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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Neural network representations of multiphase Equations of State

Abstract Equations of State model relations between thermodynamic variables and are ubiquitous in scientific modelling, appearing in modern day applications ranging from Astrophysics to Climate Science. The three desired properties of a general Equation of State model are adherence to the Laws of Thermodynamics, incorporation of phase transitions, and multiscale accuracy. Analytic models that adhere to all three are hard to develop and cumbersome to work with, often resulting in sacrificing one of these elements for the sake of efficiency. In this work, two deep-learning methods are proposed that provably satisfy the first and second conditions on a large-enough region of thermodynamic variable space. The first is based on learning the generating function (thermodynamic potential) while the second is based on structure-preserving, symplectic neural networks, respectively allowing modifications near or on phase transition regions. They can be used either “from scratch” to learn a full Equation of State, or in conjunction with a pre-existing consistent model, functioning as a modification that better adheres to experimental data. We formulate the theory and provide several computational examples to justify both approaches, highlighting their advantages and shortcomings.

Science & Technology - Other Topics↗
DOE OSTI2025

Baryon Number Violation Search

Understanding the fundamental forces and symmetries of nature has long been a central goal of particle physics. While the Standard Model (SM) provides a successful framework, it does not guarantee the conservation of baryon number B or lepton number L, thus motivating searches for their violation. Proton decay, a fundamental process violating B, has been at the forefront of experimental searches for decades.The discovery of the weak neutral current in 1973 unified the electromagnetic and weak forces and inspired the creation of Grand Unified Theories (GUTs) that also unify the strong force. In 1974, the first-ever GUT, proposed by Georgi and Glashow, naturally predicted proton decay. This prediction led to an experimental push to validate these theories, and a large underground detector boom was born. Initially designed for proton decay searches, these detectors later proved invaluable to neutrino physics.Although no evidence for proton decay has yet been observed, next-generation large detectors, such as the Deep Underground Neutrino Experiment (DUNE), offer the opportunity to improve on current experimental limits. Utilizing its Liquid Argon Time Projection Chamber (LArTPC) technology, DUNE is positioned to probe rare processes such as proton decay with increased sensitivity.This thesis presents a sensitivity study for the dominant proton decay mode predicted by Supersymmetric GUTs, p → K+ν, utilizing machine learning approaches. Two methods are explored in this thesis: a Boosted Decision Tree (BDT) analysis and a Graphical Neural Network (GNN) analysis with NuGraph. A lifetime limit of 5.36 ± 0.69 × 1033 years for 400 kt-yrs is found using the BDT, while the GNN achieves a lifetime limit of 6.19±1.26×1033 years for 400-kt-yrs. The NuGraph result offers better sensitivity compared to the current limit set by Super-Kamiokande of 5.90 × 1033 while the BDT result offers a slightly lower sensitivity.Additionally, this thesis discusses cross-section work, a first-ever foray into proton decay and atmospheric neutrinos in a vertical drift (VD) DUNE detector, and extensive hardware contributions to the DUNE Far Detector (FD) 1 Module-0, ProtoDUNE-2, which serves as a testbed for the final detector design and installation.

Stokes, Tyler D. [Louisiana State U.] (ORCID:00000↗
DOE OSTI2025

Triangle Method for Dense ReLU Layers [SWR-25-72]

This software is an implementation of the methods for initializing and training neural networks to be more efficient per parameter, described more fully below and in the related publication: In theory, depth should make a ReLU network EXPONENTIALLY more efficient by enabling it to produce an exponential number of piecewise linear sections in its output. This reasoning is largely based on the work of mathematicians that have hand-constructed networks that make good use of depth. In practice however, even very deep ReLU networks that have been randomly initialized will behave identically to their shallow counterparts - missing an entire exponential dimension of efficiency. The triangle method is a first attempt at realizing the exponential potential of deep networks. Instead of randomly setting weights, we force pairs of neurons in each layer learn to build triangles (i.e. functions from [0,1] -> [0,1] that look like triangles). This is a very efficient pattern for generating lots of linear pieces because composing two triangular functions doubles the number of pieces with each composition. The triangle method is more than just a different initialization, it is a new paradigm of training. Instead of making direct updates to the matrix weights, we do an extra step of backpropagation to collect the derivatives of the loss function with respect to the shapes of the triangles, training them to tilt left or right. This process essentially holds the networks hand throughout the loss landscape and forces it to always use depth effectively by producing triangular shapes internally. This can produce several orders of magnitude of improvement on convex one-dimensional regression problems. Much more theoretical work is needed to realize its full potential beyond this context, but the implementation in this repository will still work in arbitrary numbers of dimensions. The file Triangle_Method.py is a generalized form of the method that will build each neuron its own custom 1-d convex activation function (with exponential efficiency). Example usage on one dimensional problems can be found in Example_Usage.ipynb and an example of using this in a real neural network can be found in Example_VGG16_CIFAR10.ipynb.

