Results for “network theory (graphs)” — Page 4

DOE OSTI2022

Active learning of chemical reaction networks via probabilistic graphical models and Boolean reaction circuits

Discerning networks of many reactions among multiple interconverting species is challenging. Here, we present a reaction network identification methodology. Our methodology enumerates all stoichiometrically and chemically feasible reactions and requires statistical evidence from effluent concentrations for the inclusion or exclusion of each from the reaction network, contrasting with the commonly seen incremental approach and other work of relying heavily upon chemical intuition and assuming the reactions occurring. Using graph theory alongside an active learning design of experiments that propose maximally informative feeds, we identify the underlying reaction network with minimal laboratory runs. Here, we introduce chemistry-probabilistic graphical modeling and Boolean reaction circuits to statistically quantify which reactions occur from effluent concentrations. Our methodology accurately discerns active reactions, as showcased upon a laboratory network of cross-ketonization of furoic and lauric acid and validated upon simulated networks of thermal and CO 2 -assisted ethane dehydrogenation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Spin-informed universal graph neural networks for simulating magnetic ordering

The screening and discovery of magnetic materials are hindered by the computational cost of first-principles density-functional theory (DFT) calculations required to find the ground state magnetic ordering. Although universal machine-learning interatomic potentials (uMLIPs), also known as atomistic foundation models, offer high-fidelity models of many atomistic systems with significant speedup, they currently lack the inputs required for predicting magnetic ordering. In this work, we present a data-efficient, spin-informed graph neural network framework that incorporates spin degrees of freedom as inputs and preserves physical symmetries, extending the functionality of uMLIPs to simulate magnetic orderings. This framework speeds up DFT calculations through better initial guesses for magnetic moments, determines the ground-state ordering of bulk materials and even generalizes to magnetic ordering in surfaces. Furthermore, we implement a closed-loop anomaly detection approach that effectively addresses the classic "chicken-and-egg" problem of creating a high-quality dataset while developing a uMLIP, unearthing anomalies in large benchmark datasets and boosting model accuracy.

Xu, Wenbin↗

DOE OSTI2022

Accelerating Multiscale Materials Modeling with Machine Learning

The focus of this project is to accelerate and transform the workflow of multiscale materials modeling by developing an integrated toolchain seamlessly combining DFT, SNAP, LAMMPS, (shown in Figure 1-1) and a machine-learning (ML) model that will more efficiently extract information from a smaller set of first-principles calculations. Our ML model enables us to accelerate first-principles data generation by interpolating existing high fidelity data, and extend the simulation scale by extrapolating high fidelity data (10 2 atoms) to the mesoscale (10 4 atoms). It encodes the underlying physics of atomic interactions on the microscopic scale by adapting a variety of ML techniques such as deep neural networks (DNNs), and graph neural networks (GNNs). We developed a new surrogate model for density functional theory using deep neural networks. The developed ML surrogate is demonstrated in a workflow to generate accurate band energies, total energies, and density of the 298K and 933K Aluminum systems. Furthermore, the models can be used to predict the quantities of interest for systems with more number of atoms than the training data set. We have demonstrated that the ML model can be used to compute the quantities of interest for systems with 100,000 Al atoms. When compared with 2000 Al system the new surrogate model is as accurate as DFT, but three orders of magnitude faster. We also explored optimal experimental design techniques to choose the training data and novel Graph Neural Networks to train on smaller data sets. These are promising methods that need to be explored in the future.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Topological Machine Learning Methods for Power System Responses to Contingencies: Preprint

While deep learning tools, coupled with the emerging machinery of topological data analysis, are proven to deliver various performance gains in a broad range of applications, from image classification to biosurveillance to blockchain fraud detection, their utility in areas of high societal importance such as power system modeling and, particularly, resilience quantification in the energy sector yet remain untapped. To provide fast acting synthetic regulation and contingency reserve services to the grid while having minimal disruptions on customer quality of service, we propose a new topologybased system that depends on neural network architecture for impact metrics classification and prediction in power systems. This novel topology-based system allows one to evaluate the impact of three power system contingency types, namely, in conjunction with transmission lines, transformers, and transmission lines combined with transformers. We show that the proposed new neural network architecture equipped with local topological measures facilitates both more accurate classification of unserved load as well as the amount of unserved load. In addition, we are able to learn complex relationships between electrical properties and local topological measurements on the simulated response to contingencies for NREL-SIIP power system.

