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DOE OSTI2022

Modeling Flow and Transport in Fractured Rock using Machine Learning [Slides]

Fractured systems in the subsurface play a role in many natural and engineered applications such as geologic carbon sequestration, hydraulic fracturing and underground nuclear test detection. Structural information (fracture size, orientation, etc.) plays a key role in governing the dominant physics for these systems but can only be known statistically. Traditional modeling approaches either ignore or idealize structural information at these larger scales because we lack a computational framework that utilizes it in its entirety. The work presented here integrates computational physics, machine learning and graph theory to make a paradigm shift from computationally intensive high-fidelity models to coarse-scale graphs without loss of critical structural information. We exploit the underlying discrete structure of fracture networks in systems considering flow through fractures and fracture propagation. We demonstrate that compact graph representations require significantly fewer degrees of freedom (dof) to capture micro-fracture information and further accelerate these models with Machine Learning.

58 GEOSCIENCES↗

DOE OSTI2023

Session Introduction: Graph Representations and Algorithms in Biomedicine

Connectivity is a fundamental property of biological systems: on the cellular level, proteins interact with each other to form protein-protein interaction networks (PPIs); on the organism level, neurons are arranged in a network; and on a community-level, species can have complex relationships with one another that drive the development and balance of an ecosystem. Graphs, representations of systems consisting of entities as vertices and their connections as edges, are a useful structure to characterize many such systems. Such models can be used to understand biological systems that naturally have a network structure, including PPIs, biological neurons, and ecosystems. In today’s information age, graph representations and algorithms (often in combination with machine learning techniques) are used to organize massive amounts of related data, much of which may be heterogeneous or unstructured, and identify patterns that represent novel biological insights. PSB’s 2023 session “Graph Representations and algorithms in Biomedicine,” encompasses modern developments in graph theory and its applications to various fields of biomedicine. This session includes a wide range of research - knowledge graphs built from text-mined health data, heterogeneous networks using multi-omic databases, and graphs refined to represent uncertainty or improve memory usage.

Chrisman, Brianna S.↗

DOE OSTI2024

Bespoke Liquid/Liquid Interfaces (Final Technical Report)

The goal of DE-SC0001815 was to advance the basic science of liquid:liquid interface formation, to develop a deeper understanding of the mechanisms of phase separation and the essential relationships between solution composition, organization and dynamics that underlie the kinetic regime of solvent extraction. This included learning how interfacial organization and dynamics alters the properties of the primary coordination sphere of ions and the free energy of transport of ions complexes across a phase boundary. We relied primarily upon classical molecular dynamics studies to determine the equilibrium ensembles of these complex systems, but also utilized ab-initio MD and cluster-based density functional theory (DFT) calculations when more detailed investigation of the electronic structure was needed. We continued development of graph-theory based analyses to elucidate hierarchical correlations and expanded into geometric topology methods to quantify the collectively organized structures that can organize at a liquid/liquid interface during solute transport. One of the main conclusions was from the observation of two distinct mechanisms for solute transport - those that derive from amplifications of interfacial heterogeneity and surface roughness, and those wherein surface roughness has been dampened and instead collectively organized macrostructures work to bring solutes into the organic phase. It was our aim to create a concrete chemical model of the underlying driving forces behind interfacial primary and secondary structure formation and to map out the energetic features of solute transport so that tailored liquid/liquid can be developed that have characteristic kinetic features associated with mass transport.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2021

Directional Laplacian Centrality for Cyber Situational Awareness

Cyber operations is drowning in diverse, high-volume, multi-source data. To get a full picture of current operations and identify malicious events and actors, analysts must see through data generated by a mix of human activity and benign automated processes. Although many monitoring and alert systems exist, they typically use signature-based detection methods. We introduce a general method rooted in spectral graph theory to discover patterns and anomalies without a priori knowledge of signatures. We derive and propose a new graph-theoretic centrality measure based on the derivative of the graph Laplacian matrix in the direction of a vertex. To build intuition about our measure, we show how it identifies the most central vertices in standard network datasets and compare to other graph centrality measures. Finally, we focus our attention on studying its effectiveness in identifying important IP addresses in network flow data. Using both real and synthetic network flow data, we conduct several experiments to test our measure’s sensitivity to two types of injected attack profiles and show that vertices participating in injected attack profiles exhibit noticeable changes in our centrality measures, even when the injected anomalies are relatively small, and in the presence of simulated network dynamics.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

