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DOE OSTI2025

Learning to Simulate Aerosol Dynamics with Graph Neural Networks

Aerosol effects on climate, weather, and air quality depend on characteristics of individual particles, which are tremendously diverse and change in time. Particle-resolved models are the only models able to capture this diversity in particle physiochemical properties, and these models are computationally expensive. As a strategy for accelerating particle-resolved microphysics models, we introduce Graph-based Learning of Aerosol Dynamics (GLAD) and use this model to train a surrogate of the particle-resolved model PartMC-MOSAIC. GLAD implements a Graph Network-based Simulator (GNS), a machine learning framework that has been used to simulate particle-based fluid dynamics models. In GLAD, each particle is represented as a node in a graph, and the evolution of the particle population over time is simulated through learned message passing. Here, we demonstrate our GNS approach on a simple aerosol system that includes condensation of sulfuric acid onto particles composed of sulfate, black carbon, organic carbon, and water. A graph with particles as nodes is constructed, and a graph neural network (GNN) is then trained using the model output from PartMC-MOSAIC. The trained GNN can then be used for simulating and predicting aerosol dynamics over time. Results demonstrate the framework's ability to accurately learn chemical dynamics and generalize across different scenarios, achieving efficient training and prediction times. We evaluate the performance across four scenarios, highlighting the framework's robustness and adaptability in modeling aerosol microphysics and chemistry.

aerosol chemistry dynamics↗

DOE OSTI2023

Bound-preserving finite element approximations of the Keller–Segel equations

We report this paper aims to develop numerical approximations of the Keller–Segel equations that mimic at the discrete level the lower bounds and the energy law of the continuous problem. We solve these equations for two unknowns: the organism (or cell) density, which is a positive variable, and the chemoattractant density, which is a non-negative variable. We propose two algorithms, which combine a stabilized finite element method and a semi-implicit time integration. The stabilization consists of a nonlinear artificial diffusion that employs a graph-Laplacian operator and a shock detector that localizes local extrema. As a result, both algorithms turn out to be nonlinear and can generate cell and chemoattractant numerical densities fulfilling lower bounds. However, the first algorithm requires a suitable constraint between the space and time discrete parameters, whereas the second one does not. We design the latter to attain a discrete energy law on acute meshes. We report some numerical experiments to validate the theoretical results on blowup and nonblowup phenomena. In the blowup setting, we identify a locking phenomenon that relates the L ∞ (Ω)-norm to the L 1 (Ω)-norm limiting the growth of the singularity when supported on a macroelement.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Enhancing scalability of a matrix-free eigensolver for studying many-body localization

We propose several techniques to enhance the parallel scalability of a matrix-free eigensolver designed for studying many-body localization (MBL) of quantum spin chain models with nearest-neighbor interactions and on-site disorder. This type of problem is computationally challenging because the dimension of the associated Hamiltonian matrix grows exponentially with respect to the number of spins L, and we need to average over different realizations of the random disorder to obtain relevant statistical behavior. For each disorder realization, we need to compute eigenvalues from different regions of the spectrum and their corresponding eigenvectors. In previous work, the interior eigenstates for a single eigenvalue problem are computed via the shift-and-invert Lanczos algorithm. Due to the extremely high memory footprint of the LU factorizations, this technique is not well suited for large L’s. For example, we need thousands of compute nodes on modern high performance computing infrastructures to go beyond L = 24. The matrix-free approach does not suffer from this memory bottleneck, however, its scalability is limited by a computation and communication load imbalance. To reduce this imbalance and to significantly enhance the scalability of the matrix-free eigensolver, we reorder the matrix and leverage the consistent space runtime, CSPACER. We also show its efficiency in managing irregular communication patterns at scale compared to optimized MPI non-blocking two-sided and one-sided RMA implementation variants. This effort enables us to study MBL for spin chains with a larger number of spins. The efficiency and effectiveness of the proposed algorithm is demonstrated by computing eigenstates on a massively parallel many-core high performance computer.

