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DOE OSTI2025

SPARTA: A flux adjustment methodology to interpret complex experiments

For the accurate determination of reactivity from a detector count rate, correction of spatial effects is of prime importance. This spatial correction is often provided using simulation methodologies, but this may introduce a bias if the result of the experiment is also used as input data for the simulation. Here, this work presents a flux adjustment methodology able to infer experimental reactivity and correction of spatial effects without the need for a simulation. It can process the signal from a complex experiment such as a heat balance measurement in the TREAT reactor, where control rods are continuously adjusted to maintain a constant power. In the present work, this methodology successfully computed the reactivity and the local spatial variation of the flux of a generated signal. It also proved to be robust against noise and errors on kinetic parameters and provides a credible interpretation of a heat balance experiment in TREAT. Efficiency of flux adjustment methods for complex experiment enable a better experiment interpretation less reliant on nuclear data evaluation.

73 - NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Analyzing the impact of design factors on solar module thermomechanical durability using interpretable machine learning techniques

Solar modules in utility-scale systems are expected to maintain decades of lifetime to rival conventional energy sources. However, cyclic thermomechanical loading often degrades their long-term performance, highlighting the importance of effective design to mitigate thermal expansion mismatches between module materials. Given the complex composition of solar modules, isolating the impact of individual components on overall durability remains a challenging task. In this work, we analyze a comprehensive data set that comprises bill-of-materials (BOM) and thermal cycling power loss from 251 distinct module designs to identify the predominant design factors and their impacts on the thermomechanical durability of modules. The methodology of our analysis combines machine learning modeling (random forest) and Shapley additive explanation (SHAP) to correlate design factors with power loss and interpret the model’s decision-making. The interpretation reveals that silicon type (monocrystalline or polycrystalline), encapsulant thickness, busbar numbers, and wafer thickness predominantly influence the degradation. With lower power loss of around 0.6% on average in the SHAP analysis, monocrystalline cells present better durability than polycrystalline cells. This finding is further substantiated by statistical testing on our raw data set. The SHAP analysis also demonstrates that while thicker encapsulants lead to reduced power loss, further increasing their thickness over around 0.6 to 0.7 mm does not yield additional benefits, particularly for the front side one. In addition, other important BOM features such as the number of busbars are analyzed. This study provides a blueprint for utilizing explainable machine learning techniques in a complex material system and can potentially guide future research on optimizing the design of solar modules.

14 SOLAR ENERGY↗

DOE OSTI2026

Interpretable and flexible non-intrusive reduced-order models using reproducing kernel Hilbert spaces

This paper develops an interpretable, non-intrusive reduced-order modeling technique using regularized kernel interpolation. Existing non-intrusive approaches approximate the dynamics of a reduced-order model (ROM) by solving a data-driven least-squares regression problem for low-dimensional matrix operators. Our approach instead leverages regularized kernel interpolation, which yields an optimal approximation of the ROM dynamics from a user-defined reproducing kernel Hilbert space. We show that our kernel-based approach can produce interpretable ROMs whose structure mirrors full-order model structure by embedding judiciously chosen feature maps into the kernel. The approach is flexible and allows a combination of informed structure through feature maps and closure terms via more general nonlinear terms in the kernel. We also derive a computable a posteriori error bound that combines standard error estimates for intrusive projection-based ROMs and kernel interpolants. In conclusion, the approach is demonstrated in several numerical experiments that include comparisons to operator inference using both proper orthogonal decomposition and quadratic manifold dimension reduction.

Data-driven model reduction↗

DOE OSTI2026

Learning interpretable surface elasticity properties from bulk properties via neural network equation learners

Surface elasticity is central to understanding the mechanics and stability of surfaces and interfaces. It is characterized by quantities such as surface tension, residual surface stress, and surface stiffness. However their analytical expressions are typically difficult to derive from atomistic data, and depend strongly on modeling choices. This work presents a neural network-based equation learner which combines customized activation functions and connection-based pruning to discover parsimonious, closed-form equations for surface elasticity from atomistic simulations. Applying the method to seven face-centered cubic (FCC) metals, our equation learner uncovers interpretable equations that describe both low-Miller index and high-Miller index surface properties, capturing long-tail property distributions accurately. The discovered expressions are decoupled into two components: a universal, geometry-driven orientation function, and material-specific baseline coefficients. We find that lower-order properties such as surface tension are fundamentally geometry dependent, while higher-order properties such as surface stress and elasticity show more complex geometry and material dependence. We also relate material dependent coefficients to bulk properties, forming a clear map from bulk material properties to surface elasticity. Overall, this approach demonstrates that interpretable neurosymbolic machine learning can bridge the gap between atomistic simulations and physical laws, enabling the discovery of generalizable structure–property relationships for materials science phenomena such as surface elasticity.