Milkert, Max [National Renewable Energy Laboratory↗
DOE OSTI2024

Separable physics-informed DeepONet: Breaking the curse of dimensionality in physics-informed machine learning

The deep operator network (DeepONet) has shown remarkable potential in solving partial differential equations (PDEs) by mapping between infinite-dimensional function spaces using labeled datasets. However, in scenarios lacking labeled data, the physics-informed DeepONet (PI-DeepONet) approach, which utilizes the residual loss of the governing PDE to optimize the network parameters, faces significant computational challenges, particularly due to the curse of dimensionality. This limitation has hindered its application to high-dimensional problems, making even standard 3D spatial with 1D temporal problems computationally prohibitive. Additionally, the computational requirement increases exponentially with the discretization density of the domain. Here, to address these challenges and enhance scalability for high-dimensional PDEs, we introduce the Separable physics-informed DeepONet (Sep-PI-DeepONet). This framework employs a factorization technique, utilizing sub-networks for individual one-dimensional coordinates, thereby reducing the number of forward passes and the size of the Jacobian matrix required for gradient computations. By incorporating forward-mode automatic differentiation (AD), we further optimize computational efficiency, achieving linear scaling of computational cost with discretization density and dimensionality, making our approach highly suitable for high-dimensional PDEs. We demonstrate the effectiveness of Sep-PI-DeepONet through three benchmark PDE models: the viscous Burgers’ equation, Biot’s consolidation theory, and a parameterized heat equation. Our framework maintains accuracy comparable to the conventional PI-DeepONet while reducing training time by two orders of magnitude. Notably, for the heat equation solved as a 4D problem, the conventional PI-DeepONet was computationally infeasible (estimated 289.35 h), while the Sep-PI-DeepONet completed training in just 2.5 h. These results underscore the potential of Sep-PI-DeepONet in efficiently solving complex, high-dimensional PDEs, marking a significant advancement in physics-informed machine learning.

Neural operator↗
DOE OSTI2026

Deep Neural Networks are Adaptive to Function Regularity and Data Distribution in Approximation and Estimation

Deep learning has exhibited remarkable results across diverse areas. To understand its success, substantial research has been directed towards its theoretical foundations. Nev- ertheless, the majority of these studies examine how well deep neural networks can model functions with uniform regularities. In this paper, we explore a different angle: how deep neural networks can adapt to varying degrees of smoothness in functions and nonuni- form data distributions across different locations and scales. More precisely, we focus on a broad class of functions defined by nonlinear tree-based approximation methods. This class encompasses a range of function types, such as functions with uniform regularities and discontinuous functions. We develop nonparametric approximation and estimation theories for this class using deep ReLU networks. Our results show that deep neural networks are adaptive to the nonuniform smoothness of functions and nonuniform data distributions at different locations and scales. We apply our results to several function classes, and derive the corresponding approximation and generalization errors. The validity of our results is demonstrated through numerical experiments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Temporally-consistent koopman autoencoders for forecasting dynamical systems

Absence of sufficiently high-quality data often poses a key challenge in data-driven modeling of high-dimensional spatio-temporal dynamical systems. Koopman Autoencoders (KAEs) harness the expressivity of deep neural networks (DNNs), the dimension reduction capabilities of autoencoders, and the spectral properties of the Koopman operator to learn a reduced-order feature space with simpler, linear dynamics. However, the effectiveness of KAEs is hindered by limited and noisy training datasets, leading to poor generalizability. To address this, we introduce the Temporally-Consistent Koopman Autoencoder (tcKAE), designed to generate accurate long-term predictions even with limited and noisy training data. This is achieved through a consistency regularization term that enforces prediction coherence across different time steps, thus enhancing the robustness and generalizability of tcKAE over existing models. We provide analytical justification for this approach based on Koopman spectral theory and empirically demonstrate tcKAE’s superior performance over state-of-the-art KAE models across a variety of test cases, including simple pendulum oscillations, kinetic plasma, and fluid flow data.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Criticality analysis of nuclear binding energy neural networks