METIS↗

DOE OSTI2021

Spread Spectrum Time Domain Reflectometry (SSTDR) Digital Twin Simulation of Photovoltaic Systems for Fault Detection and Location

Utilizing spread spectrum time domain reflectometry (SSTDR) to detect, locate, and characterize faults in photovoltaic (PV) systems is examined in this paper. We present a method to obtain the model parameters that are needed to produce digital twin SSTDR responses for PV systems. The digital twin SSTDR responses could be used to predict faults within the PV systems. Here, the model parameters are the reflection and transmission coefficients at each impedance discontinuity in the PV system along with the propagation coefficients across each PV cable segment. We obtain model parameter by applying inverse modeling techniques to experimental SSTDR data associated with PV systems. Our model parameters can be used in any digital twin simulation method for modeling reflectometry in frequency-dependent and complex loads. For validation, we used the model parameters in a graph network simulation engine and adapted it to be used for SSTDR digital twin simulations in PV systems. We produced simulations for 0 to 10 PV modules connected in series. We also simulated SSTDR responses for open circuit disconnections in a PV setup containing 10 PV modules in series. Results show that all but one simulated disconnect locations match experimental disconnection locations of the same setup with an error of less than 5%.

14 SOLAR ENERGY↗

DOE OSTI2016

Development and Verification of MATLAB Functions for Pressure Drop Estimation in Crossflow Tube Bundles

The experimental data on drag coefficients in crossflow tube bundles is severely limited. It is largely contained in nomograms for a small range of tube bundle pitch ratios for both in-line and staggered bundles. These monograms and the corresponding correlations/curve fits are not readily accessible. This lack of experimental data presents a limitation when designing crossflow heat exchangers for nuclear reactors. Specifically, Molten Salt Reactors (MSRs) that utilize cross-flow configurations with turbulent molten salts flowing in the shell side are of interest. Current methods of calculating the drag coefficients are outdated and time consuming when conducting design studies (i.e. picking points off a graph). A computer script could easily run the necessary rapid calculations of the pressure drop for a large possible range of Reynolds numbers, pitch ratios and tube bundle configurations. In an effort to facilitate increased access and accuracy to crossflow pressure drop calculations, a set of MATLAB scripts have been created. These are specifically for the pressure drop and drag coefficients for flow over rows of in-line and staggered tube bundles. For verification of the scripts, the nomograms produced by Zukauskas, of which the scripts are built off, served as a comparison to the plot generated by the MATLAB scripts. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2022

CONGO²: Scalable Online Anomaly Detection and Localization in Power Electronics Networks

Rapid and accurate detection and localization of electronic disturbances simultaneously are important for preventing its potential damages and determining potential remedies. Existing anomaly detection methods are severely limited by the low accuracy, the expensive computational cost and the need for highly trained personnel. There is an urgent need for a scalable online algorithm for in-field analysis of large-scale power electronics networks. Here in this paper, we propose a fast and accurate algorithm for anomaly detection and localization of power electronics networks: stratified colored-node graph (CONGO2). This algorithm hierarchically models the change of correlated waveforms and then correlated sensors using the colored-node graph. By aggregating the change of each sensor with its neighbors’ inputs, we can spontaneously identify and localize the anomaly that cannot be detected by data collected from a single sensor. As our proposed method only focuses on the changes within a short time frame, it is highly computational efficient and only needs small data storage. Thus, our method is ideal for online and reliable anomaly detection and localization of large-scale power electronic networks. Compared to existing anomaly detection methods, our method is entirely data-driven without training data, highly accurate and reliable for wide-spectrum anomalies detection, and more importantly, capable of both detection and localization. Thus, it is ideal for infield deployment for large-scale power electronic networks. As illustrated by a distributed energy resources (DERs) power grid with 37-node, our method can effectively detect and localize various cyber and physical attacks.

42 ENGINEERING↗

DOE OSTI2024

Topological Interpretability for Deep Learning

With the growing adoption of AI-based systems across everyday life, the need to understand their decision-making mechanisms is correspondingly increasing. The level at which we can trust the statistical inferences made from AI-based decision systems is an increasing concern, especially in high-risk systems such as criminal justice or medical diagnosis, where incorrect inferences may have tragic consequences. Despite their successes in providing solutions to problems involving real-world data, deep learning (DL) models cannot quantify the certainty of their predictions. These models are frequently quite confident, even when their solutions are incorrect. This work presents a method to infer prominent features in two DL classification models trained on clinical and non-clinical text by employing techniques from topological and geometric data analysis. We create a graph of a model's feature space and cluster the inputs into the graph's vertices by the similarity of features and prediction statistics. We then extract subgraphs demonstrating high-predictive accuracy for a given label. These subgraphs contain a wealth of information about features that the DL model has recognized as relevant to its decisions. We infer these features for a given label using a distance metric between probability measures, and demonstrate the stability of our method compared to the LIME and SHAP interpretability methods. This work establishes that we may gain insights into the decision mechanism of a DL model. This method allows us to ascertain if the model is making its decisions based on information germane to the problem or identifies extraneous patterns within the data.