graph theory↗

DOE OSTI2023

Exploring NaCl-PuCl 3 molten salts with machine learning interatomic potentials and graph theory

Actinide molten salts are the basis of the liquid fuels used in molten salt reactors. Due to the inherent difficulties associated with high temperature and hazardous conditions, experimental investigations of fundamental properties of these materials are usually challenging. In this work, we describe the structure and transport of NaCl-PuCl 3 mixtures using computational techniques. Three compositions were considered (16, 25, and 36 mol% PuCl 3 ) over a temperature range (730 – 1257K) using ab initio molecular dynamics, which provided the necessary data sets for training machine learned interatomic potentials. Further, molecular dynamics simulations based on these potentials were then used to determine structure and transport properties. A substantial change was noted in the structure factor when increasing the PuCl 3 content from 25 to 36 mol%. This change is linked to the aggregation of larger Pu 3+ clusters. In addition, the similarity of the atomic environments of metal cations in molten salt systems to their solid states counterparts was investigated using an unsupervised learning technique. Finally, graph theory was employed to explore the structure and size of actinide networks. Consistent with the structure factor, a dense Pu 3+ intermolecular structure is observed within the 36 mol% PuCl 3 mixture. The structure of cation-cation inter-junctions is also discussed. In all cases, the diffusion of Pu 3+ is significantly lower than that of Na + and Cl - .

36 MATERIALS SCIENCE↗

DOE OSTI2020

Approximate Inverse Chain Preconditioner: Iteration Count Case Study for Spectral Support Solvers

As the growing availability of computational power slows, there has been an increasing reliance on algorithmic advances. However, faster algorithms alone will not necessarily bridge the gap in allowing computational scientists to study problems at the edge of scientific discovery in the next several decades. Often, it is necessary to simplify or precondition solvers to accelerate the study of large systems of linear equations commonly seen in a number of scientific fields. Preconditioning a problem to increase efficiency is often seen as the best approach; yet, preconditioners which are fast, smart, and efficient do not always exist. Following the progress of [1], we present a new preconditioner for symmetric diagonally dominant (SDD) systems of linear equations. These systems are common in certain PDEs, network science, and supervised learning among others. Based on spectral support graph theory, this new preconditioner builds off of the work of [2], computing and applying a V-cycle chain of approximate inverse matrices. This preconditioner approach is both algebraic in nature as well as hierarchically-constrained depending on the condition number of the system to be solved. Due to its generation of an Approximate Inverse Chain of matrices, we refer to this as the AIC preconditioner. We further accelerate the AIC preconditioner by utilizing precomputations to simplify setup and multiplications in the con-text of an iterative Krylov-subspace solver. While these iterative solvers can greatly reduce solution time, the number of iterations can grow large quickly in the absence of good preconditioners. Initial results for the AIC preconditioner have shown a very large reduction in iteration counts for SDD systems as compared to standard preconditioners such as Incomplete Cholesky (ICC) and Multigrid (MG). We further show significant reduction in iteration counts against the more advanced Combinatorial Multigrid (CMG) preconditioner. We have further developed no-fill sparsification techniques to ensure that the computational cost of applying the AIC preconditioner does not grow prohibitively large as the depth of the V-cycle grows for systems with larger condition numbers. Our numerical results have shown that these sparsifiers maintain the sparsity structure of our system while also displaying significant reductions in iteration counts.1 2

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Approximate Inverse Chain Preconditioner: Iteration Count Case Study for Spectral Support Solvers

As the growing availability of computational power slows, there has been an increasing reliance on algorithmic advances. However, faster algorithms alone will not necessarily bridge the gap in allowing computational scientists to study problems at the edge of scientific discovery in the next several decades. Often, it is necessary to simplify or precondition solvers to accelerate the study of large systems of linear equations commonly seen in a number of scientific fields. Preconditioning a problem to increase efficiency is often seen as the best approach; yet, preconditioners which are fast, smart, and efficient do not always exist. Following the progress of [1], we present a new preconditioner for symmetric diagonally dominant (SDD) systems of linear equations. These systems are common in certain PDEs, network science, and supervised learning among others. Based on spectral support graph theory, this new preconditioner builds off of the work of [2], computing and applying a V-cycle chain of approximate inverse matrices. This preconditioner approach is both algebraic in nature as well as hierarchically-constrained depending on the condition number of the system to be solved. Due to its generation of an Approximate Inverse Chain of matrices, we refer to this as the AIC preconditioner. We further accelerate the AIC preconditioner by utilizing precomputations to simplify setup and multiplications in the con-text of an iterative Krylov-subspace solver. While these iterative solvers can greatly reduce solution time, the number of iterations can grow large quickly in the absence of good preconditioners. Initial results for the AIC preconditioner have shown a very large reduction in iteration counts for SDD systems as compared to standard preconditioners such as Incomplete Cholesky (ICC) and Multigrid (MG). We further show significant reduction in iteration counts against the more advanced Combinatorial Multigrid (CMG) preconditioner. We have further developed no-fill sparsification techniques to ensure that the computational cost of applying the AIC preconditioner does not grow prohibitively large as the depth of the V-cycle grows for systems with larger condition numbers. Our numerical results have shown that these sparsifiers maintain the sparsity structure of our system while also displaying significant reductions in iteration counts.1 2

