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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

A machine learning approach to quantify degradation of nuclear fuels and the effects of fission products

Nuclear fuel performance is critically dependent on understanding the evolution of fuel properties under operational conditions, a complex challenge driven by chemical changes and substantial radiation damage during fission. Traditionally, property evolution has been determined via empirical data collected following irradiation. However, these empirical correlations are limited in their applicability beyond the specific conditions in which they were obtained. This study explores a novel approach to address this challenge by applying materials informatics to develop a machine learning random forest (ML-RF) model that captures the effects of fission products on fuel compounds. The model predicts formation enthalpy (ΔH f ) by leveraging extensive quantum materials property data and correlating it with material descriptors such as composition, atomic and site features, and crystal lattice properties. This ML-RF model enables rapid interpolation across the compositional and structural spaces covered by the training data, thus supporting high-throughput screening and energetic ranking of candidate phases. The model demonstrates the ability to predict ΔH f with a mean absolute error (MAE) of approximately 0.1 to 0.2 eV/atom across a wide range of compounds, including key nuclear fuel systems (U-O, U-N, U-C, U-Si, and U-Mo). For example, it was used to assess shifts in stoichiometry for UO 2 (O/M) and UN (N/M) fuels, revealing their distinct tendencies in chemical potential variation and enabling preliminary convex hull analyses. Furthermore, the model provides insights into how individual fission products affect fuel properties. Results indicate that larger fission products (e.g., Nd, Pu, Ce) have a more pronounced impact on UO 2 , while lighter ones (e.g., Zr) strongly influence UN. Here, the model developed in this work can be used to support the Accelerated Fuel Qualification approach by facilitating preliminary evaluations prior to extensive materials modeling and experimentation. To this end, the trained model has been made available to the fuel community to support ongoing fuel development efforts.

Accelerated fuel qualification↗
DOE OSTI2025

Data for: Climatic Imprint on Interfacially-Controlled Platinum-Palladium Resources

Data package for manuscript "Climatic Imprint on Interfacially-Controlled Platinum-Palladium Resources" by Emily G. Wright, Ivey Wang, Yihang Fang, Elaine D. Flynn, and Jeffrey G. Catalano. This dataset contains adsorption results from experiments designed to investigate the effect of chloride on Pd(II) adsorption to goethite and Pt(II) adsorption to hematite and goethite, including lab experiments, X-ray absorption fine structure spectroscopy, and models of retention within a laterite. See the associated manuscript for full methods information. The file "Wright2025_PtAds_data.csv" contains the target starting Pt concentration (uM), final aqueous Pt and associated error (in uM), calculated adsorbed Pt and associated error (in umol/m2), target and measured aqueous chloride (mM), target aqueous nitrate (mM), final pH, and mineral concentration/loading (g/L). Associated mineral-free controls (mineral loading = 0 g/L) are included; the aqueous Pd error was not calculated and chloride was not measured in every sample. These data appear in Figures 1, S3, S4, S5, S20, and S22 in the associated manuscript. The file "Wright2025_PdAds_data.csv" contains the target starting Pd concentration (uM), final aqueous Pd and associated error (in uM), calculated adsorbed Pd and associated error (in umol/m2), target and measured aqueous chloride (mM), and mineral concentration/loading (g/L). Associated mineral-free controls (mineral loading = 0 g/L) are included; the aqueous Pd error was not calculated and chloride was not measured in every sample. These data appear in Figures 1, S3, S4, S5, and S20 in the associated manuscript. The file "Wright2025_MineralBatches_data.csv" contains the mineral identity and BET specific surface area (m2/g) for every mineral batch synthesized and used in experiments. The annealing time used is listed for hydrothermally annealed goethite. These data appear in Table S2 in the associated manuscript. The file "Wright2025_XRD_data.csv" contains the XRD patterns for every mineral batch synthesized as the counts as a function of two theta (in degrees). See "Wright2025_MineralBatches_data.csv" for more details on specific mineral batches. These data appear in Figure S2 in the associated manuscript. The file "Wright 2025_ZetaPotential_data.csv" contains the measured zeta potentials for samples of goethite (batch G2) at pH 4 the presence of varying amounts of sodium chloride. These data appear in Table S3 in the associated manuscript. The file "Wright2025_XAFSSamples_data.csv" contains the specific mineral batch, measured final aqueous Pd or Pt (uM), measured final aqueous chloride (mM), and estimated adsorbed Pd or Pt (umol/m2) of all XAFS samples. These data appear in Tables S4, S7, S8, and S10 in the associated manuscript. The files "Wright2025_PdXAFS_data.csv" and "Wright2025_PtXAFS_data.csv" contain the normalized spectra of Pd and Pt, respectively, adsorbed to minerals at varying chloride concentrations. See "Wright2025_XAFSSamples_data.csv" for a guide to sample names. Note that "05" in a sample name is equivalent to "0.5". These data appear in Figures 2, S6, S7, S8, S12, S13, and S14 in the associated manuscript. The file "Wright2025_LateriteProfileProfileModelParameters_data.csv" include the ratio of hematite to hematite and goethite in two synthetic, modeled profiles, as well as the modeled surface areas of goethite and hematite as a function of relative depth within the modeled weathering zone. These data were used, in conjunction with equations presented in the paper, to calculate the theoretical concentrations of Pd and Pt (and the resulting Pt/Pd ratio) within the profiles. These data appear in Figure 3 in the associated manuscript. The file "Wright2025_Imagery_data.zip" is a zipped folder containing the TEM and STEM images appear in Figures S18 and S19. Individual files are labeled as either STEM (Fig. S18) or TEM (Fig. S19) with a letter representing the part of the multipart figure.

