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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 OSTI2026

Convergence Criteria for Multiphysics Simulations

The behavior of engineered systems is often influenced by multiple physical phenomena, such as mechanical deformation, heat transfer, and chemical species transport and reactions. There are often strong interactions between these phenomena, and there is increasing interest in applying coupled-physics models to improve understanding of physical behavior under complex environmental conditions. Multiple simulation frameworks that facilitate coupled-physics simulations are in widespread use, and these employ a variety of techniques to account for interactions between those physics. Many frameworks solve the physics models independently and transfer results between them. Alternatively, a single monolithic system of equations for every physics model can be formed and solved. Each of these approaches has its benefits and drawbacks, and the optimal approach varies depending on the nature of the problem. The open-source MOOSE framework was developed targeting solution of large-scale multiphysics problems. Although it provides options for all these coupling approaches, its standard approach for multiphysics solutions is to form and solve a single monolithic system of equations containing the unknowns for all physics models. MOOSE provides a streamlined approach for users to define the solution variables, the terms in the partial differential equations pertaining to each variable, and interactions between solution variables. One aspect of the monolithic solution approach that can be problematic, however, is defining appropriate convergence criteria for the nonlinear system. A standard approach is to determine convergence is to simply take a norm of the residual vector corresponding to the full vector of unknowns. However, if the residual vector contains variables for multiple physics models, the magnitudes of those variables can differ significantly, and the variables can converge at significantly different rates from each other. It is important to ensure that the variables for each of the physics are converged, and also ensure that the convergence criteria are not excessively stringent in cases when there is little change in the solution. This talk presents representative multiphysics problems to highlight these issues, and shows strategies for convergence criteria in MOOSE that are robust for multiphysics models under a variety of conditions.

97 - MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Modelling the Sensitivity of Yukon River Biogeochemical Dynamics to Environmental and Chemical Drivers: Implications for Dissolved Organic Carbon

Riverine dissolved organic carbon (DOC) is a critical biogeochemical component that transmits information from Arctic soils to the Arctic Ocean, significantly influencing carbon dynamics in this unique ecosystem. As DOC travels downstream, it undergoes transformations that alter its composition and fate. The Yukon River serves as an effective testbed for modelling these dynamics, offering sufficient scale to capture key biogeochemical processes while having a simpler hydrology than other major Arctic rivers, as well as long-term DOC observational data for model validation. To investigate DOC transformations during transit in the Yukon River, we adapted our Arctic Riverine Organic Macromolecular Model by applying regional-specific parameterisations. Our model simulates the transport and transformation of 15 organic macromolecules, including CDOM (coloured dissolved organic matter), proteins, polysaccharides, lipids, lignin phenols, and humic substances. Initial DOC concentrations were derived from observed soil organic carbon stocks in the surrounding watershed, while chemical transformations and hydrological dynamics were modelled along the river's course. Sensitivity and uncertainty analyses were conducted using a Monte Carlo approach under two experimental setups. Results revealed that variability in DOC and CDOM concentrations at the river mouth were predominantly driven by initial DOC concentration (~70% of variability explained) and dilution at confluence points (~10%). The refractory fraction of DOC explained 21%–88% of the variability in 14 macromolecular concentrations and ranked in the top five sensitive parameters for all outputs when a uniform parameter distribution was assumed. However, when a more likely variability was applied to this parameter, its influence on DOC and CDOM decreased. Given that refractory DOC accounts for ~80% of total DOC in Arctic Rivers, this suggests that most DOC resists degradation and retains its chemical composition during transport to the coastal environment. River velocity, which determines residence time, explained 8%–47% of the variability in protein, polysaccharide, lipid, pigments, and lignin phenols at the river mouth. In contrast, chemical turnover times contributed only 1%–5% to output variability. Our findings underscore the need for improved land-specific headwater observations, including seasonal soil moisture and lateral transport dynamics that control the initial tributary-specific DOC inputs. With accelerated permafrost thaw and increasing river discharge, extending our model to other Arctic River systems and seasons will enhance understanding of Arctic riverine carbon fluxes and their contributions to the Arctic Ocean.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