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Graph Neural Network Guided Evolutionary Search of Grain Boundaries in 2D Materials

Not Available

2D Materials↗

DOE OSTI2021

OrbNet Denali: A machine learning potential for biological and organic chemistry with semi-empirical cost and DFT accuracy

We present OrbNet Denali, a machine learning model for an electronic structure that is designed as a drop-in replacement for groundstate density functional theory (DFT) energy calculations. The model is a message-passing graph neural network that uses symmetryadapted atomic orbital features from a low-cost quantum calculation to predict the energy of a molecule. OrbNet Denali is trained on a vast dataset of 2.3 × 10 6 DFT calculations on molecules and geometries. This dataset covers the most common elements in biochemistry and organic chemistry (H, Li, B, C, N, O, F, Na, Mg, Si, P, S, Cl, K, Ca, Br, and I) and charged molecules. OrbNet Denali is demonstrated on several well-established benchmark datasets, and we find that it provides accuracy that is on par with modern DFT methods while offering a speedup of up to three orders of magnitude. For the GMTKN55 benchmark set, OrbNet Denali achieves WTMAD-1 and WTMAD-2 scores of 7.19 and 9.84, on par with modern DFT functionals. For several GMTKN55 subsets, which contain chemical problems that are not present in the training set, OrbNet Denali produces a mean absolute error comparable to those of DFT methods. For the Hutchison conformer benchmark set, OrbNet Denali has a median correlation coefficient of R 2 = 0.90 compared to the reference DLPNO-CCSD(T) calculation and R 2 = 0.97 compared to the method used to generate the training data (ωB97X-D3/def2- TZVP), exceeding the performance of any other method with a similar cost. Similarly, the model reaches chemical accuracy for noncovalent interactions in the S66x10 dataset. For torsional profiles, OrbNet Denali reproduces the torsion profiles of ωB97X-D3/def2-TZVP with an average mean absolute error of 0.12 kcal/mol for the potential energy surfaces of the diverse fragments in the TorsionNet500 dataset.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Defect Diffusion Graph Neural Networks for Materials Discovery in High-Temperature Energy Applications

Here, the migration of crystallographic defects dictates material properties and performance for a plethora of technological applications. Density functional theory (DFT)-based nudged elastic band (NEB) calculations are a powerful computational technique for predicting defect migration activation energy barriers, yet they become prohibitively expensive for high-throughput screening of defect diffusivities. Without introducing hand-crafted (i.e., chemistry- or structure-specific) descriptors, we propose a generalized deep learning approach to train surrogate models for NEB energies of vacancy migration by hybridizing graph neural networks with transformer encoders and simply using pristine host structures as input. With sufficient training data, computationally efficient and simultaneous inference of vacancy defect thermodynamics and migration activation energies can be obtained to compute temperature-dependent vacancy diffusivities and to down-select candidates for more thorough DFT analysis or experiments. Thus, as we specifically demonstrate for potential water-splitting materials, candidates with desired defect thermodynamics, kinetics, and host stability properties can be more rapidly targeted from open-source databases of experimentally validated or hypothetical materials.