Equation learning↗

DOE OSTI2023

A robust estimator of mutual information for deep learning interpretability

Abstract We develop the use of mutual information (MI), a well-established metric in information theory, to interpret the inner workings of deep learning (DL) models. To accurately estimate MI from a finite number of samples, we present GMM-MI (pronounced ‘Jimmie’), an algorithm based on Gaussian mixture models that can be applied to both discrete and continuous settings. GMM-MI is computationally efficient, robust to the choice of hyperparameters and provides the uncertainty on the MI estimate due to the finite sample size. We extensively validate GMM-MI on toy data for which the ground truth MI is known, comparing its performance against established MI estimators. We then demonstrate the use of our MI estimator in the context of representation learning, working with synthetic data and physical datasets describing highly non-linear processes. We train DL models to encode high-dimensional data within a meaningful compressed (latent) representation, and use GMM-MI to quantify both the level of disentanglement between the latent variables, and their association with relevant physical quantities, thus unlocking the interpretability of the latent representation. We make GMM-MI publicly available in this GitHub repository.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2025

Self-Supervised and Interpretable Anomaly Detection Using Network Transformers

Machine learning and deep neural networks (DNNs) have been proposed as a tool to identify anomalies in computer network communications. However, due the obfuscated nature of off-the-shelf machine learning models, their output often does not provide enough information to isolate the source of the anomaly to take corrective measures. In this article, we introduce the network transformer (NeT), a DNN model for anomaly detection that incorporates the graph structure of the communication network in order to improve interpretability. Further, the presented approach has the following advantages: first, enhanced interpretability by incorporating the graph structure of computer networks; second, provides a hierarchical set of features that enables analysis at different levels of granularity; second, self-supervised training that does not require labeled data. The NeT model was evaluated on a set of anomalous scenarios executed in a real industrial control system. The presented approach successfully identified the anomalies, the devices affected, and the specific connections causing the anomalies, providing a data-driven hierarchical approach to analyze the behavior of a cyber network.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

NLIZE: A Perturbation-Driven Visual Interrogation Tool for Analyzing and Interpreting Natural Language Inference Models

With the recent advances in deep learning, neural network models have obtained state-of-the-art performances for many linguistic tasks in natural language processing. However, this rapid progress also brings enormous challenges. The opaque nature of a neural network model leads to hard-to-debug-systems and difficult-to-interpret mechanisms. Here, we introduce a visualization system that, through a tight yet flexible integration between visualization elements and the underlying model, allows a user to interrogate the model by perturbing the input, internal state, and prediction while observing changes in other parts of the pipeline. We use the natural language inference problem to illustrate how a perturbation-driven paradigm can help domain experts assess the potential limitation of a model, probe its inner states, and interpret and form hypotheses about fundamental model mechanisms such as attention.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Contrasting Carbon–Water–Energy Dynamics in Perennial and Annual Bioenergy Agroecosystems Using Eddy Covariance and Interpretable Machine Learning

Understanding how agroecosystems respond to environmental variability is fundamental to predicting productivity and sustainability under a changing climate. We analyzed 55 site-years of high-frequency eddy covariance observations from five agroecosystems—two perennial grasses (miscanthus and switchgrass), two annual rotation systems (maize–soybean and sorghum–soybean), and a restored native prairie—to examine ecosystem-scale carbon, water, and energy fluxes. Using an interpretable machine-learning framework with regression tree ensembles, Shapley Additive Explanations, and Accumulated Local Effects, we quantified how environmental and temporal factors regulate gross primary productivity (GPP), evapotranspiration (ET), water-use efficiency, and the Bowen ratio. Perennials exhibited stronger physiological buffering and maintained fluxes across a broader range of temperature and moisture conditions, reflecting deeper rooting and persistent canopy cover. Annuals, in contrast, showed greater short-term variability and stronger coupling to atmospheric demand, with GPP and ET declining rapidly under low humidity or soil moisture. Differences in temperature sensitivity of Bowen ratio further revealed that perennials sustained proportionally greater sensible heat flux under cool conditions, whereas annuals exhibited constrained energy exchange when evaporative demand was low. Together, these results demonstrate that crop life cycle and canopy structure are fundamental determinants of ecosystem-scale carbon–water–energy coupling. By integrating long-term flux observations with interpretable machine learning, this study identifies the environmental drivers that shape agroecosystem function and highlights how conversion from annual to perennial feedstocks can enhance climatic resilience and alter land–atmosphere energy feedbacks. These findings provide a data-driven basis for improving crop and Earth-system models and for guiding bioenergy landscape design under future climate scenarios.

