow and a nonlinear diffusion–reaction process, as well as for estimating the parameters of a low-dimensional system of nonlinear ordinary differential equations representing compartmental models in epidemiology.

Data-driven model reduction↗

NASA NTRS1984

Some methods of computing platform transmitter terminal location estimates

A position estimation algorithm was developed to track a humpback whale tagged with an ARGOS platform after a transmitter deployment failure and the whale's diving behavior precluded standard methods. The algorithm is especially useful where a transmitter location program exists; it determines the classical keplarian elements from the ARGOS spacecraft position vectors included with the probationary file messages. A minimum of three distinct messages are required. Once the spacecraft orbit is determined, the whale is located using standard least squares regression techniques. Experience suggests that in instances where circumstances inherent in the experiment yield message data unsuitable for the standard ARGOS reduction, (message data may be too sparse, span an insufficient period, or include variable-length messages). System ARGOS can still provide much valuable location information if the user is willing to accept the increased location uncertainties.

Hoisington, C. M.↗

NASA NTRS1997

A Comparison of Soil Moisture Retrieval Models Using SIR-C Measurements over the Little Washita River Watershed

Six SIR-C L-band measurements over the Little Washita River watershed in Chickasha, Oklahoma during 11-17 April 1994 have been analyzed for studying the change of soil moisture in the region. Two algorithms developed recently for estimation of moisture content in bare soil were applied to these measurements and the results were compared with those sampled on the ground. There is a good agreement between the values of soil moisture estimated by either one of the algorithms and those measured from ground sampling for bare or sparsely vegetated fields. The standard error from this comparison is on the order of 0.05-0.06 cu cm/cu cm, which is comparable to that expected from a regression between backscattering coefficients and measured soil moisture. Both algorithms provide a poor estimation of soil moisture or fail to give solutions to areas covered with moderate or dense vegetation. Even for bare soils the number of pixels that bear no numerical solution from the application of either one of the two algorithms to the data is not negligible. Results from using one of these algorithms indicate that the fraction of these pixels becomes larger as the bare soils become drier. The other algorithm generally gives a larger fraction of these pixels when the fields are vegetation-covered. The implication and impact of these features are discussed in this article.

Wang, J. R.↗

DOE OSTI2025

Data-Efficient Methods for Determining Flory–Huggins χ Parameters in Multicomponent Polymer Formulations

Polymer formulations are essential in diverse applications including personal care products, coatings, paints, adhesives, and plastic materials. Designing these formulations requires navigating large, complex design spaces, where phase and self-assembly behavior critically impact performance. The Flory–Huggins χ parameter, which quantifies segmental miscibility, is widely used to parametrize the excess free energy of mixing in formulation models. In this work, we introduce two data-efficient, top-down methods for estimating χ parameters using the Random Phase Approximation (RPA): (i) Boundary Nonlinear Regression (Boundary-NLR), which fits theoretical spinodal boundaries to experimental phase boundaries, and (ii) Surrogate Model Inverse Parameter Estimation (SMIPE), which uses a Gaussian Process Classifier to fit sparse phase maps via a surrogate model. Both methods allow rapid parametrization of polymer field-theoretic models without the need for additional experiments. We evaluate these approaches on data sets involving polymer–solvent–nonsolvent ternary mixtures and block copolymer–solvent systems, demonstrating their robustness to experimental noise and their relevance for real-world formulation design.

copolymers↗

DOE OSTI2022

Zero-Truncated Poisson Tensor Decomposition for Sparse Count Data

We propose a novel statistical inference paradigm for zero-inflated multiway count data that dispenses with the need to distinguish between true and false zero counts. Our approach ignores all zero entries and applies zero-truncated Poisson regression on the positive counts. Inference is accomplished via tensor completion that imposes low-rank structure on the Poisson parameter space. Our main result shows that an $\textit{N}$-way rank-R parametric tensor 𝓜 ϵ (0, ∞) $I$Χ∙∙∙Χ$I$ generating Poisson observations can be accurately estimated from approximately $IR^2 \text{log}^2_2(I)$ non-zero counts for a nonnegative canonical polyadic decomposition. Several numerical experiments are presented demonstrating that our zero-truncated paradigm is comparable to the ideal scenario where the locations of false zero counts are known $\textit{a priori}$.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

