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DOE OSTI2025

Uncertainty quantification for misspecified machine learned interatomic potentials

The use of high-dimensional regression techniques from machine learning has significantly improved the quantitative accuracy of interatomic potentials. Atomic simulations can now plausibly target quantitative predictions in a variety of settings, which has brought renewed interest in robust means to quantify uncertainties. In many practical settings where model complexity is constrained (e.g., due to performance considerations), misspecification — the inability of any one choice of model parameters to exactly match all training data — is a key contributor to errors that is often disregarded. Here, we employ a recent misspecification-aware regression technique to quantify parameter uncertainties, which is then propagated to a broad range of phase and defect properties in tungsten. The propagation is performed through both brute-force resampling and implicit Taylor expansion. The propagated misspecification uncertainties robustly quantify and bound errors on a broad range of material properties. We demonstrate application to recent foundational machine learning interatomic potentials, accurately predicting and bounding errors in MACE-MPA-0 energy predictions across the diverse materials project database.

36 MATERIALS SCIENCE↗

DOE OSTI2021

High temperature oxidation of corrosion resistant alloys from machine learning

Parabolic rate constants, k p , were collected from published reports and calculated from corrosion product data (sample mass gain or corrosion product thickness) and tabulated for 75 alloys exposed to temperatures between ~800 and 2000 K (~500–1700 °C; 900–3000°F). Data were collected for environments including lab air, ambient and supercritical carbon dioxide, supercritical water, and steam. Materials studied include low- and high-Cr ferritic and austenitic steels, nickel superalloys, and aluminide materials. A combination of Arrhenius analysis, simple linear regression, supervised and unsupervised machine learning methods were used to investigate the relations between composition and oxidation kinetics. The supervised machine learning techniques produced the lowest mean standard errors. The most significant elements controlling oxidation kinetics were Ni, Cr, Al, and Fe, with Mo and Co composition also found to be significant features. The activation energies produced from the machine learning analysis were in the correct distributions for the diffusion constants for the oxide scales expected to dominate in each class.

Materials Science↗

DOE OSTI2024

Unveiling the effect of composition on nuclear waste immobilization glasses’ durability by nonparametric machine learning

Abstract Ensuring the long-term chemical durability of glasses is critical for nuclear waste immobilization operations. Durable glasses usually undergo qualification for disposal based on their response to standardized tests such as the product consistency test or the vapor hydration test (VHT). The VHT uses elevated temperature and water vapor to accelerate glass alteration and the formation of secondary phases. Understanding the relationship between glass composition and VHT response is of fundamental and practical interest. However, this relationship is complex, non-linear, and sometimes fairly variable, posing challenges in identifying the distinct effect of individual oxides on VHT response. Here, we leverage a dataset comprising 654 Hanford low-activity waste (LAW) glasses across a wide compositional envelope and employ various machine learning techniques to explore this relationship. We find that Gaussian process regression (GPR), a nonparametric regression method, yields the highest predictive accuracy. By utilizing the trained model, we discern the influence of each oxide on the glasses’ VHT response. Moreover, we discuss the trade-off between underfitting and overfitting for extrapolating the material performance in the context of sparse and heterogeneous datasets.

36 MATERIALS SCIENCE↗

DOE OSTI2018

Reevaluating growing season length controls on net ecosystem production in evergreen conifer forests

Abstract Growing season length (GSL) is a key unifying concept in ecology that can be estimated from eddy covariance-derived estimates of net ecosystem production (NEP). Previous studies disagree on how increasing GSLs may affect NEP in evergreen coniferous forests, potentially due to the variety of methods used to quantify GSL from NEP. We calculated GSL and GSL-NEP regressions at eleven evergreen conifer sites across a broad climatic gradient in western North America using three common approaches: (1) variable length (3–7 days) regressions of day of year versus NEP, (2) a smoothed threshold approach, and (3) the carbon uptake period, followed by a new approach of a method-averaged ensemble. The GSL and the GSL-NEP relationship differed among methods, resulting in linear relationships with variable sign, slope, and statistical significance. For all combinations of sites and methods, the GSL explained between 6% and 82% of NEP with p -values ranging from 0.45 to < 0.01. These results demonstrate the variability among GSL methods and the importance of selecting an appropriate method to accurately project the ecosystem carbon cycling response to longer growing seasons in the future. To encourage this approach in future studies, we outline a series of best practices for GSL method selection depending on research goals and the annual NEP dynamics of the study site(s). These results contribute to understanding growing season dynamics at ecosystem and continental scales and underscore the potential for methodological variability to influence forecasts of the evergreen conifer forest response to climate variability.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Advances in Kriging-Based Autonomous X-Ray Scattering Experiments

