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102 records · Page 6

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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↗

DOE OSTI2025

Rapid monitoring of fermentations: a feasibility study on biological 2,3-butanediol production

2,3-butanediol (2,3-BDO) is an economically important platform chemical that can be produced by the fermentation of sugars using an engineered strain of Zymomonas mobilis . These fermentations require continuous monitoring and modification of fermentation conditions to maximize 2,3-BDO yields and minimize the production of the undesired coproducts glycerol and acetoin. Because of the time required for sampling and off-line chromatographic measurement of fermentation samples, the ability of fermentation scientists to modify fermentation conditions in a timely manner is limited. The goal of this study was to test if near-infrared spectroscopy (NIRS) along with multivariate statistics could reduce the time needed for this analysis and enable real-time monitoring and control of the fermentation. In this work we developed partial least squares (PLS) calibration models to predict the concentrations of glucose, xylose, 2,3-BDO, acetoin, and glycerol in fermentations via NIRS using two different spectrometers and two different spectroscopy modalities. We first evaluated the feasibility of rapid NIRS monitoring through experiments where we measured the signals from each analyte of interest and built NIRS-based PLS models using spectra from synthetic samples containing uncorrelated concentrations of these analytes. All analytes showed unique spectral signatures, and this initial modeling showed that all analytes could be detected simultaneously. We then began work with samples from laboratory fermentation experiments and tested the feasibility of regression model development across two spectral collection modalities (at-line and on-line) and two instruments: a laboratory-grade instrument and a low-cost instrument with a more limited spectral range. All modalities showed promise in the ability to monitor Z. mobilis fermentations of glucose and xylose to 2,3-BDO. The low-cost instrument displayed a lower signal-to-noise ratio than the laboratory-grade instrument, which led to comparatively lower performance overall, but still provided sufficient accuracy to monitor fermentation trends. While the ease of use of on-line monitoring systems was favored as compared to at-line systems due to the lack of sampling required and potential for automated process control, we observed some decrease in performance due to the additional complexity of the sample matrix. We have demonstrated that NIRS combined with multivariate analysis can be used for at-line and on-line monitoring of the concentrations of glucose, xylose, 2,3-BDO, acetoin, and glycerol during Z. mobilis fermentations. The decrease in signal-to-noise ratio when using a low-cost spectrometer led to greater prediction error than the laboratory-grade spectrometer for at-line monitoring. The on-line monitoring modality showed great promise for real time process control via NIRS.

09 BIOMASS FUELS↗

DOE OSTI2025

Uncertainty Quantification Enabled by Automatic Differentiation for Hydrodynamic Simulation of Shock‐to‐Detonation Transition in High Explosives

Quantifying the effects of uncertainty in a reactive burn model on the run-to-detonation time in high explosives (HEs) provides a robust methodology for assessing the probability of an HE failing the IHE qualification standard. Moreover, uncertainty quantification helps evaluate whether the model calibration accurately represents data outside the calibration set. This study uses a specialized hydrodynamic simulation code for modeling detonation to determine the run-to-detonation time of the HE PBX 9502 for various impact velocities. To quickly approximate uncertainties in the model, a surrogate was constructed using a Taylor series expansion centered at the mean of the input parameters. To obtain the sensitivities required for constructing the Taylor series, HYP-percomplex Automatic Differentiation (HYPAD) was implemented. HYPAD is a methodology for infusing existing codes with automatic differentiation capabilities by augmenting variables with one or more imaginary units to compute step-size independent partial derivatives. These derivatives are accurate to machine precision with respect to the implemented numerical algorithm, meaning their accuracy reflects that of the underlying method (e.g., integration or discretization schemes). Using reduced order modeling techniques, the mean and standard deviation of the run-to-detonation time of a shock within PBX 9502 were computed for a number of initial impact velocities. A weighted least squares regression was then performed to obtain a best fit curve and prediction interval for the computed statistics. Historical data points from explosively driven wedge tests were utilized to validate the prediction interval, ensuring its reliability in predicting future outcomes. With this prediction interval and a known safety constraint curve, the most probable point of failure and the probability of failure for the HE PBX 9502 were determined.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Transient Catalytic Reaction Analysis Through Signal Defragmentation