The updated ITPA global H-mode confinement database: description and analysis

The multi-machine ITPA Global H-mode Confinement Database has been upgraded with new data from JET with the ITER-like wall and ASDEX Upgrade with the full tungsten wall. This paper describes the new database and presents results of regression analysis to estimate the global energy confinement scaling in H-mode plasmas using a standard power law. Various subsets of the database are considered, focusing on type of wall and divertor materials, confinement regime (all H-modes, ELMy H or ELM-free) and ITER-like constraints. Apart from ordinary least squares, two other, robust regression techniques are applied, which take into account uncertainty on all variables. Regression on data from individual devices shows that, generally, the confinement dependence on density and the power degradation are weakest in the fully metallic devices. Using the multi-machine scalings, predictions are made of the confinement time in a standard ELMy H-mode scenario in ITER. The uncertainty on the scaling parameters is discussed with a view to practically useful error bars on the parameters and predictions. One of the derived scalings for ELMy H-modes on an ITER-like subset is studied in particular and compared to the IPB98(y,2) confinement scaling in engineering and dimensionless form. Transformation of this new scaling from engineering variables to dimensionless quantities is shown to result in large error bars on the dimensionless scaling. Regression analysis in the space of dimensionless variables is therefore proposed as an alternative, yielding acceptable estimates for the dimensionless scaling. The new scaling, which is dimensionally correct within the uncertainties, suggests that some dependencies of confinement in the multi- machine database can be reconciled with parameter scans in individual devices. This includes vanishingly small dependence of confinement on line-averaged density and normalized plasma pressure (β), as well as a noticeable, positive dependence on effective atomic mass and plasma triangularity. Extrapolation of this scaling to ITER yields a somewhat lower confinement time compared to the IPB98(y, 2) prediction, possibly related to the considerably weaker dependence on major radius in the new scaling (slightly above linear). Further studies are needed to compare more flexible regression models with the power law used here. In addition, data from more devices concerning possible ‘hidden variables’ could help to determine their influence on confinement, while adding data in sparsely populated areas of the parameter space may contribute to further disentangling some of the global confinement dependencies in tokamak plasmas.

Database↗

NASA NTRSDate not supplied

The effect of modeling dose uncertainty on low-boom community noise dose-response curves

In logistic dose-response modeling, failing to account for uncertainty in estimated doses can cause an artificial flattening or attenuation of the slope of the summary curve. In Lee et al. [J. Acoust. Soc. Am. 147(4), pp. 2222-2234 (2020)], data from two NASA low-amplitude sonic boom community noise survey tests were modeled using a Bayesian multilevel logistic regression (MLR) statistical model that assumed there was no uncertainty in the noise dose estimates. However, in these community tests, the noise dose uncertainty was estimated by Page et al. [NASA/CR-2014-218180 and NASA/CR-2020-220589/Volume I] using a leave-one-out method. In the current work, a term was added to extend the Bayesian MLR model to account for the estimated noise dose uncertainty quantified in the Page et al. analyses. This uncertainty term was included in two ways, either as classical or as Berkson uncertainty, and yield similar results. When the uncertainty is accounted for in the Bayesian MLR model, the dose-response curves become 5-10% steeper, but the difference in the noise dose that elicits a 5% highly annoyed response is small (less than 1 dB). This result is encouraging for future X-59 community tests whose survey area will be sparsely populated with noise monitors.

X-59↗

DOE OSTI2024

Deep energy-pressure regression for a thermodynamically consistent EOS model

Abstract In this paper, we aim to explore novel machine learning (ML) techniques to facilitate and accelerate the construction of universal equation-Of-State (EOS) models with a high accuracy while ensuring important thermodynamic consistency. When applying ML to fit a universal EOS model, there are two key requirements: (1) a high prediction accuracy to ensure precise estimation of relevant physics properties and (2) physical interpretability to support important physics-related downstream applications. We first identify a set of fundamental challenges from the accuracy perspective, including an extremely wide range of input/output space and highly sparse training data. We demonstrate that while a neural network (NN) model may fit the EOS data well, the black-box nature makes it difficult to provide physically interpretable results, leading to weak accountability of prediction results outside the training range and lack of guarantee to meet important thermodynamic consistency constraints. To this end, we propose a principled deep regression model that can be trained following a meta-learning style to predict the desired quantities with a high accuracy using scarce training data. We further introduce a uniquely designed kernel-based regularizer for accurate uncertainty quantification. An ensemble technique is leveraged to battle model overfitting with improved prediction stability. Auto-differentiation is conducted to verify that necessary thermodynamic consistency conditions are maintained. Our evaluation results show an excellent fit of the EOS table and the predicted values are ready to use for important physics-related tasks.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1979

Results of a statistical approach to rainfall estimation using Nimbus 5 6.7 micrometers and 11.5 micrometers THIR data

Nimbus 5 6.7 mm and 11.5 mm temperature humidity infrared radiometer (THIR) data were used in a simple multiple regression scheme to test the feasibility of using these data to estimate hourly rainfall. Throughout the test area (85 W to 105 W and 45 N to 30 N) subareas (8 deg x 6 deg) were chosen from which point to point and areal statistics were obtained. Four subsets of data were used. The first consisted of only those surface stations indicating precipitation whose latitude and longitude coincided with the THIR grid points. A second used surface stations 0.1 degree from the THIR grid points. The third was a combination of subsets one and two. A reciprocal distance weighting scheme was used to derive precipitation values in data sparse areas. A fourth subset was made using these data combined with the data from subsets one and two. Point estimates resulted in negative correlations between estimated and grid derived "surface" precipitation. One degree areal estimates showed a slight improvement with a correlation coefficient of approximately 0.11. Single regression areal estimates resulted in correlations of approximately 0.11 and 0.20 for the 6.7 mm and 11.5 mm data respectively. These poor results were attributed to problems which are inherent in the satellite data (location errors, short temporal span of data, wavelength of sensors, etc.) and the lack of sufficient surface data to better verify the satellite estimate.