Machine learning methods, in particular deep learning methods such as artificial neural networks (ANNs) with many layers, have become widespread and useful tools in nuclear physics. However, these ANNs are typically treated as ‘black boxes’, with their architecture (width, depth, and weight/bias initialization) and the training algorithm and parameters chosen empirically by optimizing learning based on limited exploration. We test a non-empirical approach to understanding and optimizing nuclear physics ANNs by adapting a criticality analysis based on renormalization group flows in terms of the hyperparameters for weight/bias initialization, training rates, and the ratio of depth to width. This treatment utilizes the statistical properties of neural network initialization to find a generating functional for network outputs at any layer, allowing for a path integral formulation of the ANN outputs as a Euclidean statistical field theory. We use a prototypical example to test the applicability of this approach: a simple ANN for nuclear binding energies. We find that with training using a stochastic gradient descent optimizer, the predicted criticality behavior is realized, and optimal performance is found with critical tuning. However, the use of an adaptive learning algorithm leads to somewhat superior results without concern for tuning and thus obscures the analysis. Nevertheless, the criticality analysis offers a way to look within the black box of ANNs, which is a first step towards potential improvements in network performance beyond using adaptive optimizers.

artificial neural network↗
DOE OSTI2025

Quantifying uncertainty in machine learning for nuclear binding energy

Techniques from artificial intelligence and machine learning are increasingly employed in nuclear theory; however, the uncertainties that arise from the complex parameter manifold encoded by the neural networks are often overlooked. Epistemic uncertainties arising from training the same network multiple times for an ensemble of initial weight sets offer a first insight into the confidence of machine learning predictions, but they often come with a high computational cost. Instead, we apply a single-model uncertainty quantification method called Δ-UQ that gives epistemic uncertainties with one-time training. Here, we demonstrate our approach on a two-feature model of nuclear binding energies per nucleon with proton and neutron number pairs as inputs. We show that Δ-UQ can produce reliable and self-consistent epistemic uncertainty estimates and can be used to assess the degree of confidence in predictions made with deep neural networks.

Huang, Mengyao [Lawrence Livermore National Labora↗
DOE OSTI2026

Zentropy Theory for Transformative Functionalities of Magnetic and Superconducting Materials

The proposed research developed the zentropy theory through applications to complex magnetic materials and superconductors under the hypothesis that the emergent properties of complex magnetic materials and superconductors can be predicted by statistical mechanics of ergodic microstates with their partition functions computed from DFT-predicted free energies. The key objective is to develop approaches to systematically determine the types and number of microstates and the supercell size in DFT-based calculations through convergency of macroscopic functionalities, with the incorporation of our mixed-space approach accounting for the interactions between periodic supercells. In addition to use scientific intuitions to guide the design of important microstates, the key innovation of the proposed research is to integrate the domain knowledge and the material-property-descriptor database (MPDD) with 4 million microstates, which is supported by our deep neural network machine learning models (SIPFENN: structure-informed prediction of formation energy using neural networks) and integrated with our high throughput DFT Tool Kit (DFTTK). For complex magnetic materials, one of the objectives is to develop approaches to calculate short-range ordering from the statistical distribution of each microstate. For superconductors, the divergency of quasiparticle effective mass at a quantum critical point will be investigated, and the superconducting and non-superconducting microstates will be delineated through analysis of electronic band structure, density of states, charge density, and Fermi surface.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Materials Graph Library (MatGL), an open-source graph deep learning library for materials science and chemistry

Graph deep learning models, which incorporate a natural inductive bias for atomic structures, are of immense interest in materials science and chemistry. Here, we introduce the Materials Graph Library (MatGL), an open-source graph deep learning library for materials science and chemistry. Built on top of the popular Deep Graph Library (DGL) and Python Materials Genomics (Pymatgen) packages, MatGL is designed to be an extensible “batteries-included” library for developing advanced model architectures for materials property predictions and interatomic potentials. At present, MatGL has efficient implementations for both invariant and equivariant graph deep learning models, including the Materials 3-body Graph Network (M3GNet), MatErials Graph Network (MEGNet), Crystal Hamiltonian Graph Network (CHGNet), TensorNet and SO3Net architectures. MatGL also provides several pre-trained foundation potentials (FPs) with coverage of the entire periodic table, and property prediction models for out-of-box usage, benchmarking and fine-tuning. Finally, MatGL integrates with PyTorch Lightning to enable efficient model training.