Spannaus, Adam↗

DOE OSTI2020

Wave function analysis with a maximum flow algorithm

An efficient algorithm for computing the maximum-flow path in a network is applied to the identification of the dominant configuration state functions (CSFs) in a graphically contracted function (GCF), configuration interaction, wave function. The flow network is a space of spin-adapted CSFs represented by a Shavitt graph, wherein the nodes correspond to orbital occupations and spin quantum numbers. The graph nodes are connected by arcs, and an arc density is defined as sums of the associated squared CSF coefficients. A max-min approach determines an upper bound to the maximum possible incoming flow for each graph node. A backtracking step generates a candidate walk and is followed by a limited search of alternative branching paths for the dominant CSF. The arc density contributions are removed from the graph, and the algorithm is reapplied to the updated graph. This list of generated walks can be partitioned in order to guarantee that the dominant CSFs have been identified. All of the steps in this algorithm are computationally efficient and do not depend on the potentially large dimension of the underlying linear CSF expansion space. An analysis of low-lying valence states of C-2 illustrates the method.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2019

The all configuration mean energy multiconfiguration self-consistent-field method. I. Equal configuration weights

The All Configuration Mean Energy (ACME) conditions are a special case of state averaging for Multiconfigurational Self-Consistent-Field (MCSCF) orbital optimisation. The method is formulated using the Graphical Unitary Group Approach (GUGA) in which the Configuration State Function (CSF) basis is represented as walks within a Shavitt graph. This graphical formulation leads to efficient recursive algorithms for the energy and reduced density matrices (RDM) that are independent of the CSF dimension and that scale only as O(n2) where n is the number of occupied orbitals. The Hamiltonian matrix diagonalization step is obviated and the CSF expansion coefficients are neither referenced nor required. This allows MCSCF orbital optimisation to be performed for essentially unlimited numbers of active orbitals and arbitrarily large CSF expansions. The discussion includes various types of CSF expansion spaces, the partitioning of the essential and redundant orbital optimisation parameters, the computation of the spin-density, and the formulation of state-specific analytic gradients and nonadiabatic coupling for high-level electronic structure methods that use the ACME MCSCF orbitals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Deep structural clustering for single-cell RNA-seq data jointly through autoencoder and graph neural network

Abstract Single-cell RNA sequencing (scRNA-seq) permits researchers to study the complex mechanisms of cell heterogeneity and diversity. Unsupervised clustering is of central importance for the analysis of the scRNA-seq data, as it can be used to identify putative cell types. However, due to noise impacts, high dimensionality and pervasive dropout events, clustering analysis of scRNA-seq data remains a computational challenge. Here, we propose a new deep structural clustering method for scRNA-seq data, named scDSC, which integrate the structural information into deep clustering of single cells. The proposed scDSC consists of a Zero-Inflated Negative Binomial (ZINB) model-based autoencoder, a graph neural network (GNN) module and a mutual-supervised module. To learn the data representation from the sparse and zero-inflated scRNA-seq data, we add a ZINB model to the basic autoencoder. The GNN module is introduced to capture the structural information among cells. By joining the ZINB-based autoencoder with the GNN module, the model transfers the data representation learned by autoencoder to the corresponding GNN layer. Furthermore, we adopt a mutual supervised strategy to unify these two different deep neural architectures and to guide the clustering task. Extensive experimental results on six real scRNA-seq datasets demonstrate that scDSC outperforms state-of-the-art methods in terms of clustering accuracy and scalability. Our method scDSC is implemented in Python using the Pytorch machine-learning library, and it is freely available at https://github.com/DHUDBlab/scDSC.

Gan, Yanglan↗

DOE OSTI2018

Numerically approximating centrality for graph ranking guarantees

Many real-world datasets can be represented as graphs. Using iterative solvers to approximate graph centrality measures allows us to obtain a ranking vector on the nodes of the graph, consisting of a number for each vertex in the graph identifying its relative importance. In this study the centrality measures we use are Katz Centrality and PageRank. Given an approximate solution, we use the residual to accurately estimate how much of the ranking matches the ranking given by the exact solution. Using probabilistic matrix norms, we obtain bounds on the accuracy of the approximation compared to the exact solution with respect to the highly ranked nodes and apply numerical analysis to the computation of centrality with iterative methods. This relates the numerical accuracy of the linear solver to the data analysis accuracy of finding the correct ranking. In particular, we answer the question of which pairwise rankings are reliable given an approximate solution to the linear system. Experiments on many real-world undirected and directed networks up to several million vertices and several hundred million edges validate our theory and show that we are able to accurately estimate large portions of the approximation. We also analyze the difference between global centrality scores and personalized scores (w.r.t. specific seed vertices). By analyzing convergence error, we develop confidence in the ranking schemes of data mining. We show we are able to accurately guarantee ranking of vertices with an approximation to centrality metrics faster than current methods.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Systematic planning of moving target defence for maximising detection effectiveness against false data injection attacks in smart grid