Ormsby, J. P.↗

DOE OSTI2025

Accurate and uncertainty-aware multi-task prediction of HEA properties using prior-guided deep Gaussian processes

Surrogate modeling techniques have become indispensable in accelerating the discovery and optimization of high-entropy alloys (HEAs), especially when integrating computational predictions with sparse experimental observations. This study systematically evaluates the training and testing performance of four prominent surrogate models—conventional Gaussian processes (cGP), Deep Gaussian processes (DGP), encoder-decoder neural networks for multi-output regression and eXtreme Gradient Boosting (XGBoost)—applied to a hybrid dataset of experimental and computational properties of the 8-component HEA system Al-Co-Cr-Cu-Fe-Mn-Ni-V. We specifically assess their capabilities in predicting correlated material properties, including yield strength, hardness, modulus, ultimate tensile strength, elongation, and average hardness under dynamic/quasi-static conditions, alongside auxiliary computational properties. The comparison highlights the strengths of hierarchical deep modeling approaches in handling heteroscedastic, heterotopic, and incomplete data commonly encountered in materials science. Our findings illustrate that combined surrogate models such as DGPs infused with machine-learned priors outperform other surrogates by effectively capturing inter-property correlations and by assimilating prior knowledge. This enhanced predictive accuracy positions the combined surrogate models as powerful tools for robust and data-efficient materials design.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Using automated machine learning for the upscaling of gross primary productivity

Estimating gross primary productivity (GPP) over space and time is fundamental for understanding the response of the terrestrial biosphere to climate change. Eddy covariance flux towers provide in situ estimates of GPP at the ecosystem scale, but their sparse geographical distribution limits larger-scale inference. Machine learning (ML) techniques have been used to address this problem by extrapolating local GPP measurements over space using satellite remote sensing data. However, the accuracy of the regression model can be affected by uncertainties introduced by model selection, parameterization, and choice of explanatory features, among others. Recent advances in automated ML (AutoML) provide a novel automated way to select and synthesize different ML models. In this work, we explore the potential of AutoML by training three major AutoML frameworks on eddy covariance measurements of GPP at 243 globally distributed sites. We compared their ability to predict GPP and its spatial and temporal variability based on different sets of remote sensing explanatory variables. Explanatory variables from only Moderate Resolution Imaging Spectroradiometer (MODIS) surface reflectance data and photosynthetically active radiation explained over 70 % of the monthly variability in GPP, while satellite-derived proxies for canopy structure, photosynthetic activity, environmental stressors, and meteorological variables from reanalysis (ERA5-Land) further improved the frameworks' predictive ability. We found that the AutoML framework Auto-sklearn consistently outperformed other AutoML frameworks as well as a classical random forest regressor in predicting GPP but with small performance differences, reaching an r 2 of up to 0.75. We deployed the best-performing framework to generate global wall-to-wall maps highlighting GPP patterns in good agreement with satellite-derived reference data. This research benchmarks the application of AutoML in GPP estimation and assesses its potential and limitations in quantifying global photosynthetic activity.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRSDate not supplied

Characterizing Spatiotemporal Uncertainty in Interpolated Meteorological Data

Interpolated meteorological data invariably contain errors. These errors have structure in time and space, particularly autocorrelation, which can cause the effects of errors to compound when model outputs are aggregated temporally or spatially. One way to account for this uncertainty is with a probabilistic model from which samples can be drawn that are coherent with respect to underlying spatial and temporal covariance structure. This work describes a probabilistic method for spatial interpolation of point-wise meteorological time series. Observational data from weather stations are generally sparse in space and dense in time (but sometimes missing). The method works by projecting time series onto orthogonal basis vectors and spatially interpolating each resulting component independently. Under suitable assumptions, and data transformations to better satisfy those assumptions, Gaussian process regression provides a complete description of the joint predictive distribution over a Gaussian random field. Spatiotemporally coherent realizations are generated as the sum of conditional (spatial) simulations of each orthogonal (temporal) component. Data-derived and generic orthogonal bases are considered. In addition to spatial interpolation, imputation of missing observational data is examined. The method is applied using near-surface air temperature over the Western United States and validated by comparing theoretical versus actual coverage of predictive distributions and analyzing the degree to which spatial and temporal covariance structure is reproduced. Computational considerations, relating to conditional simulation of random fields, are also addressed.

Conor T Doherty↗