NASA NTRS1990

Using minimal spanning trees to compare the reliability of network topologies

Graph theoretic methods are applied to compute the reliability for several types of networks of moderate size. The graph theory methods used are minimal spanning trees for networks with bi-directional links and the related concept of strongly connected directed graphs for networks with uni-directional links. A comparison is conducted of ring networks and braided networks. The case is covered where just the links fail and the case where both links and nodes fail. Two different failure modes for the links are considered. For one failure mode, the link no longer carries messages. For the other failure mode, the link delivers incorrect messages. There is a description and comparison of link-redundancy versus path-redundancy as methods to achieve reliability. All the computations are carried out by means of a fault tree program.

Leister, Karen J.↗

DOE OSTI2023

Reduced-Order Models of Static Power Grids based on Spectral Clustering

For large-scale interconnected power systems that cover large geographical areas, certain electrical studies are required so that appropriate decisions ensure system reliability and low cost. For such studies, it is often neither practical nor necessary to model in detail the entire power system, which is increasingly complex due to a more diverse range of grid assets to choose from in both short and long-term planning. The goal of this paper is to present a methodology to reduce the order of large-scale power networks based on spectral graph theory given that current methods for static network reduction are not scalable. A brief analysis of some spectral clustering properties to determine which graph Laplacian matrix should be used and why is included. The analysis shows that the utilization of the normalized graph Laplacian is more advantageous for clustering purposes. Techniques are proposed to approximate cost functions for the aggregated generators. This is done via linear regression. The reduced-order model obtained with the proposed methodology has an accuracy above 94% and solves the scalability issue commonly present in other reduction methods. If the utilization of the reduced-order model is either constrained to load levels above mid-peak demand, or cost functions of aggregated units are approximated via a piecewise quadratic approach, then the error distribution is in the order of 10^-3. .

Baquedano-Aguilar, Mario D.↗

DOE OSTI2020

Using Graph Edit Distance for Noisy Subgraph Matching of Semantic Property Graphs

The subgraph matching problem is a fundamental problem in graph theory that is known to be NP-complete. In this study, performers were asked to develop algorithms to search for semantic property graphs that were subgraphs of a large knowledge graph. The templates provided contained structural information about the subgraphs and some attributes for each node and edge. There also exists a similarity measure between a set of attribute values that occurs on every node and edge. Algorithms performed well in the case where an exact match existed, but performers were also provided templates that had noise added such that there existed no match in the knowledge graph. Performers were asked to find the closest matches to those noisy subgraphs. To evaluate performance on this task, we developed a version of the graph edit distance algorithm to measure the cost of editing the template graph so that it is isomorphic in structure and attributes to the performer submission.

Ebsch, Christopher L.↗

DOE OSTI2020

Max-independent set and the quantum alternating operator ansatz

he maximum-independent set (MIS) problem of graph theory using the quantum alternating operator ansatz is studied. We perform simulations on the Rigetti Forest simulator for the square ring, K 2,3 , and K3,3 graphs and analyze the dependence of the algorithm on the depth of the circuit and initial states. The probability distribution of observation of the feasible states representing maximum-independent sets is observed to be asymmetric for the MIS problem, which is unlike the Max-Cut problem where the probability distribution of feasible states is symmetric. For asymmetric graphs, it is shown that the algorithm clearly favors the independent set with the larger number of elements even for finite circuit depth. Finally, we also compare the approximation ratios for the algorithm when we choose different initial states for the square ring graph and show that it is dependent on the choice of the initial state.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

A Look Inside the Black Box: Using graph-theoretical descriptors to interpret a Continuous-Filter Convolutional Neural Network (CF-CNN) trained on the global and local minimum energy structures of neutral water clusters