The Temporal Analysis of Products (TAP) pulse response technique provides valuable insights into catalytic function and reaction kinetics. However, complex fragmentation patterns in the TAP mass spectrometry signals can complicate precise quantification, particularly when analyzing transient gas flux data typical of TAP experiments. This work demonstrates a standard defragmentation method that deconvolves transient TAP signals while maintaining the temporal resolution of the experiment. First, the integrals of calibration gas fluxes are used to determine the fingerprint fragmentation pattern and construct a fragmentation matrix. This matrix is then used to defragment experimental flux data at each recorded time point via a non-negative least squares regression. The effectiveness of this method is demonstrated using virtual data and control experiments with a TAP reactor system. The defragmentation is then applied to the more complex propane dehydrogenation reaction on a chromia/alumina catalyst, which can contain up to ten significant gas species in the reactor outlet. Initial propane pulsing reveals an induction period during which propane is fully oxidized to CO2, followed by partial reduction to CO. Afterwards, there is a transition in chemistries towards coking and propylene production. Our example illustrates a practical method for the accurate determination of the time-dependent reactant/product concentrations and rates for a thorough analysis of the propane dehydrogenation kinetics. This approach can be broadly applied to any transient mass spectrometry experiment for a better understanding of catalyst-reaction dynamics.

36 - MATERIALS SCIENCE↗

DOE OSTI2020

Comparison of machine learning techniques to optimize the analysis of plutonium surrogate material via a portable LIBS device

The utilization of machine learning techniques has become commonplace in the analysis of optical emission spectra. These methods are often limited to variants of principal components analysis (PCA), partial-least squares (PLS), and artificial neural networks (ANNs). A plethora of other techniques exist and are well established in the world of data science, yet are seldom investigated for their use in spectroscopic problems. In this study, machine learning techniques were used to analyze optical emission spectra of laser-induced plasma from ceria pellets doped with silicon in order to predict silicon content. Additionally, a boosted regression ensemble model was created, and its predictive accuracy was compared to that of traditional PCA, PLS, and ANN regression models. Boosted regression tree ensembles yielded fits with R-squared (R2) values as high as 0.964 and mean-squared errors of prediction (MSEPs) as low as 0.074, providing the most accurate predictive model. Neural networks performed with slightly lower R2 values and higher MSEPs compared to the ensemble methods, thus indicating susceptibility to overfitting.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Application of Partial Least Squares Approaches to Pyroprocessing ER Data

Multivariate approaches show promise for application to process monitoring for safeguards of pyroprocessing. Past MPACT work explored the application of Principal Component Analysis (PCA) to detect off-normal conditions in pyroprocessing electrorefiner (ER) data from in the Hot Fuel Examination Facility (HFEF) at Idaho National Laboratory (INL) known as the Scalable Pyrochemical Recycling testbed (SPyRe) ER. PCA, however, does not consider the output variables. In FY24, multivariate analysis was extended from PCA to Partial Least Squares (PLS) analysis. PLS maximizes the variance between both the input signals and output variables. In the case of this work, PLS was applied in two different manners: Predictive PLS and Discriminant PLS. Predictive PLS maximizes the covariance between the process variables of the ER and the measured U concentration from in-situ voltammetry. Discriminant PLS maximizes the covariance between the process variables and a set of training process “states” such as known off-normal conditions. By projecting into the latent variable space in PLS, the process variables can be regressed onto the outputs and predictions can be made for new data sets. In this work, by applying predictive PLS, a penalized non-linear PLS approach was able to make predictions of concentration based on test and training data and detect when operations were off-normal. However, the predictive PLS does not classify the signals to which off-normal operations are attributable. Discriminant PLS can be used to classify off-normal operations but is inadequate to properly classify specific off-normal classes like power supply faults when the Discriminant PLS model is only specifically trained to detect that off-normal class. When all faults are trained against the observation data, all three operational classes are accurately classified and distinguished. Thus, future application of latent variable techniques should not select any given method, but should use a mixture of PCA, Predictive PLS, and Discriminant PLS.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2021

Non-intrusive data-driven model reduction for differential–algebraic equations derived from lifting transformations

In this paper we present a non-intrusive data-driven approach for model reduction of nonlinear systems. The approach considers the particular case of nonlinear partial differential equations (PDEs) that form systems of partial differential–algebraic equations (PDAEs) when lifted to polynomial form. Such systems arise, for example, when the governing equations include Arrhenius reaction terms (e.g., in reacting flow models) and thermodynamic terms (e.g., the Helmholtz free energy terms in a phase-field solidification model). Using the known structured form of the lifted algebraic equations, the approach computes the reduced operators for the algebraic equations explicitly, using straightforward linear algebra operations on the basis matrices. The reduced operators for the differential equations are inferred from lifted snapshot data using operator inference, which solves a linear least squares regression problem. The approach is illustrated for the nonlinear model of solidification of a pure material. The lifting transformations reformulate the solidification PDEs as a system of PDAEs that have cubic structure. The operators of the lifted system for this solidification example have affine dependence on key process parameters, permitting us to learn a parametric reduced model with operator inference. Numerical experiments show the effectiveness of the resulting reduced models in capturing key aspects of the solidification dynamics.