Abstract Moving target defence (MTD) has been gaining traction to thwart false data injection attacks against state estimation (SE) in the power grid. MTD actively perturbs the reactance of transmission lines equipped with distributed flexible AC transmission system (D‐FACTS) devices to falsify the attacker's knowledge about the system configuration. However, the existing literature has not systematically studied what influences the detection effectiveness of MTD and how it can be improved based on the topology analysis. These problems are tackled here from the perspective of an MTD plan in which the D‐FACTS placement is determined. We first exploit the relation between the rank of the composite matrix and the detecting effectiveness. Then, we rigorously derive upper and lower bounds on the attack detecting probability of MTDs with a given rank of the composite matrix. Furthermore, we analyse existing planning methods and highlight the importance of bus coverage by D‐FACTS devices. To improve the detection effectiveness, we propose a novel graph theory–based planning algorithm to retain the maximum rank of the composite matrix while covering all necessary buses. Comparative results on multiple systems show the high detecting effectiveness of the proposed algorithm in both DC‐ and AC‐SE.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2021

Detecting hidden layers from spreading dynamics on complex networks

When dealing with spreading processes on networks it can be of the utmost importance to test the reliability of data and identify potential unobserved spreading paths. In this paper we address these problems and propose methods for hidden layer identification and reconstruction. We also explore the interplay between difficulty of the task and the structure of the multilayer network describing the whole system where the spreading process occurs. Our methods stem from an exact expression for the likelihood of a cascade in the susceptible-infected model on an arbitrary graph. We then show that by imploring statistical properties of unimodal distributions and simple heuristics describing joint likelihood of a series of cascades one can obtain an estimate of both existence of a hidden layer and its content with success rates far exceeding those of a null model. Furthermore, we conduct our analyses on both synthetic and real-world networks providing evidence for the viability of the approach presented.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Expanding the design space of stratospheric aerosol geoengineering to include precipitation-based objectives and explore trade-offs

Previous climate modeling studies demonstrate the ability of feedback-regulated, stratospheric aerosol geoengineering with injection at multiple independent latitudes to meet multiple simultaneous temperature-based objectives in the presence of anthropogenic climate change. However, the impacts of climate change are not limited to rising temperatures but also include changes in precipitation, loss of sea ice, and many more; knowing how a given geoengineering strategy will affect each of these climate metrics is vital to understanding the limits and trade-offs of geoengineering. Here, we first introduce a new method of visualizing the design space in which desired climate outcomes are represented by 2-D surfaces on a 3-D graph. Surface orientations represent how different injection choices influence that objective, and intersecting surfaces represent objectives which can be met simultaneously. Using this representation as a guide, we present simulations of two new strategies for feedback-regulated aerosol injection, using the Community Earth System Model with the Whole Atmosphere Community Climate Model – CESM1(WACCM). The first simultaneously manages global mean temperature, tropical precipitation centroid, and Arctic sea ice extent, while the second manages global mean precipitation, tropical precipitation centroid, and Arctic sea ice extent. Both simulations control the tropical precipitation centroid to within 5 % of the goal, and the latter controls global mean precipitation to within 1% of the goal. Additionally, the first simulation overcompensates sea ice, while the second undercompensates sea ice; all of these results are consistent with the expectations of our design space model. In addition to showing that precipitation-based climate metrics can be managed using feedback alongside other goals, our simulations validate the utility of our design space visualization in predicting our climate model behavior under a given geoengineering strategy, and together they help illustrate the fundamental limits and trade-offs of stratospheric aerosol geoengineering.

58 GEOSCIENCES↗

DOE OSTI2019

Message-passing neural networks for high-throughput polymer screening

Machine learning methods have shown promise in predicting molecular properties, and given sufficient training data, machine learning approaches can enable rapid high-throughput virtual screening of large libraries of compounds. Graph-based neural network architectures have emerged in recent years as the most successful approach for predictions based on molecular structure and have consistently achieved the best performance on benchmark quantum chemical datasets. However, these models have typically required optimized 3D structural information for the molecule to achieve the highest accuracy. These 3D geometries are costly to compute for high levels of theory, limiting the applicability and practicality of machine learning methods in high-throughput screening applications. In this study, we present a new database of candidate molecules for organic photovoltaic applications, comprising approximately 91,000 unique chemical structures. Compared to existing datasets, this dataset contains substantially larger molecules (up to 200 atoms) as well as extrapolated properties for long polymer chains. We show that message-passing neural networks trained with and without 3D structural information for these molecules achieve similar accuracy, comparable to state-of-the-art methods on existing benchmark datasets. Furthermore, these results therefore emphasize that for larger molecules with practical applications, near-optimal prediction results can be obtained without using optimized 3D geometry as an input. We further show that learned molecular representations can be leveraged to reduce the training data required to transfer predictions to a new density functional theory functional.