14 SOLAR ENERGY↗

DOE OSTI2024

Cluster expansion by transfer learning for phase stability predictions

Recent progress towards universal machine-learned interatomic potentials holds considerable promise for materials discovery. Yet the accuracy of these potentials for predicting phase stability may still be limited. In contrast, cluster expansions provide accurate phase stability predictions but are computationally demanding to parameterize from first principles, especially for structures of low dimension or with a large number of components, such as interfaces or multimetal catalysts. We overcome this trade-off via transfer learning. Using Bayesian inference, we incorporate prior statistical knowledge from machine-learned and physics-based potentials, enabling us to sample the most informative configurations and to efficiently fit first-principles cluster expansions. Furthermore, this algorithm is tested on Pt:Ni, showing robust convergence of the mixing energies as a function of sample size with reduced statistical fluctuations.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Postdisaster Routing of Movable Energy Resources for Enhanced Distribution System Resilience: A Deep Reinforcement Learning-Based Approach

The deployment of movable energy resources (MERs) can be an effective strategy to restore critical loads to enhance power system resilience when no other energy sources are available after the occurrence of an extreme event. Since the optimal locations of MERs following an extreme event are dependent on system operating states (e.g., the loads at each node, on/off status of system branches, and so on), existing analytical and population-based approaches must repeat the entire analysis and calculation when the system operating states change. On the contrary, if deep reinforcement learning (DRL)-based algorithms are sufficiently trained with a wide range of scenarios, they can quickly find optimal or near-optimal locations irrespective of changes in system states. A deep Q-learning-based approach is proposed for optimal MER deployment to enhance power system resilience. MERs can be also utilized to complement other types of resources, if available. The proposed approach operates in two stages after the occurrence of extreme events. In the first stage, the distribution network is represented as a graph, and the network is then reconfigured using tie switches by using Kruskal’s spanning forest search algorithm (KSFSA). To maximize critical load recovery, the optimal or near-optimal locations of MERs are chosen in the second stage. Further, case studies on a 33-node distribution system and a modified IEEE 123-node system demonstrate the effectiveness of the proposed approach for postdisaster routing of MERs.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2026

Stakeholder-guided holistic, Adaptive Framework for enhancing community Energy Resilience (SAFER) (Final Technical Report)

The Stakeholder-guided holistic, Adaptive Framework for enhancing community Energy Resilience (SAFER) project advances resilience science and engineering by addressing challenges in rural Kansas communities where aging infrastructure, extreme weather, and socioeconomic disparities heighten vulnerability to energy disruptions. Traditional approaches often focus on technical performance while overlooking community concerns and priorities. SAFER responds by integrating community perspectives with advanced analytical frameworks to create a holistic model for measuring and improving resilience. Project objectives included developing novel resilience metrics, advancing modeling frameworks that capture interdependencies across infrastructures, and embedding community-centric indicators directly into planning processes for distributed energy resources. The key technical innovations included the creation of self-organizing map (SOM)-based indices for objective resilience quantification, hetero-functional graph theory (HFGT) models linking power, water, transportation, and community assets, and graph neural network (GNN) tools for identifying critical nodes in complex systems. Community-centric energy planning was demonstrated through optimal siting and sizing of (photovoltaic) PV and battery storage, ensuring resilience enhancements also addressed energy burden and energy insecurity. SAFER engaged community partners in Dodge City and Ford County through surveys, focus groups, and workshops, generating more than 600 responses that established baseline measures of energy burden, financial insecurity, and willingness-to-pay to avoid outages. This data, organized in terms of a community capitals framework, informed the development of weighted reliability indices that better reflect community costs than traditional utility metrics. SAFER’s GNN-based critical node identification framework identified expert-labelled critical nodes with over 99% accuracy, while also uncovering additional functionalities essential for proactive resilience planning. The project’s models demonstrated that optimal PV and storage deployment could improve resilience indices by over 11 percent, with dispatch strategies further enhancing outcomes, confirming both the technical effectiveness and economic feasibility of these approaches. Through its combined emphasis on rigorous modeling, community-focused planning, and community engagement, SAFER advances the state of resilience research while delivering direct benefits to rural communities. The project provides tools, guidelines, and resilience heatmaps that help utilities, local governments, and residents better anticipate disruptions, prioritize investments, and strengthen the capacity to withstand and recover from energy-related hazards. Furthermore, the developed HFG and GNN frameworks are designed for transferability, allowing them to be adapted for resilience planning in other communities with minimal retraining. This inductive learning capability provides a scalable pathway to extend the SAFER project’s impact. Thus, creating a foundation for a nationally applicable model of infrastructure resilience. Additionally, the HFG can also be extended to include other FEMA community lifelines.