42 ENGINEERING↗

DOE OSTI2024

Rapid subsurface analysis of frequency-domain thermoreflectance images with K-means clustering

K-means clustering analysis is applied to frequency-domain thermoreflectance (FDTR) hyperspectral image data to rapidly screen the spatial distribution of thermophysical properties at material interfaces. Performing FDTR while raster scanning a sample consisting of 8.6 μm of doped-silicon (Si) bonded to a doped-Si substrate identifies spatial variation in the subsurface bond quality. Routine thermal analysis at select pixels quantifies this variation in bond quality and allows assignment of bonded, partially bonded, and unbonded regions. Performing this same routine thermal analysis across the entire map, however, becomes too computationally demanding for rapid screening of bond quality. To address this, K-means clustering was used to reduce the dimensionality of the dataset from more than 20 000 pixel spectra to just K = 3 component spectra. The three component spectra were then used to express every pixel in the image through a least-squares minimized linear combination providing continuous interpolation between the components across spatially varying features, e.g., bonded to unbonded transition regions. Fitting the component spectra to the thermal model, thermal properties for each K cluster are extracted and then distributed according to the weighting established by the regressed linear combination. Thermophysical property maps are then constructed and capture significant variation in bond quality over 25 μm length scales. The use of K-means clustering to achieve these thermal property maps results in a 74-fold speed improvement over explicit fitting of every pixel.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Multivariate regression modelling for gender prediction using volatile organic compounds from hand odor profiles via HS-SPME-GC-MS

The efficacy of using human volatile organic compounds (VOCs) as a form of forensic evidence has been well demonstrated with canines for crime scene response, suspect identification, and location checking. Although the use of human scent evidence in the field is well established, the laboratory evaluation of human VOC profiles has been limited. This study used Headspace-Solid Phase Microextraction-Gas Chromatography-Mass Spectrometry (HS-SPME-GC-MS) to analyze human hand odor samples collected from 60 individuals (30 Females and 30 Males). The human volatiles collected from the palm surfaces of each subject were interpreted for classification and prediction of gender. The volatile organic compound (VOC) signatures from subjects’ hand odor profiles were evaluated with supervised dimensional reduction techniques: Partial Least Squares-Discriminant Analysis (PLS-DA), Orthogonal-Projections to Latent Structures Discriminant Analysis (OPLS-DA), and Linear Discriminant Analysis (LDA). The PLS-DA 2D model demonstrated clustering amongst male and female subjects. The addition of a third component to the PLS-DA model revealed clustering and minimal separation of male and female subjects in the 3D PLS-DA model. The OPLS-DA model displayed discrimination and clustering amongst gender groups with leave one out cross validation (LOOCV) and 95% confidence regions surrounding clustered groups without overlap. The LDA had a 96.67% accuracy rate for female and male subjects. The culminating knowledge establishes a working model for the prediction of donor class characteristics using human scent hand odor profiles.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2022

Dynamic calibration of differential equations using machine learning, with application to turbulence models

We present a methodology for calibration of parametric ordinary and partial differential equation models, using off-the-shelf software for back-propagation in Neural Networks (NN). As a prototypical example, we consider calibration of a Reynolds-averaged Navier-Stokes (RANS) turbulence closure model, against ground truth data from direct numerical simulations (DNS) of two different turbulent flows. Numerical time integration is represented as a custom NN, where only the RANS model parameters are trainable. A loss function is defined to quantify the mismatch between the NN prediction and the ground truth over a predefined, finite time integration window. This loss function is then minimized using a gradient descent method utilizing the back-propagation algorithm. Furthermore, this dynamic approach to training is to be contrasted with a static approach, wherein a least square regression estimate for parameters is obtained in the limit of an infinitesimal time integration window. In a first test of static and dynamic approaches against ground truth data generated by the model, the former proves to be significantly faster and more accurate than the latter at recovering the parameters. When both calibration approaches are tested against DNS data, for which it is known that the model cannot achieve a perfect fit, the static approach yields a good prediction only for short times, while the dynamic approach results in physical and stable predictions over the entire integration window. After optimization of the dynamic approach for time step, spatial resolution, stability, and physics-based constraints, we obtain a 50% improvement of outcomes over those obtained from the existing, manually calibrated set of parameters, demonstrating the merits of this systematic and automated procedure.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Regularization via f -Divergence: An Application to Multi-Oxide Spectroscopic Analysis