Autonomous experimentation is an emerging paradigm for scientific discovery, wherein measurement instruments are augmented with decision-making algorithms, allowing them to autonomously explore parameter spaces of interest. We have recently demonstrated a generalized approach to autonomous experimental control, based on generating a surrogate model to interpolate experimental data, and a corresponding uncertainty model, which are computed using a Gaussian process regression known as ordinary Kriging (OK). We demonstrated the successful application of this method to exploring materials science problems using x-ray scattering measurements at a synchrotron beamline. Here, we report several improvements to this methodology that overcome limitations of traditional Kriging methods. The variogram underlying OK is global and thus insensitive to local data variation. We augment the Kriging variance with model-based measures, for instance providing local sensitivity by including the gradient of the surrogate model. As with most statistical regression methods, OK minimizes the number of measurements required to achieve a particular model quality. However, in practice this may not be the most stringent experimental constraint; e.g. the goal may instead be to minimize experiment duration or material usage. We define an adaptive cost function, allowing the autonomous method to balance information gain against measured experimental cost. We provide synthetic and experimental demonstrations, validating that this improved algorithm yields more efficient autonomous data collection.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Gene-environment interactions due to quantile-specific heritability of triglyceride and VLDL concentrations

"Quantile-dependent expressivity" is a dependence of genetic effects on whether the phenotype (e.g., triglycerides) is high or low relative to its distribution in the population. Quantile-specific offspring-parent regression slopes (β OP ) were estimated by quantile regression for 6227 offspring-parent pairs. Quantile-specific heritability (h 2 ), estimated by 2β OP /(1 + $\Gamma$ spouse ), decreased 0.0047 ± 0.0007 (P = 2.9 × 10 -14 ) for each one-percent decrement in fasting triglyceride concentrations, i.e., h 2 ± SE were: 0.428 ± 0.059, 0.230 ± 0.030, 0.111 ± 0.015, 0.050 ± 0.016, and 0.033 ± 0.010 at the 90th, 75th, 50th, 25th, and 10th percentiles of the triglyceride distribution, respectively. Consistent with quantile-dependent expressivity, 11 drug studies report smaller genotype differences at lower (post-treatment) than higher (pre-treatment) triglyceride concentrations. This meant genotype-specific triglyceride changes could not move in parallel when triglycerides were decreased pharmacologically, so that subtracting pre-treatment from post-treatment triglyceride levels necessarily created a greater triglyceride decrease for the genotype with a higher pre-treatment value (purported precision-medicine genetic markers). In addition, sixty-five purported gene-environment interactions were found to be potentially attributable to triglyceride's quantile-dependent expressivity, including gene-adiposity (APOA5, APOB, APOE, GCKR, IRS-1, LPL, MTHFR, PCSK9, PNPLA3, PPARγ2), gene-exercise (APOA1, APOA2, LPL), gene-diet (APOA5, APOE, INSIG2, LPL, MYB, NXPH1, PER2, TNFA), gene-alcohol (ALDH2, APOA5, APOC3, CETP, LPL), gene-smoking (APOC3, CYBA, LPL, USF1), gene-pregnancy (LPL), and gene-insulin resistance interactions (APOE, LPL).