Accumulated Local Effects↗

DOE OSTI2023

Improving the Estimation of the Atmospheric Water Vapor Pressure Using Interpretable Long Short-Term Memory Networks: Dataset, Python code, and trained models

Atmospheric water vapor pressure is an essential meteorological control on land surface and hydrologic processes. It is not as frequently observed as other meteorologic conditions, but often inferred through the August–Roche–Magnus formula by simply assuming dew point and daily minimum temperatures are equivalent or by empirically correlating the two temperatures using an aridity correction. The performance of both methods varies considerably across different regions and during different time periods; obtaining consistently accurate estimates across space and time remains a great challenge. We applied an interpretable Long Short-Term Memory (iLSTM) network conditioned on static, location specific attributes to estimate daily vapor pressure for 83 FLUXNET sites in the United States and Canada. This data package includes all raw data of the 83 FLUXNET sites, input data for model training/validation/test, trained models and results, and python codes for the manuscript "Improving the Estimation of the Atmospheric Water Vapor Pressure Using an Interpretable Long Short-term Memory Network". Specifically, it consists of five parts. - First, "1_Daymet_data_83sites.zip" includes raw data downloaded from Daymet for the 83 sites used in the paper according to their longitude and latitude, in which vapor pressure is used. It also includes a pre-processed CSV data file combining all data from the 83 sites which is specifically used for the paper. - Second, "2_Fluxnet2015_data_83sites.zip" includes raw half hourly data of the 83 sites downloaded from FLUXNET2015 data portal, pre-processed daily data of the 83 sites, a CSV file including combined pre-processed daily data of the 83 sites, and a CSV file including the information (site ID, site name, latitude, longitude, data available period) of the 83 sites. - Third, "3_MODIS_LAI_data_83sites_raw.zip" includes raw leaf area index (LAI) data downloaded from the AppEEARs data portal. - Fourth, "4_Scripts.zip" includes all scripts related to model training and post-processing of a trained model, and a jupyter notebook showing an example for model post-processing. Two typo errors in files titled "run2get_args.py" and "postprocess.py" were corrected on March 27, 2024 to avoid confusions. - Finally, "Trained_models_and_results.zip" includes three folders and three files with suffix ".npy", and each folder corresponds to one file with suffix ".npy" with the same title. Each of the three folders include all trained models associated with one iLSTM model configuration (35 models for each configuration, details are described in the paper). Each file with suffix ".npy" includes the post-processed results of the corresponding 35 models under one iLSTM model configuration.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2019

Ecohydrologic separation alters interpreted hydrologic stores and fluxes in a headwater mountain catchment

Recent studies have demonstrated that compartmentalized pools of water preferentially supply either plant transpiration (poorly mobile water) or streamflow and groundwater (highly mobile water) in some catchments, a phenomenon referred to as ecohydrologic separation. Additionally, the omission of processes accounting for ecohydrologic separation in standard applications of hydrological models is expected to influence estimates of water residence times and plant water availability. However, few studies have tested this expectation or investigated how ecohydrologic separation alters interpretations of stores and fluxes of water within a catchment. In this study, we compare two rainfall-runoff models that integrate catchment-scale representations of transport, one that incorporates ecohydrologic separation and one that does not. The models were developed for a second-order watershed at the H.J. Andrews Experimental Forest (Oregon, USA), the site where ecohydrologic separation was first observed, and calibrated against multiple years of stream discharge and chloride concentration. Model structural variations caused mixed results for differences in calibrated parameters and differences in storage between reservoirs. However, large differences in catchment storage volumes and fluxes arise when considering only mobile water. These changes influence interpreted residence times for streamflow-generating water, demonstrating the importance of ecohydrologic separation in catchment-scale water and solute transport.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Interpretations of the ATLAS measurements of Higgs boson production and decay rates and differential cross-sections in pp collisions at $\sqrt{s}$ = 13 TeV