14 SOLAR ENERGY↗

DOE OSTI2025

Equivariant Graph Attention Network - 3D Conformers & Feature Fusion

EGAN-3F (Equivariant Graph Attention Network - 3D Conformers & Feature Fusion) presents an innovative approach for predicting binding affinity between small molecules and protein targets, a fundamental task in drug discovery. Traditional structure-based methods often depend on protein-ligand complex structures obtained from crystallography or molecular docking. In contrast, ligand-only machine learning models using 1D or 2D representations such as SMILES have been developed to predict binding affinity without structural information about the target; however, their accuracy is often limited due to the lack of 3D ligand information. EGAN-3F addresses this limitation by integrating spatially aware graph learning with traditional descriptor-based features. We systematically investigate how combining 2D and 3D molecular representations enhances binding affinity prediction from SMILES strings. This approach underscores the importance of modeling conformational diversity and incorporating chemically meaningful descriptors to improve predictive accuracy. The key innovation of EGAN-3F lies in its ability to achieve robust ligand-based binding affinity predictions without requiring protein-ligand complex structures, effectively bridging the gap between purely structural and ligand-only modeling paradigms.

Shim, Heesung [Lawrence Livermore National Laborat↗

DOE OSTI2020

An Overview of the Circular Economy Lifecycle Assessment and VIsualization (CELAVI) Framework

A circular economy emphasizes the efficient use of all resources (e.g., materials, land, water). Despite anticipated overall benefits to society, the transition to a circular economy is likely to create regional differences in impacts. Current tools are unable to fully evaluate these potential externalities, which will be important for informing research prioritization and regional decision making. This presentation will review and contrast nine current impact assessment methods and describe their granularity, scope, data requirements, and capabilities within the context of identifying regional and sectoral transfers of impacts that could result from transitioning to a circular economy for energy systems. The review of current approaches highlights the need for a new hybrid circularity assessment framework that leverages multiple methods. We describe one such approach: the Circular Economy Lifecycle Assessment and VIsualization (CELAVI) framework. CELAVI uses system dynamics to model material flows for multiple circular economy pathways, network theory to track the spatial and sectoral flow of functional units across a graph, and discrete event simulation to to step through time and evaluate lifecycle assessment data at each time step. The framework is designed to be flexible and scalable enough to accommodate multiple energy materials and multiple energy technologies. CELAVI's hybridization of multiple existing methods yields additional capabilities, which may help answer questions about how flows between the technosphere and ecosphere may evolve if the circularity of energy systems is modified.

circular economy↗

DOE OSTI2025

OpenSn: A massively parallel, open-source simulation environment for discrete ordinates radiation transport

OpenSn is an open-source, massively parallel deterministic radiation transport code for solving the discrete-ordinates ( S N ) form of the Boltzmann transport equation on unstructured, arbitrary polyhedral meshes. It supports high-fidelity simulations involving steady-state, eigenvalue, and adjoint problems for neutral particles (e.g., neutrons, photons, multi-particles), using the multigroup approximation in energy. OpenSn combines angular discretization via discrete ordinates with a discontinuous Galerkin finite element method (DGFEM) in space, enabling accurate resolution of transport physics on arbitrary polyhedral cells, included locally refined spatial grids. It includes multiple angular quadrature types, including locally refined angular quadratures. Written in modern C++ with a Python API, OpenSn runs efficiently on platforms ranging from laptops to supercomputers. The transport sweep algorithm is implemented using a task-based, directed-acyclic-graph (DAG) approach for each angle and supports asynchronous parallelism across thousands of MPI ranks. Group-set aggregation improves compute intensity, and synthetic acceleration techniques (e.g., diffusion synthetic acceleration, second-moment method) enhance solver convergence. OpenSn has been verified on reactor physics problems and demonstrated excellent weak and strong scaling performance on more than 32,768 processes, making it a versatile and robust platform for large-scale transport simulations in complex geometries.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