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2020

Quantile-specific heritability of sibling leptin concentrations and its implications for gene-environment interactions

“Quantile-dependent expressivity” occurs when the effect size of a genetic variant depends upon whether the phenotype (e.g., leptin) is high or low relative to its distribution. Leptin concentrations are strongly related to adiposity, whose heritability is quantile dependent. Whether inheritance of leptin concentrations is quantile dependent, and whether this explains the greater heritability in women than men in accordance with their greater adiposity, and explains other gene-environment interactions, remains to be determined. Therefore, leptin and leptin receptor concentrations from 3068 siblings in 1133 sibships from the Framingham Heart Study Third Generation Cohort were analyzed. Free leptin index (FLI) was calculated as the ratio of leptin to soluble leptin receptor concentrations. Full-sib (β FS ) regression slopes were robustly estimated by quantile regression with nonparametric significance assigned from 1000 bootstrap samples. The analyses showed β FS increased significantly with increasing percentiles of the offspring’s age- and sex-adjusted leptin distribution (P linear = 0.0001), which was accelerated at the higher concentrations (P quadratic = 0.0003). β FS at the 90th percentile (0.418 ± 0.066) was 4.7-fold greater than at the 10th percentile (0.089 ± 0.032, P difference = 3.6 × 10 –6 ). Consistent with quantile-dependent expressivity, the β FS was greater in female sibs, which was attributable to their higher leptin concentrations. Reported gene-environment interactions involving adiposity and LEP , LEPR , MnSOD , PPARγ , PPARγ2 , and IRS-1 polymorphisms were consistent with quantile-dependent expressivity of leptin concentrations. β FS for leptin receptor concentrations and free leptin index also increased significantly with increasing percentiles of their distributions (P linear = 0.04 and P linear = 8.5 × 10 –6 , respectively). In conclusion, inherited genetic and shared environmental effects on leptin concentrations were quantile dependent, which likely explains male–female differences in heritability and some gene-environment interactions.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2021

QUBO formulations for training machine learning models

Abstract Training machine learning models on classical computers is usually a time and compute intensive process. With Moore’s law nearing its inevitable end and an ever-increasing demand for large-scale data analysis using machine learning, we must leverage non-conventional computing paradigms like quantum computing to train machine learning models efficiently. Adiabatic quantum computers can approximately solve NP-hard problems, such as the quadratic unconstrained binary optimization (QUBO), faster than classical computers. Since many machine learning problems are also NP-hard, we believe adiabatic quantum computers might be instrumental in training machine learning models efficiently in the post Moore’s law era. In order to solve problems on adiabatic quantum computers, they must be formulated as QUBO problems, which is very challenging. In this paper, we formulate the training problems of three machine learning models—linear regression, support vector machine (SVM) and balanced k-means clustering—as QUBO problems, making them conducive to be trained on adiabatic quantum computers. We also analyze the computational complexities of our formulations and compare them to corresponding state-of-the-art classical approaches. We show that the time and space complexities of our formulations are better (in case of SVM and balanced k-means clustering) or equivalent (in case of linear regression) to their classical counterparts.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Uncertainty quantification for Bayesian active learning in rupture life prediction of ferritic steels

Abstract Three probabilistic methodologies are developed for predicting the long-term creep rupture life of 9–12 wt%Cr ferritic-martensitic steels using their chemical and processing parameters. The framework developed in this research strives to simultaneously make efficient inference along with associated risk, i.e., the uncertainty of estimation. The study highlights the limitations of applying probabilistic machine learning to model creep life and provides suggestions as to how this might be alleviated to make an efficient and accurate model with the evaluation of epistemic uncertainty of each prediction. Based on extensive experimentation, Gaussian Process Regression yielded more accurate inference ( $$Pearson\;correlation\;coefficent> 0.95$$ P e a r s o n c o r r e l a t i o n c o e f f i c e n t > 0.95 for the holdout test set) in addition to meaningful uncertainty estimate (i.e., coverage ranges from 94 to 98% for the test set) as compared to quantile regression and natural gradient boosting algorithm. Furthermore, the possibility of an active learning framework to iteratively explore the material space intelligently was demonstrated by simulating the experimental data collection process. This framework can be subsequently deployed to improve model performance or to explore new alloy domains with minimal experimental effort.