Measurements of the Higgs boson production times decay rates and differential cross-sections have recently been performed by the ATLAS experiment in several decay channels using up to 139 fb -1 of proton-proton collision data at $\sqrt{s}$ = 13 TeV recorded at the Large Hadron Collider. This paper presents multiple interpretations of these Higgs boson measurements. Measurements of production-mode cross-sections, simplified template cross-sections and fiducial differential cross-sections in different decay channels are reparameterised in terms of the impact of Standard Model effective field theory operators, and constraints are reported on the corresponding Wilson coefficients. Production and decay rate measurements are interpreted in UV-complete extensions of the Standard Model, namely the two-Higgs-doublet model (2HDM) near the alignment limit and the Minimal Supersymmetric Standard Model (MSSM) for various MSSM benchmark scenarios. The constraints on the 2HDM parameters (cos(β - α), tanβ) and the MSSM parameters (m A , tanβ) are complementary to those obtained from direct searches for additional Higgs bosons.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Interpretable, extensible linear and symbolic regression models for charge density prediction using a hierarchy of many-body correlation descriptors

Here, density functional theory (DFT) is routinely used to make electronic structure predictions for high-throughput screening of materials and molecules for technologically relevant areas, like the identification of better catalysts, electronic materials, and drug discovery. However, the DFT formalism is limited by (a) its poor (quadratic-to-quartic) scaling, and (b) the need to perform repeated eigenvalue computations of the electronic Hamiltonian as part of its self-consistent field (SCF) iteration procedure to obtain the converged ground state electron density, ρ (r). Approaches that directly predict ρ (r) of a structure with high accuracy can accelerate conventional SCF calculations and can also be used in linearly scaling methods such as orbital-free DFT. To this end, we present a procedure to predict the ground state electron density of molecular and periodic three-dimensional systems directly from the atomic structure with a particular emphasis on physical interpretability. In our framework, ρ (r) is modeled using many-body correlation descriptors that accurately capture the effects of local atomic arrangements in the neighborhood of a grid point. Our use of a linear regression scheme to fit to charge density data enables transparent analysis of the relative contributions of various types of local atomic correlations. By systematically including increasingly complex correlations, our model is shown to accurately predict ρ (r) for a variety of chemically and electronically diverse systems — amorphous Ge, Al(001) slab, crystalline Ga 2 O 3 , molecular benzene, and polyethylene. We then demonstrate a symbolic regression-based protocol to construct easily computable, interpretable features from lower-order correlations that significantly improves our electron density predictions with effectively no increase in the computational cost.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Recommendations to standardize reporting, execution, and interpretation of X-ray Absorption Spectroscopy measurements

In July of 2022, a National Science Foundation (NSF)- and US Department of Energy (DOE)-sponsored workshop was held on the topic of rigor and reproducibility (R&R) in thermal, heterogeneous catalysis. As a result of the workshop, a report has been published entitled "Addressing Rigor and Reproducibility in Thermal, Heterogeneous Catalysis"[1]. This manuscript summarizes one section of the report: "Recommendations for catalyst characterization by X-ray absorption spectroscopy". Here, the section focuses exclusively on X-ray absorption spectroscopy (XAS) and is narrowly focused on recommendations for the collection and interpretation of XAS data for routine experiments. Therefore, one should not expect a detailed guide for each different experiment that one may perform nor are the recommendations designed to be overly prescriptive. However, the report is designed to draw attention to key pitfalls and common problems in the collection, reporting, analysis and interpretation of XAS studies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

An artificial intelligence’s interpretation of complex high-resolution in situ transmission electron microscopy data

Complicated nano- and atomic-scale processes with sub-angstrom spatial resolution and millisecond time resolution visualized by in situ transmission electron microscopy (TEM) are often highly dynamical and time consuming to analyze and interpret. Here, we report how variational autoencoders (VAEs) can provide an artificial intelligence’s interpretation of high-resolution in situ TEM data by condensing and deconvoluting complicated atomic-scale dynamics into a latent space with reduced dimensionality. We designed a VAE model with high latent dimensions capable of deconvoluting information from complex high-resolution TEM data. We demonstrate how this model, with high latent dimensions trained on atomically resolved TEM images of lead sulfide (PbS) nanocrystals, is able to capture movements and perturbations of periodic lattices in both simulated and real in situ TEM data. Importantly, the VAE model shows the capability of detecting and deconvoluting dynamical nanoscale physical processes, such as the rotation of crystal lattices and intra-particle ripening during the annealing of semiconductor nanocrystals.