chemistry↗
DOE OSTI2024

Scalar bounded-from-below conditions from Bayesian active learning

We present a procedure leveraging Bayesian deep active learning to rapidly produce highly accurate approximate bounded-from-below conditions for arbitrary renormalizable scalar potentials, in the form of a neural network which may be saved and exported for use in arbitrary parameter space scans. We explore the performance of our procedure on three different scalar potentials with either highly nontrivial or unknown symbolic bounded-from-below conditions (the most general two-Higgs doublet model, the three-Higgs doublet model, and a version of the Georgi-Machacek model without custodial symmetry). We find that we can produce fast and highly accurate binary classifiers for all three potentials. Furthermore, for the potentials for which no known symbolic necessary and sufficient conditions on boundedness-from-below exist, our classifiers substantially outperform some common approximate analytical methods, such as producing tractable sufficient but not necessary conditions or evaluating boundedness-from-below conditions for scenarios in which only a subset of the theory’s fields achieve vacuum expectation values. Our methodology can be readily adapted to any renormalizable scalar field theory. For the community’s use, we have developed a package, BFBrain, which allows for the rapid implementation of our analysis procedure on user-specified scalar potentials with a high degree of customizability. Published by the American Physical Society 2024

Astronomy & Astrophysics↗
DOE OSTI2026

Artificial intelligence-driven approaches for materials design and discovery

Materials design is an important component of modern science and technology, yet traditional approaches rely heavily on trial and error and can be inefficient. Computational techniques, enhanced by modern artificial intelligence, have reshaped the landscape of designing new materials. Among these approaches, inverse design has shown great promise in designing materials that meet specific property requirements. Here, in this Review, we present key computational advances in materials design over the past few decades. We follow the evolution of relevant materials design techniques, from high-throughput forward machine learning methods and evolutionary algorithms, to advanced artificial intelligence strategies such as reinforcement learning and deep generative models. We highlight the paradigm shift from conventional screening approaches to inverse generation driven by deep generative models. Finally, we discuss current challenges and future perspectives of materials inverse design. This Review may serve as a brief guide to the approaches, progress and outlook of designing future functional materials with technological relevance.

computational methods↗
DOE OSTI2025

Deep potential molecular dynamics simulations of ion-enhanced etching of silicon by atomic chlorine

The continued development of plasma-assisted processing techniques requires a fundamental understanding of plasma-surface interactions. Molecular dynamics (MD) simulations have been employed to complement experimental studies and better understand the properties of such systems. Recently, machine learning (ML) methods have enabled the development of ab initio-based interatomic potentials, which can be generalized to complex combinations of multiple atom types. In this work, we use ML potentials developed using the Deep Potential Molecular Dynamics (DeepMD) framework to provide a model of ion-enhanced etching of Si by Cl atoms. We demonstrate the importance of proper selection of the training data set to the accuracy of the DeepMD model and compare our results to MD results using empirical potentials, as well as to experimental measurements. Exposure of undoped Si at 300 K to thermal Cl atoms yields a steady-state Cl coverage of 1.25 monolayers, which is slightly lower than the value obtained in previous experimental studies. Predictions of Si etch yields by simultaneous Cl atom and Ar + ion impacts as a function of ion energy, neutral to ion flux ratio, and angle of incidence of the ions are in reasonably good agreement with classical MD results and experimental measurements. Finally, etch yields and SiCl x mixed layer thicknesses during simultaneous bombardment of the Si(100) surface by Cl atoms and Cl + ions are in good agreement with experimental data. In conclusion, the present work is a necessary condition for the extension of the DeepMD procedure to more complex systems of interest in plasma-surface interactions.