58 GEOSCIENCES↗
DOE OSTI2024

Generalization error guaranteed auto-encoder-based nonlinear model reduction for operator learning

Many physical processes in science and engineering are naturally represented by operators between infinite-dimensional function spaces. The problem of operator learning, in this context, seeks to extract these physical processes from empirical data, which is challenging due to the infinite or high dimensionality of data. An integral component in addressing this challenge is model reduction, which reduces both the data dimensionality and problem size. In this paper, we utilize low-dimensional nonlinear structures in model reduction by investigating Auto-Encoder-based Neural Network (AENet). AENet first learns the latent variables of the input data and then learns the transformation from these latent variables to corresponding output data. Our numerical experiments validate the ability of AENet to accurately learn the solution operator of nonlinear partial differential equations. Furthermore, we establish a mathematical and statistical estimation theory that analyzes the generalization error of AENet. Finally, our theoretical framework shows that the sample complexity of training AENet is intricately tied to the intrinsic dimension of the modeled process, while also demonstrating the robustness of AENet to noise.

Auto-encoder↗
DOE OSTI2025

Aemulus ν: precision halo mass functions in wνCDM cosmologies

Precise and accurate predictions of the halo mass function for cluster mass scales in wνCDM cosmologies are crucial for extracting robust and unbiased cosmological information from upcoming galaxy cluster surveys. Here, we present a halo mass function emulator for cluster mass scales (≳ 1013 M ⊙/h) up to redshift z = 2 with comprehensive support for the parameter space of wνCDM cosmologies allowed by current data. Based on the Aemulus ν suite of simulations, the emulator marks a significant improvement in the precision of halo mass function predictions by incorporating both massive neutrinos and non-standard dark energy equation of state models. This allows for accurate modeling of the cosmology dependence in large-scale structure and galaxy cluster studies. We show that the emulator, designed using Gaussian Process Regression, has negligible theoretical uncertainties compared to dominant sources of error in future cluster abundance studies. Our emulator is publicly available (https://github.com/DelonShen/aemulusnu_hmf), providing the community with a crucial tool for upcoming cosmological surveys such as LSST and Euclid.

cluster counts↗
DOE OSTI2025

Slimmer Geminals For Accurate F12 Electronic Structure Models

The Slater-type F12 geminal length scales originally tuned for the second-order Mo̷ller-Plesset F12 method are too large for higher-order F12 methods formulated using the SP (diagonal fixed-coefficient spin-adapted) F12 ansatz. The new geminal parameters reported herein reduce the basis set incompleteness errors (BSIEs) of absolute coupled-cluster singles and doubles F12 correlation energies by a significant─and increase with the cardinal number of the basis─margin. The effect of geminal reoptimization is especially pronounced for the cc-pVXZ-F12 basis sets (specifically designed for use with F12 methods) relative to their conventional aug-cc-pVXZ counterparts. The BSIEs of relative energies are less affected, but substantial reductions can be obtained, especially for atomization energies and ionization potentials with the cc-pVXZ-F12 basis sets. The new geminal parameters are therefore recommended for all applications of high-order F12 methods, such as coupled-cluster F12 methods and transcorrelated F12 methods.