20 FOSSIL-FUELED POWER PLANTS↗

DOE OSTI2022

Cost function for low-dimensional manifold topology assessment

Abstract In reduced-order modeling, complex systems that exhibit high state-space dimensionality are described and evolved using a small number of parameters. These parameters can be obtained in a data-driven way, where a high-dimensional dataset is projected onto a lower-dimensional basis. A complex system is then restricted to states on a low-dimensional manifold where it can be efficiently modeled. While this approach brings computational benefits, obtaining a good quality of the manifold topology becomes a crucial aspect when models, such as nonlinear regression, are built on top of the manifold. Here, we present a quantitative metric for characterizing manifold topologies. Our metric pays attention to non-uniqueness and spatial gradients in physical quantities of interest, and can be applied to manifolds of arbitrary dimensionality. Using the metric as a cost function in optimization algorithms, we show that optimized low-dimensional projections can be found. We delineate a few applications of the cost function to datasets representing argon plasma, reacting flows and atmospheric pollutant dispersion. We demonstrate how the cost function can assess various dimensionality reduction and manifold learning techniques as well as data preprocessing strategies in their capacity to yield quality low-dimensional projections. We show that improved manifold topologies can facilitate building nonlinear regression models.

42 ENGINEERING↗

DOE OSTI2024

Intercomparison of sensible and latent heat flux measurements from combined eddy covariance, energy balance, and Bowen ratio methods above a grassland prairie

We present a comparison of four different methods of measuring sensible (H) and latent (LE) heat fluxes for a year over a mixed grass prairie ecosystem in the Nebraska SandHills [eddy covariance (EC), energy balance/Bowen ratio (EBBR), residual energy (RES), modified Bowen ratio (MBR) methods]. Additionally, we developed a set of quality control criteria for each method and present a simplification to the traditional EBBR setup. Using EC as reference, all methods yielded similar estimates of yearly H (regression slopes (m) ~ 2% from unity; H EC > H EBBR , H RES , and H MBR ). For yearly LE, EBBR and RES yielded similar estimates with EC (m ~ 2% from unity; LE EC < LE EBBR and LE RES ), while a larger bias was found from MBR (m ~ 8% from unity; LE EC > LE MBR ). At shorter time scales (~ hourly), moderate scatter was found about linear regression fits for H between EBBR and EC (R 2 = 0.81), with smaller scatter between RES and MBR, and EC (R 2 = 0.91). For LE, smaller scatter was also measured between EC, and EBBR and RES (R 2 = 0.89 and 0.87, respectively), with the larger scatter between EC and MBR (R 2 = 0.65). This suggests methods other than EC may be well suited to longer-term applications (≥ yearly), but have larger uncertainty on individual measurements.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

The Q 10 of in situ microbial soil respiration varies with mean annual temperature, precipitation, pH, and plant cover: a meta-analysis and spatial prediction of Q 10

The temperature sensitivity of soil microbial respiration, commonly quantified using the Q 10 coefficient, is a key parameter in carbon cycle models. Uncovering how environmental factors affect in situ Q 10 values can therefore provide critical insight into potential shifts in global carbon stocks under climate change. We collected data from previously published field experiments that measured soil microbial respiration across a range of temperatures. We hypothesized that the Q 10 coefficient of in situ soil microbial respiration would vary based on environmental factors including mean annual temperature (MAT), mean annual precipitation (MAP), plant cover type, pH, soil C:N, and latitude. Linear regression revealed that Q 10 correlates negatively with MAT and MAP and positively with pH and absolute latitude. Additionally, average Q 10 varied significantly across different plant cover types; it was highest in mountain grasslands and lowest in tropical moist forests. Variation in microbial Q 10 across environmental factors may arise from underlying mechanisms such as enzyme kinetics, substrate availability and complexity, and microbial adaptation. To capture patterns in Q 10 more comprehensively, we developed a multiple linear regression model of Q 10 based on the most individually significant environmental drivers and applied it to public datasets to generate a global map of predicted Q 10 . Q 10 was higher in high-latitude and high-altitude regions, where large permafrost carbon stores are vulnerable to thawing and decomposition. We also compared fits between the Q 10 equation and a model produced from macromolecular rate theory (MMRT). We found that the MMRT model had the superior fit and may be better suited to model temperature sensitivity of complex biological reactions. Overall, our results emphasize that relationships between microbial Q 10 and environmental variables should be accounted for in climate models. Incorporating these variations in the Q 10 parameter, rather than using a fixed value, will help predict whether CO 2 emissions will be buffered or exacerbated by soil microbial respiration under climate change.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Machine learning prediction of incidence of Alzheimer’s disease using large-scale administrative health data