In this paper, we explore the application of convolutional neural networks (CNNs) for predicting the chemical composition of complex geologic samples in a simulated Martian atmospheric environment. Specifically, we aim to characterize oxide weight percentages (wt.%) of rock samples analyzed by remote Laser-Induced Breakdown Spectroscopy (LIBS), framing the problem as a multi-target regression task . Neural networks trained on LIBS spectra are prone to overfitting due to high spectral complexity, limited labeled data, and measurement noise. While regularization is critical for improving generalization, common methods (e.g., ℓ 2 regularization) impose constraints not directly tied to data distribution properties. We propose a novel regularization method based on a specific ƒ-divergence induced by a graph-based estimator, designed to constrain the distributional discrepancy between predictions and targets. This regularizer serves a dual purpose: (a) mitigating overfitting by enforcing a constraint on the distributional difference between predictions and noisy targets, and (b) acting as an auxiliary loss that penalizes large divergences. To enable backpropagation, we develop a differentiable approximation of this particular ƒ-divergence, making the method feasible for neural networks. Experiments on ChemCam and SuperCam LIBS calibration spectra show that mathematical equation-divergence regularization outperforms or matches standard regularization methods (ℓ 1 , ℓ 2 , dropout) and the classical baseline, partial least squares (PLS). Combining ƒ-divergence regularization with standard regularization yields further performance gains, indicating that distributional regularization is useful in this context giving a promising direction for robust model training in planetary science applications. Source code is publicly available at Klein and Li (2025), https://doi.org/10.11578/dc.20250530.7.

58 GEOSCIENCES↗

DOE OSTI2021

Inorganic characterization of switchgrass biomass using laser-induced breakdown spectroscopy

The inorganic characterization of 74 samples of switchgrass using laser-induced breakdown spectroscopy (LIBS) was undertaken. Determination of ash and inorganic elements content in biomass materials is vital for feedstock screening for bioconversion processes. Hierarchical models using principal component analysis (PCA) and partial least square analysis (PLS) were used to determine the presence of specific elemental micronutrients that are important in determining plant health for robust biomass production. LIBS uses a 532 nm laser with 45 mJ of laser power to excite the samples of switchgrass plant material and the emission of all the elements present in the plant samples were recorded in single spectra with a wide wavelength range of 200–800 nm. The results were compared to the laboratory standard technique, e.g., ICP-OES technique, to determine the true values for major micronutrients such as, silicon (Si), potassium (K), calcium (Ca), magnesium (Mg), phosphorus (P), and sulfur (S). Overall, our objectives were: 1) To determine the spectral features of switchgrass containing different amounts of these elements and 2) To examine the viability of this technique for determining the quality of the feedstock in terms of its inorganic composition. Cross-validation results showed that the broad-based model developed is promising for inorganics prediction in switchgrass. The LIBS validation prediction for the micronutrient elements mentioned here have been obtained. The regression coefficients for Si, were obtained to be 0.995, 0.994 for calibration and validation respectively, in case of Ca the regression coefficients were, 0.994 and 0.992 for calibration and validation. Similarly, in the case of Mg and K these were calculated to be 0.992 and 0.985, and 0.994 and 0.993 respectively. The regression coefficients are not as good as those for the elements mentioned, in case of the two elements S and P. They are 0.957, and 0.878, and 0.952 and 0.894 respectively for calibration, validation for the two elements. This demonstrates that LIBS-based techniques are inherently well suited for diverse environmental applications. Furthermore, LIBS along with PLS model can show capability in determining the viability of switchgrass as a biomass in the production of biofuels and survivability of switchgrass in processes associated with climate change. LIBS can help determining which switchgrass would be appropriate for a specific conversion process that favors low ash content overall or low value of specific inorganics.

59 BASIC BIOLOGICAL SCIENCES↗