Powell, Samuel R. [Virginia Polytechnic Inst. and ↗
DOE OSTI2026

Using Density-Corrected DFT to Understand Density-Driven and Functional-Dependent Errors in Ab Initio Simulations of the Hydrated Electron

The hydrated electron, an excess electron in liquid water, plays a crucial role in a plethora of chemical processes, motivating extensive research efforts to characterize its structure, dynamics, and reactivity in solution. Recent theoretical approaches to understanding this intriguing object have involved ab initio simulations based on density functional theory (DFT). Although DFT allows for the study of hydrated electron reactivity and quantum mechanical behavior, it is well-known that anionic systems can suffer from significant density-driven errors (DDEs). Density-corrected DFT (DC-DFT) provides a framework to mitigate such errors; the method reduces DDEs by replacing the self-consistent (SC) density associated with a given density functional with the Hartree–Fock (HF) density. Since HF densities tend to be more localized than DFT SC densities, the DC-DFT scheme significantly improves errors in calculations where the SC density is spuriously delocalized. Here, we investigate how the use of density correction affects the calculated properties of the DFT-simulated (PBEh) hydrated electron, a particularly challenging diffuse anionic system to simulate. First, we analyze charge delocalization in a system consisting of a model octahedral hydrated electron water cluster (the so-called Kevan structure) along with a spatially separated sulfur atom. We show that the use of density correction indeed reduces DDEs in comparison to a standard DFT global hybrid functional. We then propagate molecular dynamics trajectories of the hydrated electron using DC-DFT, where we find that DC further localizes electron density in the cavity region, a signature of reduced charge delocalization. Unfortunately, the decreased radius of gyration of the spin density and corresponding tightening of the local solvation structure from density correction causes predicted observables to deviate further from experimental measurements than when density correction is not employed. Here, we argue that DC’s worse agreement with experiment results from the removal of a fortuitous cancellation of errors that is intrinsic to the PBEh functional. This indicates that the difficulties with DFT to simulate hydrated electrons are primarily due to the inherent approximations in DFT rather than to density-driven errors.

Density functional theory↗
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 OSTI2024

Evaluation of the Planetary Boundary Layer Height From ERA5 Reanalysis With MOSAiC Observations Over the Arctic Ocean

The planetary boundary layer height (PBLH) is a crucial indicator reflecting the region of the atmosphere characterized by continuous turbulence. Here, we use radiosonde and surface meteorological observations (4–7 times per day, year-round measurements) during the Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC) expedition to derive the PBLH (PBLH MOSAiC ), and further evaluate the PBLH from the ERA5 reanalysis (PBLH ERA5 ). Comparisons between PBLH MOSAiC and PBLH ERA5 from different perspectives reveal that: (a) The overestimation of PBLH ERA5 when the sea ice concentration is >90% is significant with the centered root mean squared error reaching up to 201 m; (b) The difference between the two products is notably pronounced in cold seasons, while it is comparatively diminished in warm seasons; (c) In neutral boundary layers, differences in PBLH ERA5 are larger compared with stable and convective boundary layers. In addition, the analysis of error sources indicates that the bias of PBLH ERA5 is sensitive to the bias of vertical thermal structure and wind speed profiles in ERA5 data sets in all conditions. Finally, we find a Random Forest model effectively reduces the bias of PBLH ERA5 with the index of agreement reaching up to 0.71 in the test data set, while a multiple linear regression demonstrates comparable performance to the Random Forest model.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Benchmarking machine learning strategies for phase-field problems