Nationwide population-based cohort provides a new opportunity to build an automated risk prediction model based on individuals’ history of health and healthcare beyond existing risk prediction models. We tested the possibility of machine learning models to predict future incidence of Alzheimer’s disease (AD) using large-scale administrative health data. From the Korean National Health Insurance Service database between 2002 and 2010, we obtained de-identified health data in elders above 65 years (N = 40,736) containing 4,894 unique clinical features including ICD-10 codes, medication codes, laboratory values, history of personal and family illness and socio-demographics. To define incident AD we considered two operational definitions: “definite AD” with diagnostic codes and dementia medication (n = 614) and “probable AD” with only diagnosis (n = 2026). We trained and validated random forest, support vector machine and logistic regression to predict incident AD in 1, 2, 3, and 4 subsequent years. For predicting future incidence of AD in balanced samples (bootstrapping), the machine learning models showed reasonable performance in 1-year prediction with AUC of 0.775 and 0.759, based on “definite AD” and “probable AD” outcomes, respectively; in 2-year, 0.730 and 0.693; in 3-year, 0.677 and 0.644; in 4-year, 0.725 and 0.683. The results were similar when the entire (unbalanced) samples were used. Important clinical features selected in logistic regression included hemoglobin level, age and urine protein level. This study may shed a light on the utility of the data-driven machine learning model based on large-scale administrative health data in AD risk prediction, which may enable better selection of individuals at risk for AD in clinical trials or early detection in clinical settings.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Discovering nuclear models from symbolic machine learning

Numerous phenomenological nuclear models have been proposed to describe specific observables within different regions of the nuclear chart. However, developing a unified model that describes the complex behavior of all nuclei remains an open challenge. Here, we explore whether symbolic Machine Learning (ML) can rediscover traditional nuclear physics models or identify alternatives with improved simplicity, fidelity, and predictive power. To address this challenge, we developed a Multi-objective Iterated Symbolic Regression approach that handles symbolic regressions over multiple target observables, accounts for experimental uncertainties and is robust against high-dimensional problems. As a proof of principle, we applied this method to describe the nuclear binding energies and charge radii of light and medium mass nuclei. Our approach identified simple analytical relationships based on the number of protons and neutrons, providing interpretable models with precision comparable to state-of-the-art nuclear models. Additionally, we integrated this ML-discovered model with an existing complementary model to estimate the limits of nuclear stability. These results highlight the potential of symbolic ML to develop accurate nuclear models and guide our description of complex many-body problems.

Nuclear structure↗

DOE OSTI2023

Band gap predictions of double perovskite oxides using machine learning

Abstract The compositional and structural variety inherent to oxide perovskites spawn wide-ranging applications. In perovskites, the band gap E g , a key material parameter for these applications, can be optimally controlled by varying the composition. Here, we implement a hierarchical screening process in which two cross-validated and predictive machine learning models for band gap classification and regression, trained using exhaustive datasets that span 68 elements of the periodic table, are applied sequentially. The classification model separates wide band gap materials, with E g ≥ 0.5 eV, from materials which have zero or relatively small band gaps, namely E g < 0.5 eV, and the second regression model quantitatively predicts the gap value of the wide band gap compounds. The study down-selects 13,589 cubic oxide perovskite compositions that are predicted to be experimentally formable, thermodynamically stable, and have a wide band gap. Of these, a subset of 310 compounds, which are predicted to be stable and formable with a confidence greater than 90%, are identified for further investigation. Our models are methodically analyzed via performance metrics and inter-dependence of model features to gain physical insight into the band gap prediction problem. Design maps to identify the variation of band gap with substitution of different elements are also presented.