A Continuous Filter Convolutional Neural Network (CF-CNN) was trained to predict the potential energy of water cluster networks \ce{(H2O)_{\textit{N}}}, \textit{N}=10--30, corresponding to local minima lying within 5 kcal/mol from the putative minima taken from a newly published database containing over 5 million unique networks. The chemical sampling space of the database was characterized using chemical descriptors derived from graph theory, which led to the identification of important trends in the topology, connectivity, polygon structures associated with the various networks as a function of cluster size. The resulting graphs are available alongside the original database at \url{https://sites.uw.edu/wdbase/}. The CF-CNN trained on a subset of 500,000 networks for (\textit{N}=10, 30) yielded a mean absolute error of 0.002$\pm$0.002 kcal/mol per water molecule, giving the trained CF-CNN the highest accuracy of any neural network-based surrogate model to date. In addition, clusters of sizes not included in the training set exhibited errors of the same magnitude, indicating that the CF-CNN ptotocol is general enough to accurately predict energies of networks for both smaller and larger sizes than those used during training. The graph-theoretical descriptors were developed in order to analyze the properties of the full database and interpret the predictive power of the CF-CNN. Using topology measures, such as the Wiener index and the average shortest path length along with two similarity measures, we showed that all networks from the test set were within the range of the ones from the training set, suggesting that the training set covered the chemical space of interest quite well. Our graph analysis suggests that the mean degree and number of polygons for networks with larger errors tend to lie further from the mean than those with lower errors. The generality of the used CF-CNN was thus demonstrated, while the use of the graph-theoretical descriptors assisted in interpreting the predicted results.

Bilbrey, Jenna A.↗

DOE OSTI2022

A Julia Framework for Graph-Structured Nonlinear Optimization

Graph theory provides a convenient framework for modeling and solving structured optimization problems. Under this framework, the modeler can arrange/assemble the components of an optimization model (variables, constraints, objective functions, and data) within nodes and edges of a graph, and this representation can be used to visualize, manipulate, and solve the problem. In this work, we present a Julia framework for modeling and solving graph-structured nonlinear optimization problems. Our framework integrates the modeling package Plasmo.jl (which facilitates the construction and manipulation of graph models) and the nonlinear optimization solver MadNLP.jl (which provides capabilities for exploiting graph structures to accelerate solution). We illustrate with a simple example how model construction and manipulation can be performed in an intuitive manner using Plasmo.jl and how the model structure can be exploited by MadNLP.jl. We also demonstrate the scalability of the framework by targeting a large-scale, stochastic gas network problem that contains over 1.7 million variables.

Cole, David↗

NASA NTRS2004

Network Theory: A Primer and Questions for Air Transportation Systems Applications

A new understanding (with potential applications to air transportation systems) has emerged in the past five years in the scientific field of networks. This development emerges in large part because we now have a new laboratory for developing theories about complex networks: The Internet. The premise of this new understanding is that most complex networks of interest, both of nature and of human contrivance, exhibit a fundamentally different behavior than thought for over two hundred years under classical graph theory. Classical theory held that networks exhibited random behavior, characterized by normal, (e.g., Gaussian or Poisson) degree distributions of the connectivity between nodes by links. The new understanding turns this idea on its head: networks of interest exhibit scale-free (or small world) degree distributions of connectivity, characterized by power law distributions. The implications of scale-free behavior for air transportation systems include the potential that some behaviors of complex system architectures might be analyzed through relatively simple approximations of local elements of the system. For air transportation applications, this presentation proposes a framework for constructing topologies (architectures) that represent the relationships between mobility, flight operations, aircraft requirements, and airspace capacity, and the related externalities in airspace procedures and architectures. The proposed architectures or topologies may serve as a framework for posing comparative and combinative analyses of performance, cost, security, environmental, and related metrics.

Holmes, Bruce J.↗

DOE OSTI2024

Beyond nothingness in the formation and functional relevance of voids in polymer films

Abstract Voids—the nothingness—broadly exist within nanomaterials and impact properties ranging from catalysis to mechanical response. However, understanding nanovoids is challenging due to lack of imaging methods with the needed penetration depth and spatial resolution. Here, we integrate electron tomography, morphometry, graph theory and coarse-grained molecular dynamics simulation to study the formation of interconnected nanovoids in polymer films and their impacts on permeance and nanomechanical behaviour. Using polyamide membranes for molecular separation as a representative system, three-dimensional electron tomography at nanometre resolution reveals nanovoid formation from coalescence of oligomers, supported by coarse-grained molecular dynamics simulations. Void analysis provides otherwise inaccessible inputs for accurate fittings of methanol permeance for polyamide membranes. Three-dimensional structural graphs accounting for the tortuous nanovoids within, measure higher apparent moduli with polyamide membranes of higher graph rigidity. Our study elucidates the significance of nanovoids beyond the nothingness, impacting the synthesis‒morphology‒function relationships of complex nanomaterials.