Abstract We present a comprehensive benchmarking framework for evaluating machine-learning approaches applied to phase-field problems. This framework focuses on four key analysis areas crucial for assessing the performance of such approaches in a systematic and structured way. Firstly, interpolation tasks are examined to identify trends in prediction accuracy and accumulation of error over simulation time. Secondly, extrapolation tasks are also evaluated according to the same metrics. Thirdly, the relationship between model performance and data requirements is investigated to understand the impact on predictions and robustness of these approaches. Finally, systematic errors are analyzed to identify specific events or inadvertent rare events triggering high errors. Quantitative metrics evaluating the local and global description of the microstructure evolution, along with other scalar metrics representative of phase-field problems, are used across these four analysis areas. This benchmarking framework provides a path to evaluate the effectiveness and limitations of machine-learning strategies applied to phase-field problems, ultimately facilitating their practical application.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Structural coherence model for predicting molten salt thermal conductivity informed by the pair distribution function

To enable thermal behavior prediction and design optimization of molten salt reactors, thermal conductivity of molten salts must be characterized in terms of salt composition and temperature. Current theoretical models fail to provide consistent approximations for all halide mixtures, particularly actinide-bearing melts. This study aims to link the short-range order structure of molten salts to the mean free path of energy carriers through a simple structural coherence model informed by the partial pair distribution function. The proposed method is used to predict the thermal conductivity of 33 alkali and alkaline earth halide salts. Predictions approximate experimental measurements with a mean absolute error of 15.7% for dissociating, complexing, and actinide salts, including unary LiCl, NaCl, and MgCl 2 as well as mixtures LiF–NaF–KF (FLiNaK), LiF–BeF 2 (FLiBe), and NaCl–UCl 3 . The work provides evidence for the validity of energy carrier descriptions of molecular-level heat transfer in molten salts, with implications for improved theories of liquid energy transport in general.

Actinide mixtures↗
DOE OSTI2024

RELAP5-3D validation studies based on the High Temperature Test facility

In the spring and summer of 2019, experiments were conducted at the High Temperature Test Facility (HTTF) that form the basis of an upcoming high-temperature gas-cooled reactor (HTGR) thermal hydraulics (T/H) benchmark. HTTF is an integral effects test facility for HTGR T/H modeling validation. This paper presents RELAP5-3D models of two of those experiments: PG-27, a pressurized conduction cooldown (PCC); and PG-29, a depressurized conduction cooldown (DCC). These models used the RELAP5-3D model of HTTF originally developed by Paul Bayless as a starting point. The sensitivity analysis and uncertainty quantification code, RAVEN was used to perform calibration studies for the steady-state portion of PG-27. Here we developed four PG-27 calibrations based on steady-state conditions. These calibrations all used an effective thermal conductivity equal to 36 % of the measured thermal conductivity, but they differed with respect to the frictional pressure drops and radial conduction models. These models all captured the trends in steady-state temperature distributions and transient temperature behavior well. All four calibrations show room for improvement in predicting the transient temperature rise. The smallest error in temperature rise during the transient was a 21 % underprediction, and the largest was a 48 % underprediction. The errors in transient temperature rise are largely a result of a mismatch in power density between the RELAP5-3D model and the experiment due to the location of active heater rods along the boundary between heat structures in the model. The best of these calibrations was applied to PG-29 to model the DCC. Once again, temperatures during the transient were underpredicted but trends in temperature were captured. The RELAP5-3D model captured trends in the data but could not reproduce measured temperatures exactly. This result is not attributed to deficiencies in the experimental data or to RELAP5–3D itself. Rather, this result likely arises due to the some of the assumptions and decisions made when the RELAP5-3D model was first developed, prior to the execution of HTTF experiments. An agreement in prediction of temperature trends but challenges reproducing HTTF temperatures within measurement uncertainty is consistent with previous analyses of HTTF in the literature. Future RELAP5-3D validation activities centered around HTTF may be able to provide greater insight into the code’s capabilities for HTGR modeling with a more finely nodalized model.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

A Semi-supervised Hybrid Machine Learning Framework for the Qualification of Resistance Spot Welds

• Industries requiring high structural integrity, including automotive, aerospace, and construction, place considerable significance on weld quality classification. • The inspection normally involves human expertise through predefined quality metrics that are subjective, error-prone, and time-intensive • The challenge to classification model development is the scarcity of labeled data and imbalanced distributions in the data that are labeled. • This work develops a new hybrid methodology that achieves clustering using KMeans++ together with supervised classification to overcome these challenges. • The ensemble-based classifiers were identified as optimal, with accuracy enhancements of up to 8% using the pseudo-labeled dataset. • The work provides practical insight into feature engineering and machine learning integration in industrial quality assurance applications.