47 OTHER INSTRUMENTATION↗

DOE OSTI2023

Interpreting omics data with pathway enrichment analysis

Pathway enrichment analysis is indispensable for interpreting omics datasets and generating hypotheses. However, the foundations of enrichment analysis remain elusive to many biologists. Here, in this study, we discuss best practices in interpreting different types of omics data using pathway enrichment analysis and highlight the importance of considering intrinsic features of various types of omics data. We further explain major components that influence the outcomes of a pathway enrichment analysis, including defining background sets and choosing reference annotation databases. To improve reproducibility, we describe how to standardize reporting methodological details in publications. This article aims to serve as a primer for biologists to leverage the wealth of omics resources and motivate bioinformatics tool developers to enhance the power of pathway enrichment analysis.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2020

The influence of environmental microseismicity on detection and interpretation of small-magnitude events in a polar glacier setting

Glacial environments exhibit temporally variable microseismicity. To investigate how microseismicity influences event detection, we implement two noise-adaptive digital power detectors to process seismic data from Taylor Glacier, Antarctica. We add scaled icequake waveforms to the original data stream, run detectors on the hybrid data stream to estimate reliable detection magnitudes and compare analytical magnitudes predicted from an ice crack source model. We find that detection capability is influenced by environmental microseismicity for seismic events with source size comparable to thermal penetration depths. When event counts and minimum detectable event sizes change in the same direction (i.e. increase in event counts and minimum detectable event size), we interpret measured seismicity changes as ‘true’ seismicity changes rather than as changes in detection. Generally, one detector (two degree of freedom (2dof)) outperforms the other: it identifies more events, a more prominent summertime diurnal signal and maintains a higher detection capability. We conclude that real physical processes are responsible for the summertime diurnal inter-detector difference. One detector (3dof) identifies this process as environmental microseismicity; the other detector (2dof) identifies it as elevated waveform activity. Our analysis provides an example for minimizing detection biases and estimating source sizes when interpreting temporal seismicity patterns to better infer glacial seismogenic processes.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

Interpretation of high-harmonic fast-wave propagation in the scrape-off layer of NSTX-U as a geometrically bounded-waveguide mode

This paper revisits the onset of high-harmonic fast-wave (HHFW) propagation in the scrape-off layer (SOL) plasma of the NSTX/NSTX-U spherical tokamak, motivated by past HHFW heating and current drive experiments and modelling. Previously, the fast-wave propagation in the SOL was correlated with the opening (suppression) of the fast-wave right-hand cutoff layer in front of the antenna. In this work, the SOL propagation is interpreted as a geometric waveguide mode guided by the SOL geometry, whose radial width can be comparable to the wave’s perpendicular wavelength in the HHFW regime. A two-dimensional circular model is first employed using full-wave solvers to characterise the poloidal eigenmode structures and to clarify their relationship to annulus resonance. By progressively adding a tokamak-like magnetic-field configuration, starting from a uniform axial field, the effects of magnetic-field gradients and pitch on the SOL waveguide mode are characterised. The poloidal mode numbers supported by the SOL plasma agree well with analytic estimates, indicating that an anisotropic plasma in a bounded geometry selectively supports and amplifies the resonant poloidal mode number. Additionally, two-dimensional axisymmetric NSTX-U simulations demonstrate that the SOL eigenmode features identified in the circular model persist in the experimentally relevant configurations. A control approach based on lengthening the wave perpendicular wavelength relative to the SOL width, including a higher magnetic (B)-field operation, is discussed. The analysis here shows the key role of a bounded geometry in interpreting HHFW eigenmode coupling and propagation in the NSTX-U SOL plasma.

plasma heating↗

DOE OSTI2026

Deciphering the Solvation Structure of Aqueous ZnCl 2 Solutions from X-ray Absorption Spectra Using the Interpretable Graph Neural Network

Machine learning (ML) provides powerful pathways for predicting spectroscopic observables from atomic structures, but its broader impact depends on making model predictions interpretable in terms of physical and chemical principles. Here, we introduce a physics-guided graph neural network (GNN) model that predicts Zn K-edge X-ray spectroscopy (XAS) spectra of aqueous ZnCl 2 solutions. Training data are generated from ab initio XAS calculations on molecular dynamics snapshots obtained using a machine learning interatomic potential. The GNN reproduces experimental spectra across concentrations from dilute (<0.1 m) to highly concentrated (30 m, “water-in-salt”) regimes and scales efficiently to large, disordered liquid systems beyond the reach of conventional ab initio approaches. Gradient-based attribution analysis reveals that the model learns physically meaningful structure-spectrum relationships. Ligand-specific attributions reflect orbital hybridization patterns and the origin of the excitations derived from the density functional theory. Bond-length attributions recover spectral shifts consistent with multiple-scattering theory. Finally, this work bridges data-driven prediction with electronic-structure theory, establishing a general paradigm for interpretable ML that links atomic structure, electronic structure, and spectroscopic observables.

25 ENERGY STORAGE↗