36 MATERIALS SCIENCE↗

NASA NTRS2002

An Efficient Scheme for Updating Sparse Cholesky Factors

Raghavan had earlier developed the software package DCSPACK which can be used for solving sparse linear systems where the coefficient matrix is symmetric and positive definite (this project was not funded by NASA but by agencies such as NSF). DSCPACK-S is the serial code and DSCPACK-P is a parallel implementation suitable for multiprocessors or networks-of-workstations with message passing using MCI. The main algorithm used is the Cholesky factorization of a sparse symmetric positive positive definite matrix A = LL(T). The code can also compute the factorization A = LDL(T). The complexity of the software arises from several factors relating to the sparsity of the matrix A. A sparse N x N matrix A has typically less that cN nonzeroes where c is a small constant. If the matrix were dense, it would have O(N2) nonzeroes. The most complicated part of such sparse Cholesky factorization relates to fill-in, i.e., zeroes in the original matrix that become nonzeroes in the factor L. An efficient implementation depends to a large extent on complex data structures and on techniques from graph theory to reduce, identify, and manage fill. DSCPACK is based on an efficient multifrontal implementation with fill-managing algorithms and implementation arising from earlier research by Raghavan and others. Sparse Cholesky factorization is typically a four step process: (1) ordering to compute a fill-reducing numbering, (2) symbolic factorization to determine the nonzero structure of L, (3) numeric factorization to compute L, and, (4) triangular solution to solve L(T)x = y and Ly = b. The first two steps are symbolic and are performed using the graph of the matrix. The numeric factorization step is of dominant cost and there are several schemes for improving performance by exploiting the nested and dense structure of groups of columns in the factor. The latter are aimed at better utilization of the cache-memory hierarchy on modem processors to prevent cache-misses and provide execution rates (operations/second) that are close to the peak rates for dense matrix computations. Currently, EPISCOPACY is being used in an application at NASA directed by J. Newman and M. James. We propose the implementation of efficient schemes for updating the LL(T) or LDL(T) factors computed in DSCPACK-S to meet the computational requirements of their project. A brief description is provided in the next section.

Raghavan, Padma↗

DOE OSTI2024

A General Materials Data Science Framework for Quantitative 2D Analysis of Particle Growth from Image Sequences

Abstract Phase transformations are a challenging problem in materials science, which lead to changes in properties and may impact performance of material systems in various applications. We introduce a general framework for the analysis of particle growth kinetics by utilizing concepts from machine learning and graph theory. As a model system, we use image sequences of atomic force microscopy showing the crystallization of an amorphous fluoroelastomer film. To identify crystalline particles in an amorphous matrix and track the temporal evolution of the particle dispersion, we have developed quantitative methods of 2D analysis. 700 image sequences were analyzed using a neural network architecture, achieving 0.97 pixel-wise classification accuracy as a measure of the correctly classified pixels. The growth kinetics of isolated and impinged particles were tracked throughout time using these image sequences. The relationship between image sequences and spatiotemporal graph representations was explored to identify the proximity of crystallites from each other. The framework enables the analysis of all image sequences without the requirement of sampling for specific particles or timesteps for various materials systems.

36 MATERIALS SCIENCE↗

DOE OSTI2020

De Sitter diagrammar and the resummation of time

Light scalars in inflationary spacetimes suffer from logarithmic infrared divergences at every order in perturbation theory. This corresponds to the scalar field values in different Hubble patches undergoing a random walk of quantum fluctuations, leading to a simple toy “landscape” on superhorizon scales, in which we can explore questions relevant to eternal inflation. However, for a sufficiently long period of inflation, the infrared divergences appear to spoil computability. Some form of renormalization group approach is thus motivated to resum the log divergences of conformal time. Such a resummation may provide insight into De Sitter holography. We present here a novel diagrammatic analysis of these infrared divergences and their resummation. Basic graph theory observations and momen- tum power counting for the in-in propagators allow a simple and insightful determination of the leading-log contributions. One thus sees diagrammatically how the superhorizon sector consists of a semiclassical theory with quantum noise evolved by a first-order, interacting classical equation of motion. This rigorously leads to the “Stochastic Inflation” ansatz developed by Starobinsky to cure the scalar infrared pathology nonperturbatively. Our approach is a controlled approximation of the underlying quantum field theory and is systematically improvable.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Symmetry reduction of tensor networks in many-body theory: I. Automated symbolic evaluation of SU(2) algebra