Artificial neural networks↗
DOE OSTI2024

Graph neural networks for CO 2 solubility predictions in Deep Eutectic Solvents

Deep Eutectic Solvents (DESs) are a promising class of solvents for CO 2 capture. DESs are complex mixtures that can be designed to optimize CO solubility and overall capture process efficiency. However, the vast design landscape of DES mixtures makes experimental investigation prohibitive; as such, there is a need for computational models that can quickly and efficiently navigate the design space and inform data collection efforts. In this work, we propose Graph Neural Network (GNN) models for predicting CO 2 solubility for DESs; the GNN leverages a mixture graph representation that captures the molecular structure of the DES components as well as their intermolecular interactions. Here, we compare the GNN framework against alternative architectures (neural networks, graph convolution networks, and random forests) and data representations (molecular fingerprints, sigma profiles, and graphs). We show that the proposed approach offers superior predictive performance; specifically, we show that solubility can be predicted reliably directly from molecular structure (without the need of using sigma profiles as proposed in previous studies). This result is important, as obtaining sigma profiles requires expensive density functional theory computations. We also explored the ability of GNNs to predict solubility for new DES mixtures and operating conditions. We found that the model extrapolates across temperature reliably. However, we also found deficiencies in the ability of the model to predict solubility for DES mixtures, pressures, and molar ratio not included in the training sets; we show that this is due to an inherent lack of chemical diversity in datasets available in the literature. The proposed computational capabilities can thus help navigate the design space of DES and inform data collection efforts. Our models, data, and benchmarks are shared as Python code implemented in Jupyter notebooks.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRSDate not supplied

GeoAI advances in specific landform mapping

Landform mapping (also referred to as geomorphology or geomorphometry) can be divided into two domains: general and specific (Evans 2012). Whereas general landform mapping categorizes all elements of the study area into landform classes, such as ridges, valleys, peaks, and depressions, the mapping of specific landforms requires the delineation (even if fuzzy) of individual landforms. The former is mainly driven by physical properties such as elevation, slope, and curvature. The latter, however, must consider the cognitive (human) reasoning that discriminates individual landforms in addition to these physical properties (Arundel and Sinha 2018). Both mapping forms are important. General geomorphometry is needed to understand geological and ecological processes and as boundary layer input to climate and environmental models. Specific geomorphometry supports such activities as disaster management and recovery, emergency response, transportation, and navigation. In the United States, individual landforms of interest are named in the U.S. Geological Survey (USGS) Geographic Names Information System, a point dataset captured specifically to digitize geographic names from the USGS Historical Topographic Map Collection (HTMC). Named landform extent is represented only by the name placement in the HTMC. Recent work has investigated CNN-based deep learning methods to capture these extents in machine-readable form. These studies first relied on physical properties (Arundel et al. 2020) and then included the HTMC as a band in RGB images in limited testing (Arundel et al. 2023). Results from the HTMC dataset surpassed those using just physical properties and using the HTMC alone performed best due to the hillshading and elevation (contour) data incorporated into the topographic maps. However, results fell short of an operational capacity to map all named landforms in the United States. Thus, our current work expands upon past research by focusing on the HTMC and physical information as inputs and the named landform label extents. Specifically, we propose to leverage pre-trained foundation models for segmentation and optical character recognition (OCR) models to jointly map landforms in the United States. Our approach aims to bridge the disparities among the independent information sources to facilitate informed decision-making. The modeling pipeline performs (1) segmentation using the physical information and (2) information extraction using OCR, in parallel. Then a computer vision approach merges the two branches into a labeled segmentation. References: Arundel, Samantha T., Wenwen Li, and Sizhe Wang. 2020. “GeoNat v1.0: A Dataset for Natural Feature Mapping with Artificial Intelligence and Supervised Learning.” Transactions in GIS 24 (3): 556–72. https://doi.org/10.1111/tgis.12633. Arundel, Samantha T, and Gaurav Sinha. 2018. “Validating GEOBIA Based Terrain Segmentation and Classification for Automated Delineation of Cognitively Salient Landforms BT - Proceedings of Workshops and Posters at the 13th International Conference on Spatial Information Theory (COSIT 2017).” In Proceedings of Workshops and Posters at the 13th International Conference on Spatial Information Theory (COSIT 2017), Lecture Notes in Geoinformation and Cartography, edited by Paolo Fogliaroni, Andrea Ballatore, and Eliseo Clementini, 9–14. Cham: Springer International Publishing. Arundel, Samantha T., Gaurav Sinha, Wenwen Li, David P. Martin, Kevin G. McKeehan, and Philip T. Thiem. 2023. “Historical Maps Inform Landform Cognition in Machine Learning.” Abstracts of the ICA 6 (August): 1–2. https://doi.org/10.5194/ica-abs-6-10-2023. Evans, Ian S. 2012. “Geomorphometry and Landform Mapping: What Is a Landform?” Geomorphology 137 (1): 94–106. https://doi.org/10.1016/j.geomorph.2010.09.029.