The active CGCG 077-102 NED02 galaxy within the Abell 2063 galaxy cluster

Context.Within the framework of investigating the link between the central super massive black holes in the cores of galaxies and the galaxies themselves, we detected a variable X-ray source in the center of CGCG 077-102 NED02, which is a member of the CGCG 077-102 galaxy pair within the Abell 2063 cluster of galaxies. Aims.Our goal is to combine X-ray and optical data to demonstrate that this object harbors an active super massive black hole in its core, and to relate this to the dynamical status of the galaxy pair within the Abell 2063 cluster. Methods.We usedChandraandXMM-Newtonarchival data to derive the X-ray spectral shape and variability. We also obtained optical spectroscopy to detect the expected emission lines that are typically found in active galactic nuclei. Finally, we used public ZTF imaging data to investigate the optical variability. Results.There is no evidence of multiple X-ray sources or extended components within CGCG 077-102 NED02. Single X-ray spectral models fit the source well. We detect significant, nonrandom inter-observation 0.5–10 keV X-ray flux variabilities, for observations separated by ∼4 days for short-term variations and by up to ∼700 days for long-term variations. Optical spectroscopy points toward a passive galaxy for CGCG 077-102 NED01 and a Seyfert for CGCG 077-102 NED02. The classification of CGCG 077-102 NED02 is also consistent with its X-ray luminosity of over 10 42 erg s −1 . We do not detect short-term variability in the optical ZTF light curves. However, we find a significant long-term stochastic variability in theg-band that can be well described by the damped random walk model with a best-fit characteristic damping timescale ofτ DRW = 30 −12 +28 days. Finally, the CGCG 077-102 galaxy pair is deeply embedded within the Abell 2063 potential, with a long enough history within this massive structure to have been affected by the influence of this cluster for a long time. Conclusions.Our observations point toward a moderately massive black hole in the center of CGCG 077-102 NED02 of ∼10 6 M ⊙ . As compared to another similar pair in the literature, CGCG 077-102 NED02 is not heavily obscured, perhaps because of the surrounding intracluster medium ram-pressure stripping.

Astronomy & Astrophysics↗

DOE OSTI2024

Physical discovery in representation learning via conditioning on prior knowledge

Recent advances in electron, scanning probe, optical, and chemical imaging and spectroscopy yield bespoke data sets containing the information of structure and functionality of complex systems. In many cases, the resulting data sets are underpinned by low-dimensional simple representations encoding the factors of variability within the data. The representation learning methods seek to discover these factors of variability, ideally further connecting them with relevant physical mechanisms. However, generally, the task of identifying the latent variables corresponding to actual physical mechanisms is extremely complex. Here, we present an empirical study of an approach based on conditioning the data on the known (continuous) physical parameters and systematically compare it with the previously introduced approach based on the invariant variational autoencoders. The conditional variational autoencoder (cVAE) approach does not rely on the existence of the invariant transforms and hence allows for much greater flexibility and applicability. Interestingly, cVAE allows for limited extrapolation outside of the original domain of the conditional variable. However, this extrapolation is limited compared to the cases when true physical mechanisms are known, and the physical factor of variability can be disentangled in full. We further show that introducing the known conditioning results in the simplification of the latent distribution if the conditioning vector is correlated with the factor of variability in the data, thus allowing us to separate relevant physical factors. We initially demonstrate this approach using 1D and 2D examples on a synthetic data set and then extend it to the analysis of experimental data on ferroelectric domain dynamics visualized via piezoresponse force microscopy.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2024

The rate of extreme coronal line emitting galaxies in the Sloan Digital Sky Survey and their relation to tidal disruption events