Rogers, Jeremy K. [Savannah River National Laborat↗
DOE OSTI2025

The impact of curation errors in the PDBBind Database on machine learning predictions of protein–protein binding affinity

The PDBBind database has been widely utilized for the computational prediction of protein–protein binding affinities. While the accuracy of the PDBBind-curated equilibrium dissociation constants (K D ) has been reported for the protein–ligand subset of the PDBBind database, the curation accuracy has not been reported for the protein–protein subset. Here, we present a detailed manual analysis for the subset of PDBBind records with PubMed Central Open Access primary publications and find that ~19% of these records had K D values that were not supported by their primary publications. The impact of these putative curation errors on the machine learning-based prediction of K D from experimental protein–protein 3D structures was evaluated and correcting the curation errors improved the Pearson correlation coefficient between measured and random forest-predicted log 10 (K D ) values by ~8 percentage points. This finding underscores the importance of dataset accuracy for computational modelling and highlights the need for more stringent curation processes when extracting information from the scientific literature.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Spatio-temporal Fourier Transformer for Long-term Dynamics Prediction (StFT) v1.0

We propose a novel machine learning model spatio-temporal Fourier transformer (StFT) to emulate long-term dynamics of multi-scale and multi-physics systems. Our method StFT overcomes the limitations of rapid error accumulation, particularly in long-term forecasting of systems characterized by complex and coupled dynamics. StFT achieves outstanding accuracy and computational efficiency by effectively capturing multi-scale interactions, and quantify the uncertainties inherent in the predictions. Our model leverages a structured hierarchy of StFT blocks, and explicitly captures dynamics across both macro- and micro- spatial scales. Evaluations conducted on three benchmark datasets (plasma, fluid, and atmospheric dynamics) demonstrate the advantages of our approach over state-of-the-art ML methods.

Bai, Zhe [Lawrence Berkeley National Laboratory (L↗
DOE OSTI2025

Quantifying and simulating the weather forecast uncertainty for advanced building control

Weather forecast uncertainty is unavoidable despite technological advancements. Accurately quantifying and modelling this uncertainty is essential for developing and comparing advanced building controllers. In this study, we present a structured approach using a first-order autoregressive model (AR(1)) to model uncertainty in ambient temperature and global solar irradiation (GHI) forecasts. We analyzed weather data from four cities and employed Jensen–Shannon divergence (JSD) to evaluate the similarity between synthetic and actual forecast errors. The average JSD values for temperature are 0.027 (Berkeley), 0.021 (Leuven), 0.018 (Berlin), and 0.008 (Oslo), and for GHI, the average JSD values are 0.016 (Berkeley), 0.058 (Leuven), and 0.013 (Berlin). The low JSD values indicate a high similarity between the synthetic and real forecast error distributions. Further, our approach successfully generates synthetic weather forecasts that mirror the statistical properties of actual forecasts. The implementation of our method for uncertain forecast generation is being added to the BOPTEST framework.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Computationally Guided and Experimentally Validated Design of Custom Chelators for Critical Mineral Recovery