Abstract The ongoing progress in (nuclear) many-body theory is accompanied by an ever-rising increase in complexity of the underlying formalisms used to solve the stationary Schrödinger equation. The associated working equations at play in state-of-the-art ab initio nuclear many-body methods can be analytically reduced with respect to angular-momentum, i.e. SU (2), quantum numbers whenever they are effectively employed in a symmetry-restricted context. The corresponding procedure constitutes a tedious and error-prone but yet an integral part of the implementation of those many-body frameworks. Indeed, this symmetry reduction is a key step to advance modern simulations to higher accuracy since the use of symmetry-adapted tensors can decrease the computational complexity by orders of magnitude. While attempts have been made in the past to automate the (anti-) commutation rules linked to Fermionic and Bosonic algebras at play in the derivation of the working equations, there is no systematic account to achieve the same goal for their symmetry reduction. In this work, the first version of an automated tool performing graph-theory-based angular-momentum reduction is presented. Taking the symmetry-unrestricted expressions of a generic tensor network as an input, the code provides their angular-momentum-reduced form in an error-safe way in a matter of seconds. Several state-of-the-art many-body methods serve as examples to demonstrate the generality of the approach and to highlight the potential impact on the many-body community.

Tichai, A.↗

DOE OSTI2024

Quantum Simulations of Radiation Damage in a Molecular Polyethylene Analog

Abstract An atomic‐level understanding of radiation‐induced damage in simple polymers like polyethylene is essential for determining how these chemical changes can alter the physical and mechanical properties of important technological materials such as plastics. Ensembles of quantum simulations of radiation damage in a polyethylene analog are performed using the Density Functional Tight Binding method to help bind its radiolysis and subsequent degradation as a function of radiation dose. Chemical degradation products are categorized with a graph theory approach, and occurrence rates of unsaturated carbon bond formation, crosslinking, cycle formation, chain scission reactions, and out‐gassing products are computed. Statistical correlations between product pairs show significant correlations between chain scission reactions, unsaturated carbon bond formation, and out‐gassing products, though these correlations decrease with increasing atom recoil energy. The results present relatively simple chemical descriptors as possible indications of network rearrangements in the middle range of excitation energies. Ultimately, the work provides a computational framework for determining the coupling between nonequilibrium chemistry in polymers and potential changes to macro‐scale properties that can aid in the interpretation of future radiation damage experiments on plastic materials.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

DOE OSTI2023

Engineering of increased L-Threonine production in bacteria by combinatorial cloning and machine learning

The goal of this study is to develop a general strategy for bacterial engineering using an integrated synthetic biology and machine learning (ML) approach. This strategy was developed in the context of increasing L-threonine production in Escherichia coli ATCC 21277. A set of 16 genes was initially selected based on metabolic pathway relevance to threonine biosynthesis and used for combinatorial cloning to construct a set of 385 strains to generate training data (i.e., a range of L-threonine titers linked to each of the specific gene combinations). Hybrid (regression/classification) deep learning (DL) models were developed and used to predict additional gene combinations in subsequent rounds of combinatorial cloning for increased L-threonine production based on the training data. As a result, E. coli strains built after just three rounds of iterative combinatorial cloning and model prediction generated higher L-threonine titers (from 2.7 g/L to 8.4 g/L) than those of patented L-threonine strains being used as controls (4-5 g/L). Interesting combinations of genes in L-threonine production included deletions of the tdh, metL, dapA, and dhaM genes as well as overexpression of the pntAB, ppc, and aspC genes. Mechanistic analysis of the metabolic system constraints for the best performing constructs offers ways to improve the models by adjusting weights for specific gene combinations. Graph theory analysis of pairwise gene modifications and corresponding levels of L-threonine production also suggests additional rules that can be incorporated into future ML models.

60 APPLIED LIFE SCIENCES↗