High-ionization iron coronal lines (CLs) are a rare phenomenon observed in galaxy and quasi-stellar object spectra that are thought to be created by high-energy emission from active galactic nuclei and certain types of transients. In cases known as extreme coronal line emitting galaxies (ECLEs), these CLs are strong and fade away on a time-scale of years. The most likely progenitors of these variable CLs are tidal disruption events (TDEs), which produce sufficient high-energy emission to create and sustain the CLs over these time-scales. To test the possible connection between ECLEs and TDEs, we present the most complete variable ECLE rate calculation to date and compare the results to TDE rates from the literature. To achieve this, we search for ECLEs in the Sloan Digital Sky Survey (SDSS). We detect sufficiently strong CLs in 16 galaxies, more than doubling the number previously found in SDSS. Using follow-up spectra from the Dark Energy Spectroscopic Instrument and Gemini Multi-Object Spectrograph, Wide-field Infrared Survey Explorer mid-infrared observations, and Liverpool Telescope optical photometry, we find that none of the nine new ECLEs evolve in a manner consistent with that of the five previously discovered variable ECLEs. Using this sample of five variable ECLEs, we calculate the galaxy-normalized rate of variable ECLEs in SDSS to be $R_\mathrm{G}=3.6~^{+2.6}_{-1.8}~(\mathrm{statistical})~^{+5.1}_{-0.0}~(\mathrm{systematic})\times 10^{-6}~\mathrm{galaxy}^{-1}~\mathrm{yr}^{-1}$. The mass-normalized rate is $R_\mathrm{M}=3.1~^{+2.3}_{-1.5}~(\mathrm{statistical})~^{+4.4}_{-0.0}~(\mathrm{systematic})\times 10^{-17}~\mathrm{M_\odot ^{-1}}~\mathrm{yr}^{-1}$ and the volumetric rate is $R_\mathrm{V}=7~^{+20}_{-5}~(\mathrm{statistical})~^{+10}_{-0.0}~(\mathrm{systematic})\times 10^{-9}~\mathrm{Mpc}^{-3}~\mathrm{yr}^{-1}$. Our rates are one to two orders of magnitude lower than TDE rates from the literature, which suggests that only 10–40 per cent of all TDEs produce variable ECLEs. Additional uncertainties in the rates arising from the structure of the interstellar medium have yet to be included.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2026

Fast Active-Set Thresholding Method for Nonnegative Least Squares

Nonnegative Least Squares (NNLS) is a fundamental constrained optimization problem encountered in many applications such as image deblurring, signal processing, nonnegative matrix factorization, magnetic microscopy, and hyperspectral imaging. Active-set based methods are a common class of algorithms for solving NNLS which identify the optimal variable set of the NNLS solution. They do so by iteratively solving a series of unconstrained least squares problems, identifying which variables violate the nonnegativity constraints, and then swapping variables in/out of consideration until the optimal set of variables is found. Several variations improving upon this method exist in the literature. In this work, we propose an active-set swap heuristic which further improves upon existing active-set based methods for NNLS. Our optimizations are based upon adding multiple variables to the passive set within a threshold of the smallest gradient value and removing variables within a similar threshold of the closest boundary constraint. We leverage these optimizations to yield a Fast Active-Set Thresholding NNLS (FAST-NNLS) algorithm which significantly outperforms the existing state-of-the-art NNLS algorithms for a wide range of problems. Rigorous convergence guarantees are proven for the proposed method. We demonstrate the effectiveness of our proposed method on multiple synthetic datasets and two realworld text analysis applications. In doing so, we present the most comprehensive NNLS solver comparison in the literature to date.