Selective, high throughput separation of target critical metals from complex environments such as fly ash leachates and mining process streams presents a significant challenge for economical production. Custom chelators and sorbents are an attractive technology for selective metal extraction, however it can be difficult to predict their performance, and significant experimental efforts are often required to develop chelating technologies. Here, we present a computational strategy focused on modelling chelator-metal binding interactions and benchmark these results versus experimental data. A computational pipeline combining forcefield, semiempirical, and meta-GGA methods with a thermodynamic framework optimized for error cancellation has been developed to predict binding energies of chelator complexes towards critical mineral recovery applications. This approach, originally validated on [2.2.2] cryptates binding mono- and divalent cations, demonstrated robust predictive capabilities with an R2 of 0.850 against experimental aqueous binding energies. The workflow includes metadynamics for exploring high-dimensional potential energy surfaces and a cluster-continuum model for accurate yet computationally efficient solvation modeling. Error cancellation between solvation energies of free and chelator-coordinated ions enables faster convergence, even with finite cluster sizes. Initial studies on the cryptates revealed consistent metal-ligand coordination patterns, with systematic variations influenced by ion size and charge, highlighting key structural features linked to binding selectivity. Further studies of a proprietary chelator have resulted in identification of previously unreported selectivity towards economically significant metals, which in-house experiments have confirmed, demonstrating the feasibility of this approach. By applying this methodology to new chelators targeting critical minerals such as lithium, cobalt, nickel and other strategic metals, we aim to accelerate the discovery of next-generation chelators for efficient recovery, recycling, and separation processes. This computational framework serves as the backbone of a high-throughput design pipeline tailored for sustainable resource utilization and may be applied to a wide range of systems to meet experimental needs.

computational materials↗
DOE OSTI2026

Parametric reduced order models for graded lattice structures

Graded lattice structures, characterized by smoothly varying mechanical properties, hold significant promise for optimizing material distribution in advanced engineering applications. However, accurately modeling these structures poses substantial computational challenges due to the continuous geometric variations within their unit cells. Here, to address these challenges, this paper introduces a novel Efficient Reduced Order Model (EROM) that integrates the Matrix Discrete Empirical Interpolation Method (MDEIM) and Discrete Empirical Interpolation Method (DEIM) with polynomial regression to efficiently manage geometric parametrization in lattice structures. Unlike traditional reduced order models (ROMs) that require extensive precomputed libraries for each geometric configuration, our approach enables continuous geometric variations through a flexible algebraic formulation, significantly reducing computational costs while preserving high accuracy. The method constructs projection matrices for individual unit cells that can be efficiently assembled into global systems, leveraging the repetitive nature of lattice structures. Numerical studies demonstrate that our EROM achieves displacement errors below 1% and von Mises stress prediction errors below 4%, coupled with computational speedups exceeding two orders of magnitude compared to full-order simulations. The proposed method's modularity and scalability make it particularly suitable for design optimization and real-time simulation of functionally graded lattice structures, with applications spanning aerospace to biomedical engineering.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

Combining geometric-optical and spectral invariants theories for modeling canopy fluorescence anisotropy

The spectral invariants theory ( p -theory) has received much attention in the field of quantitative remote sensing over the past few decades and has been adopted for modeling of canopy solar-induced chlorophyll fluorescence (SIF). However, the spectral invariant properties (SIP) in simple analytical formulae have not been applied for modeling canopy fluorescence anisotropy primarily because they are parameterized in terms of leaf total scattering, which precludes the differentiation between forward and backward leaf SIF emissions. In this study, we have developed the canopy-SIP SIF model by combining geometric-optical (GO) theory to account for asymmetric leaf SIF forward and backward emissions at the first-order scattering and by modeling multiple scattering based on the p-theory, thus avoiding the dependence on radiative transfer models. The applicability of the model simulations especially over 3D heterogeneous canopies was improved by incorporating canopy structure through multi-angular clumping index, and by modeling single scattering from the four components of the scene in view according to the GO approach. The results show good consistency with both the state-of-the-art SIF models and multi-angular field SIF observations over grass and chickpea canopies. Further, the coefficient of determination (R²) between the simulated SIF and field measurements was 0.75 (red) and 0.74 (far-red) for chickpea, and 0.65 (both red and far-red) for grass. The average relative error was approximately 3% for 1D homogeneous scenes when comparing the canopy-SIP SIF model simulations to the SCOPE model simulations, and around 4% for the 3D heterogeneous scene when comparing to the LESS model simulations. The results indicate that the proposed approach for separating asymmetric leaf SIF emissions is a robust way to keep a balance between satisfactory simulation accuracy and efficiency. Model simulations suggest that neglecting the leaf SIF asymmetry can lead to an underestimation of canopy red SIF by 6.3% to 42.6% for various leaf biochemical and canopy structural parameters. This study presents a simple but efficient analytical approach for canopy fluorescence modeling, with potential for large-scale canopy fluorescence simulations.

3D heterogeneous structure↗