36 MATERIALS SCIENCE↗

DOE OSTI2016

Satellite NO 2 retrievals suggest China has exceeded its NO x reduction goals from the twelfth Five-Year Plan

China’s twelfth Five-Year Plan included pollution control measures with a goal of reducing national emissions of nitrogen oxides (NO x ) by 10% by 2015 compared with 2010. Multiple linear regression analysis was used on 11-year time series of all nitrogen dioxide (NO 2 ) pixels from the Ozone Monitoring Instrument (OMI) over 18 NO 2 hotspots in China. The regression analysis accounted for variations in meteorology, pixel resolution, seasonal effects, weekday variability and year-to-year variability. The NO 2 trends suggested that there was an increase in NO 2 columns in most areas from 2005 to around 2011 which was followed by a strong decrease continuing through 2015. The satellite results were in good agreement with the annual official NO x emission inventories which were available up until 2014. We show the value of evaluating trends in emission inventories using satellite retrievals. It further shows that recent control strategies were effective in reducing emissions and that recent economic transformations in China may be having an effect on NO 2 columns. The satellite information for 2015 suggests that emissions have continued to decrease since the latest inventories available and have surpassed the goals of the twelfth Five-Year Plan.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2018

Solvent-free spectroscopic method for high-throughput, quantitative screening of fatty acids in yeast biomass

Sustainable biofuels and bioproducts technologies are being developed by fermentation of sugars present and released from pretreated cellulosic biomass to lipids using oleaginous yeasts. Detailed analytical characterization of lipid content through cultivation under different scenarios not only is a bottleneck that slows down development of improved strains and processes, this process also creates significant chemical waste. Since lipids exhibit a dominant, distinct, and unique fingerprint in the NIR spectrum, the use of multivariate linear regression of respective wavelengths can be used for the prediction of intracellular lipid content present in the yeast biomass. In this work, we present data on the multivariate quantitative correlation of NIR spectra with measured lipid content in different oleaginous yeast strains. This work is the first demonstration of the rapid, non-destructive, lipid quantification on as little as 10 mg of yeast biomass in a 96-well format, preventing significant chemical pollution by applying a real-time monitoring process. We demonstrate a distinct correlation of lipid content with the accumulation of select fatty acids of the lipids for 5 different yeast species, among which, for S. cerevisiae and L. starkeyi , in-depth calibration curves were developed from 65 and 154 unique samples, respectively. Laslty, we demonstrate that NIR spectra can be used to accurately predict intracellular lipid content using multivariate linear regression analysis in a manner of minutes, avoiding the need for lengthy chemical analyses that are resource intensive.

09 BIOMASS FUELS↗

DOE OSTI2019

Hammett neural networks: prediction of frontier orbital energies of tungsten–benzylidyne photoredox complexes

The successful application of Hammett parameters as input features for regressive machine learning models is demonstrated and applied to predict energies of frontier orbitals of highly reducing tungsten–benzylidyne complexes of the form W($\equiv$]CArR)L 4 X. Using a reference molecular framework and the meta- and para-substituent Hammett parameters of the ligands, the models predict energies of frontier orbitals that correlate with redox potentials. The regressive models capture the multivariate character of electron-donating trends as influenced by multiple substituents even for non-aryl ligands, harnessing the breadth of Hammett parameters in a generalized model. We find a tungsten catalyst with tetramethylethylenediamine (tmeda) equatorial ligands and axial methoxyl substituents that should attract significant experimental interest since it is predicted to be highly reducing when photoactivated with visible light. The utilization of Hammett parameters in this study presents a generalizable and compact representation for exploring the effects of ligand substitutions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