Cobb, Benjamin [Georgia Institute of Technology]↗

DOE OSTI2025

HydroFish: freshwater fish co-occurrence with hydropower plants and non-powered dams in conterminous United States sub-basins

The HydroFish dataset lists all existing hydropower plants (EHAs) and non-powered dams (NPDs; ≥ 0.001 MW potential nominal capacity), delineates the hydrologic sub-basins in which they are situated, and then lists all freshwater fish species reported to occur in those sub-basins. This dataset was compiled using the HydroBio dataset (https://hydrosource.ornl.gov/data/datasets/hydrobio/) and contains 24 total variables that describe hydrologic sub-basins, each unique EHA (plant ID and name, geographic coordinates, permit type, capacity, etc.) and NPD (ID value, known names, geographic coordinates, and estimated potential nominal capacity), and freshwater fish species in the sub-basin (common and scientific name, origin, and migratory and threat status). The HydroBio dataset was built using Oak Ridge National Laboratory’s Existing Hydropower Assets Dataset (2024 version) and Non-powered Dam Technical Potential Dataset (2024 version), and NatureServe’s fish species distribution dataset (2023 version). The dataset also contains summary variables that report the unique number of EHAs, NPDs, and freshwater fish species per sub-basin. The HydroFish dataset contains two unique data files: 1) a .csv metadata file describing the dataset variables, and 2) a .csv data file containing the actual dataset. Note that there may be many rows per unique existing hydropower plant or non-powered dam given that distinct species are listed per existing plant or NPD per sub-basin. The dataset is downloadable as a zip file containing the metadata and dataset files.

Bozeman, Bryan [Oak Ridge National Laboratory (ORN↗

DOE OSTI2025

Using feature importance as an exploratory data analysis tool on Earth system models

Abstract. Machine learning (ML) models are commonly used to generate predictions, but these models can also support the discovery of new science. Generating accurate predictions necessitates that a model captures the structure of the underlying data. If the structure is properly extracted, ML could be a useful exploratory and evidential tool. In this paper, we present a case study that demonstrates the use of ML for exploratory data analysis (EDA) in the climate space. We apply the ML explainability method of spatiotemporal zeroed feature importance (stZFI) to understand how climate-variable associations evolve over space and time. Our analyses focus on data from ensembles of Earth system models (ESMs) which provide data on different climate states and conditions. We elect to work with ESM ensembles since they allow us to compare feature importance across alternative scenarios not available with observed data. The ensembles also account for natural variability so that we can distinguish between signal and noise due to natural climate variability when computing feature importance. The use of perturbed initial condition ensembles introduces variability mimicking the natural variability in the atmosphere; thus the signals emerging using feature importance (FI) can be evaluated against the natural variability in the climate system. For our analyses, we consider the 1991 volcanic eruption of Mount Pinatubo, which was a large stratospheric aerosol injection. We explore the climate pathway associated with the eruption from aerosols to radiation to temperature at both the near-surface and stratospheric levels. In addition to applying the method to data generated from two different ESMs, we apply stZFI to reanalysis data to compare the associations identified by stZFI. We show how stZFI tracks the importance of aerosol optical depth over time on forecasting temperatures. This case study illustrates usefulness of an ML tool (stZFI) for EDA on a well-studied climate exemplar.

Ries, Daniel (ORCID:0000000250294647)↗

DOE OSTI2025

Global teleconnections influencing large-scale drought in the United States using SVDI