14 SOLAR ENERGY↗

DOE OSTI2024

Phase Diagrams of Alloys and Their Hydrides via On-Lattice Graph Neural Networks and Limited Training Data

Efficient prediction of sampling-intensive thermodynamic properties is needed to evaluate material performance and permit high-throughput materials modeling for a diverse array of technology applications. To alleviate the prohibitive computational expense of high-throughput configurational sampling with density functional theory (DFT), surrogate modeling strategies like cluster expansion are many orders of magnitude more efficient but can be difficult to construct in systems with high compositional complexity. We therefore employ minimal-complexity graph neural network models that accurately predict and can even extrapolate to out-of-train distribution formation energies of DFT-relaxed structures from an ideal (unrelaxed) crystallographic representation. This enables the large-scale sampling necessary for various thermodynamic property predictions that may otherwise be intractable and can be achieved with small training data sets. Two exemplars, optimizing the thermodynamic stability of low-density high-entropy alloys and modulating the plateau pressure of hydrogen in metal alloys, demonstrate the power of this approach, which can be extended to a variety of materials discovery and modeling problems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Moiré Patterns in Pt Overlayers on Gold: A Graph Neural Network Interatomic Potential Study

Overlayer structures in bimetallic catalysts are relevant to a variety of catalytic reactions, particularly in electrocatalysis for fuel cell applications. Previous computational studies largely consider these overlayer structures to be those of a pseudomorphic overlayer, where there is a 1:1 atomic ratio between the overlayer and the support metal. Our previous work based on density functional theory (DFT) has shown that there exist nonstoichiometric overlayer structures that are more stable than the stoichiometric ones. Here, in this work, we developed a graph neural network interatomic potential (GNN-IP) to analyze structures formed in Pt overlayers on Au(111). The GNN-IP was used to explore properties of nonstoichiometric overlayers at length scales that are prohibitively expensive to pursue with planewave DFT calculations. In particular, we examined large Pt islands on top of a 48 × 48 Au(111) unit cell to explore the influence of the rotational angle (α) between the Pt overlayer and support Au(111) on both the stability of and the preferred atomic density in the overlayer. Island structures with smaller rotational angles between the Pt overlayer and Au(111) tend to be more stable. Further, smaller rotational angles tend to result in lower atomic density in the Pt overlayer.

chemical structure↗

DOE OSTI2020

Prediction of organic homolytic bond dissociation enthalpies at near chemical accuracy with sub-second computational cost

Bond dissociation enthalpies (BDEs) of organic molecules play a fundamental role in determining chemical reactivity and selectivity. However, BDE computations at sufficiently high levels of quantum mechanical theory require substantial computing resources. In this paper, we develop a machine learning model capable of accurately predicting BDEs for organic molecules in a fraction of a second. We perform automated density functional theory (DFT) calculations at the M06-2X/def2-TZVP level of theory for 42,577 small organic molecules, resulting in 290,664 BDEs. A graph neural network trained on a subset of these results achieves a mean absolute error of 0.58 kcal mol-1 (vs DFT) for BDEs of unseen molecules. We further demonstrate the model on two applications: first, we rapidly and accurately predict major sites of hydrogen abstraction in the metabolism of drug-like molecules, and second, we determine the dominant molecular fragmentation pathways during soot formation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

CELAVI (Circular Economy Lifecycle Assessment and VIsualization) [SWR-20-87]

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. The Circular Economy Lifecycle Assessment and VIsualization (CELAVI) framework allows stakeholders to quantify and visualize potential regional and sectoral transfers of impacts that could result from transitioning to a circular economy, with particular focus on energy materials. The framework uses system dynamics to model material flows for multiple circular economy pathways and decisions are based on learning-by-doing and are implemented via cost and strategic value of different circular economy pathways. It uses 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 to accommodate multiple energy materials and multiple energy technologies. The primary goal of CELAVI is to help answer questions about how material flows and environmental and economic impacts of energy systems might change if the circularity of energy systems increases.

Eberle, Annika↗

DOE OSTI2022

CELAVI (Circular Economy Lifecycle Assessment and VIsualization) v.1.3.1 9/30/2022 [SWR-20-87]

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. The Circular Economy Lifecycle Assessment and VIsualization (CELAVI) framework allows stakeholders to quantify and visualize potential regional and sectoral transfers of impacts that could result from transitioning to a circular economy, with particular focus on energy materials. The framework uses system dynamics to model material flows for multiple circular economy pathways and decisions are based on learning-by-doing and are implemented via cost and strategic value of different circular economy pathways. It uses 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 to accommodate multiple energy materials and multiple energy technologies. The primary goal of CELAVI is to help answer questions about how material flows and environmental and economic impacts of energy systems might change if the circularity of energy systems increases.

Eberle, Annika↗