machine learning↗
DOE OSTI2025

Accurate and uncertainty-aware multi-task prediction of HEA properties using prior-guided deep Gaussian processes

Surrogate modeling techniques have become indispensable in accelerating the discovery and optimization of high-entropy alloys (HEAs), especially when integrating computational predictions with sparse experimental observations. This study systematically evaluates the training and testing performance of four prominent surrogate models—conventional Gaussian processes (cGP), Deep Gaussian processes (DGP), encoder-decoder neural networks for multi-output regression and eXtreme Gradient Boosting (XGBoost)—applied to a hybrid dataset of experimental and computational properties of the 8-component HEA system Al-Co-Cr-Cu-Fe-Mn-Ni-V. We specifically assess their capabilities in predicting correlated material properties, including yield strength, hardness, modulus, ultimate tensile strength, elongation, and average hardness under dynamic/quasi-static conditions, alongside auxiliary computational properties. The comparison highlights the strengths of hierarchical deep modeling approaches in handling heteroscedastic, heterotopic, and incomplete data commonly encountered in materials science. Our findings illustrate that combined surrogate models such as DGPs infused with machine-learned priors outperform other surrogates by effectively capturing inter-property correlations and by assimilating prior knowledge. This enhanced predictive accuracy positions the combined surrogate models as powerful tools for robust and data-efficient materials design.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Pressure-induced structural and dielectric changes in liquid water at room temperature

Understanding the pressure-dependent dielectric properties of water is crucial for a wide range of scientific and practical applications. In this study, we employ a deep neural network trained on density functional theory data to investigate the dielectric properties of liquid water at room temperature across a pressure range of 0.1–1000 MPa. We observe a nonlinear increase in the static dielectric constant ɛ 0 with increasing pressure, a trend that is qualitatively consistent with experimental observations. This increase in ɛ 0 is primarily attributed to the increase in water density under compression, which enhances collective dipole fluctuations within the hydrogen-bonding network as well as the dielectric response. Despite the increase in ɛ 0 , our results reveal a decrease in the Kirkwood correlation factor G K with increasing pressure. Furthermore, this decrease in G K is attributed to pressure-induced structural distortions in the hydrogen-bonding network, which weaken dipolar correlations by disrupting the ideal tetrahedral arrangement of water molecules.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2020

Evaluation of global terrestrial evapotranspiration using state-of-the-art approaches in remote sensing, machine learning and land surface modeling

Evapotranspiration (ET) is critical in linking global water, carbon and energy cycles. However, direct measurement of global terrestrial ET is not feasible. Here, we first reviewed the basic theory and state-of-the-art approaches for estimating global terrestrial ET, including remote-sensing-based physical models, machine-learning algorithms and land surface models (LSMs). We then utilized 4 remote-sensing-based physical models, 2 machine-learning algorithms and 14 LSMs to analyze the spatial and temporal variations in global terrestrial ET. The results showed that the ensemble means of annual global terrestrial ET estimated by these three categories of approaches agreed well, with values ranging from 589.6 mm/yr (6.56×10^4 cu.km/yr) to 617.1 mm/yr (6.87×10^4 cu.km/yr). For the period from 1982 to 2011, both the ensembles of remote-sensing-based physical models and machine-learning algorithms suggested increasing trends in global terrestrial ET (0.62 mm/sq.yr with a significance level of p<0.05 and 0.38 mm yr−2 with a significance level of p<0.05, respectively). In contrast, the ensemble mean of the LSMs showed no statistically significant change (0.23 mm/sq.yr, p>0.05), although many of the individual LSMs reproduced an increasing trend. Nevertheless, all 20 models used in this study showed that anthropogenic Earth greening had a positive role in increasing terrestrial ET. The concurrent small interannual variability, i.e., relative stability, found in all estimates of global terrestrial ET, suggests that a potential planetary boundary exists in regulating global terrestrial ET, with the value of this boundary being around 600 mm/yr. Uncertainties among approaches were identified in specific regions, particularly in the Amazon Basin and arid/semiarid regions. Improvements in parameterizing water stress and canopy dynamics, the utilization of new available satellite retrievals and deep-learning methods, and model–data fusion will advance our predictive understanding of global terrestrial ET.

surface modeling↗