Understanding recent large-scale drought patterns and the mechanisms producing extreme drought events is vital for future drought forecasts and understanding future drought risks. Increasingly, vapor pressure deficit (VPD) has been used as an important measure of evaporative demand and proxy for drought detection. In this study, VPD is used to calculate the new Standardized VPD Drought Index (SVDI) with NASA North American Land Data Assimilation System (NLDAS) data. Previous studies have shown that SVDI accurately identifies the timing and magnitude short-term droughts in the United States (U.S). In the present study, SVDI is now used to identify large-scale drought patterns between 1980 and 2021 and drought variability driven by selected global teleconnections originating in the Pacific and Atlantic Oceans. Spatial drought characteristics were extracted from SVDI using empirical orthogonal function (EOF) analysis. Then a k-means clustering algorithm was applied to both EOF principal components and primary teleconnections, including the El Nino-Southern Oscillation (ENSO) and Pacific Decadal Oscillation (PDO) to identify drought events driven by the Pacific Ocean. Results show that the SVDI is useful in evaluating large-scale drought variability in the U.S. related to global teleconnections, and that mechanisms influencing summer drought patterns in the Western and Southwestern U.S. are driven by a tropical-extratropical interactions originating in the equatorial Pacific Ocean related to ENSO dynamics with interdecadal variability modulated by PDO. The large-scale droughts in the Central and Southern U.S., like those in 2011 and 2012, on the other hand, are driven by the North Pacific Ocean warm pool during a strong negative PDO, which subsequently influenced variability in the Bermuda-Azores High in the Atlantic Ocean. In summer 2011, the Bermuda-Azores High weakened, reducing the onshore winds and moisture transport along the eastern Gulf of Mexico and contributing to ongoing drought in the region. The Northern Pacific and Atlantic Ocean sea surface temperatures (SSTs) have increased between 1980 and 2021. In conclusion, as SSTs continue to rise in the Northern Pacific Ocean, one consequence of the coupled North Pacific warm pool and atmospheric dynamics, is to increase summer drought variability over a large region in the southern and midwestern U.S. under global warming.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Evaluation of Autoconversion Representation in E3SMv2 Using an Ensemble of Large-Eddy Simulations of Low-Level Warm Clouds

In numerical atmospheric models that treat cloud and rain droplet populations as separate condensate categories, precipitation initiation in warm clouds is often represented by an autoconversion rate (Au), which is the rate of formation of new rain droplets through the collisions of cloud droplets. Being a function of the cloud droplet size distribution (DSD), the local Au is commonly parameterized as a function of DSD moments: cloud droplet number (n c ) and mass (q c ) concentrations. When applied in a large-scale model, the grid-mean Au must also include a correction, or enhancement factor, to account for the horizontal variability of the cloud properties across the model grid. In this study, we evaluate the Au representation in the Energy Exascale Earth System Model version 2 (E3SMv2) climate model using large-eddy simulations (LES), which explicitly resolve cloud droplet spectra, and therefore the local Au, as well as its spatial variability. The analysis of an ensemble of warm low-level cloud cases shows that the E3SMv2 formulation represents the Au reasonably well compared to the horizontally averaged explicitly computed rate from LES. The agreement, however, comes from a combination of an underestimated E3SM-tuned local Au rate and an overestimated subgrid cloud variability enhancement factor. The latter bias is traced to neglecting the horizontal variability of n c and its co-variability with q c in parameterizing the grid-mean Au.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

Forced Component Estimation Statistical Method Intercomparison Project (ForceSMIP)

Anthropogenic climate change is unfolding rapidly, yet its regional manifestation can be obscured by internal variability. A primary goal of climate science is to identify the externally forced climate response from among the noise of internal variability. Separating the forced response from internal variability can be addressed in climate models by using a large ensemble to average over different possible realizations of internal variability. However, with only one realization of the real world, it is a major challenge to isolate the forced response directly in observations. In the Forced Component Estimation Statistical Method Intercomparison Project (ForceSMIP), contributors used existing and newly developed statistical and machine learning methods to estimate the forced response over 1950–2022 within individual realizations of the climate system. Participants used neural networks, linear inverse models, fingerprinting methods, and low-frequency component analysis, among other approaches. These methods were trained using large ensembles from multiple climate models and then applied to observations. Here, we evaluate method performance within large ensembles and investigate the estimates of the forced response in observations. Our results show that many different types of methods are skillful for estimating the forced response in climate models, though the relative skill of individual methods varies depending on the variable and evaluation metric. Methods with comparable skill in models can give a wide range of estimates of the forced response pattern in observations, illustrating the epistemic uncertainty in forced response estimates. ForceSMIP gives new insights into the forced response in observations, its uncertainty, and methods for its estimation.

Climate attribution↗

DOE OSTI2025

Evapotranspiration Partitioning Using Flux Tower Data in a Semi-Arid Ecosystem

Information about evapotranspiration (ET) and its components, that is, evaporation and transpiration, is crucial for a wide range of water and ecosystem management applications. However, partitioning ET into its two components is often challenging because of their spatiotemporal variabilities and lack of process understanding. This study developed a machine learning (ML) framework to shed light on ET processes and assess the relative importance of different drivers by incorporating hydrometeorology and biomass productivity variables. The Shapley Additive Explanations (SHAP) approach was applied to enhance explainability and rank the importance of ET drivers and their components. A total of 62 variables covering hydrometeorological and biomass productivity dimensions were considered from the Reynolds Creek Critical Zone Observatory (CZO) station in Idaho. The variable importance assessment identified the leading drivers individually for evaporation, transpiration and ET (soil water content for evaporation, vapour pressure deficit for transpiration and soil water content for ET). The results further highlighted the value of combining hydrometeorological and biomass productivity variables to achieve better predictability of ET processes.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Monitoring covariance in multivariate time series: Comparing machine learning and statistical approaches

Abstract In complex systems with multiple variables monitored at high‐frequency, variables are not only temporally autocorrelated, but they may also be nonlinearly related or exhibit nonstationarity as the inputs or operation changes. One approach to handling such variables is to detrend them prior to monitoring and then apply control charts that assume independence and stationarity to the residuals. Monitoring controlled systems is even more challenging because the control strategy seeks to maintain variables at prespecified mean levels, and to compensate, correlations among variables may change, making monitoring the covariance essential. In this paper, a vector autoregressive model (VAR) is compared with a multivariate random forest (MRF) and a neural network (NN) for detrending multivariate time series prior to monitoring the covariance of the residuals using a multivariate exponentially weighted moving average (MEWMA) control chart. Machine learning models have an advantage when the data's structure is unknown or may change. We design a novel simulation study with nonlinear, nonstationary, and autocorrelated data to compare the different detrending models and subsequent covariance monitoring. The machine learning models have superior performance for nonlinear and strongly autocorrelated data and similar performance for linear data. An illustration with data from a reverse osmosis process is given.

Weix, Derek↗

DOE OSTI2024

Characterizing climate pathways using feature importance on echo state networks

The 2022 National Defense Strategy of the United States listed climate change as a serious threat to national security. Climate intervention methods, such as stratospheric aerosol injection, have been proposed as mitigation strategies, but the downstream effects of such actions on a complex climate system are not well understood. The development of algorithmic techniques for quantifying relationships between source and impact variables related to a climate event (i.e., a climate pathway) would help inform policy decisions. Data-driven deep learning models have become powerful tools for modeling highly nonlinear relationships and may provide a route to characterize climate variable relationships. In this paper, we explore the use of an echo state network (ESN) for characterizing climate pathways. ESNs are a computationally efficient neural network variation designed for temporal data, and recent work proposes ESNs as a useful tool for forecasting spatiotemporal climate data. However, ESNs are noninterpretable black-box models along with other neural networks. The lack of model transparency poses a hurdle for understanding variable relationships. We address this issue by developing feature importance methods for ESNs in the context of spatiotemporal data to quantify variable relationships captured by the model. We conduct a simulation study to assess and compare the feature importance techniques, and we demonstrate the approach on reanalysis climate data. In the climate application, we consider a time period that includes the 1991 volcanic eruption of Mount Pinatubo. This event was a significant stratospheric aerosol injection, which acts as a proxy for an anthropogenic stratospheric aerosol injection. Furthermore, we are able to use the proposed approach to characterize relationships between pathway variables associated with this event that agree with relationships previously identified by climate scientists.

black-box models↗

DOE OSTI2024

Adaptive immersed isogeometric level-set topology optimization

Here, this paper presents for the first time an adaptive immersed approach for level-set topology optimization using higher-order truncated hierarchical B-spline discretizations for design and state variable fields. Boundaries and interfaces are represented implicitly by the iso-contour of one or multiple level-set functions. An immersed finite element method, the eXtended IsoGeometric Analysis, is used to predict the physical response. The proposed optimization framework affords different adaptively refined higher-order B-spline discretizations for individual design and state variable fields. The increased continuity of higher-order B-spline discretizations together with local refinement enables direct control over the accuracy of the representation of each field while simultaneously reducing computational cost compared to uniformly refined discretizations. A flexible mesh adaptation strategy enables local refinement based on geometric measures or physics-based error indicators. These adaptive discretization and analysis approaches are integrated into gradient-based optimization schemes, evaluating the design sensitivities using the adjoint method. Numerical studies illustrate the features of the proposed framework with static, linear elastic, multi-material, two- and three-dimensional problems. The examples provide insight into the effect of refining the design variable field on the optimization result and the convergence rate of the optimization process. Using coarse higher-order B-spline discretizations for level-set fields promotes the development of smooth designs and suppresses the emergence of small features. Moreover, adaptive mesh refinement for state variable fields results in a reduction of overall computational cost. Higher-order B-spline discretizations are especially interesting when evaluating gradients of state variable fields due to their higher inter-element continuity.

36 MATERIALS SCIENCE↗

DOE OSTI2024

On Gibbs Equilibrium and Hillert Nonequilibrium Thermodynamics

During his time at Royal Institute of Technology (Kungliga Tekniska högskolan) in Sweden, the present author learned nonequilibrium thermodynamics from Mats Hillert. The key concepts are the separation of internal and external variables of a system and the definitions of potentials and molar quantities. In equilibrium thermodynamics derived by Gibbs, the internal variables are not independent and can be fully evaluated from given external variables. While irreversible thermodynamics led by Onsager focuses on internal variables though often mixed with external variables. Hillert integrated them together by first emphasizing their differences and then examining their connections. His philosophy was reflected by the title of his book “Phase Equilibria, Phase Diagrams and Phase Transformations” that puts equilibrium, nonequilibrium, and internal processes on equal footing. Here, in the present paper honoring Hillert, the present author reflects his experiences with Hillert and his work in last 40 years and expresses his gratitude for all the wisdom and support from him in terms of “Hillert nonequilibrium thermodynamics” and discusses some recent topics that the present author has been working on.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Explainable machine learning to quantify the value of proximal remote sensing in latent energy flux estimation

Proximal remote sensing has the potential to provide critical information on vegetation biophysical factors that can predict land-atmosphere exchange of water and energy. Latent energy (LE) flux is traditionally estimated using process-based models which rely on vegetation parameters that change during the growing season. Data-driven models have the potential to address these issues by offering flexible predictor selection and more efficient utilization of the information in predictor sets. These models require careful choice of predictors to avoid redundancy and allow robust cross-validation. In this study we present a systematic and comprehensive evaluation of machine learning (ML) models to assess the capability of meteorological and proximal sensing data for predicting LE at a half-hourly temporal resolution across multiple growing seasons for an agricultural system. The results presented here demonstrate that a model using four environmental predictors in combination with two proximal sensing variables can capture 88 % of the variability in LE. ML models using only three predictors (one meteorological and two proximal remote sensing) captured 81 % of LE variability, offering the best trade-off between performance and complexity. An ML model utilizing only two predictors, one proximal remote sensing variable and downwelling radiation, captured 77 % of LE variability. These results demonstrate the power of proximal remote sensing and meteorological observations to estimate land-atmosphere water vapor exchange, providing a solution where more direct methods such as eddy covariance are not available and for evaluations of agronomic management and genotypic variations.

60 APPLIED LIFE SCIENCES↗