Graph Neural Network (GNN) for Property Prediction
Presented at the DOE-NETL 2020 Virtual Meeting - SMART Initiative Annual Review Meeting November 2-3, 2020, 11/2
Riedl, Michael↗
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Graph Sampling for Visual Analytics
Effectively visualizing large graphs and capturing the statistical properties are two challenging tasks. To aid in these two tasks, many sampling approaches for graph simplification have been proposed, falling into three categories: node sampling, edge sampling, and traversal-based sampling. It is still unknown which approach is the best. We evaluate commonly used graph sampling methods through a combined visual and statistical comparison of graphs sampled at various rates. We conduct our evaluation on three graph models: random graphs, small-world graphs, and scale-free graphs. Initial results indicate that the effectiveness of a sampling method is dependent on the graph model, the size of the graph, and the desired statistical property. This benchmark study can be used as a guideline in choosing the appropriate method for a particular graph sampling task, and the results presented can be incorporated into graph visualization and analysis tools.
97 MATHEMATICS AND COMPUTING↗
Graph neural networks predict energetic and mechanical properties for models of solid solution metal alloy phases
Here, we developed a PyTorch-based architecture called HydraGNN that implements graph convolutional neural networks (GCNNs) to predict the formation energy and the bulk modulus for models of solid solution alloys for various atomic crystal structures and relaxed volumes. We trained the GCNN surrogate model on a dataset for nickel–niobium (NiNb) generated by the embedded atom model (EAM) empirical interatomic potential for demonstration purposes. The dataset was generated by calculating the formation energy and the bulk modulus as a prototypical elastic property for optimized geometries starting from initial body-centered cubic (BCC), face-centered cubic (FCC), and hexagonal compact packed (HCP) crystal structures, with configurations spanning the possible compositional range for each of the three types of initial crystal structures. Numerical results show that the GCNN model effectively predicts both the formation energy and the bulk modulus as function of the optimized crystal structure, relaxed volume, and configurational entropy of the model structures for solid solution alloys.
36 MATERIALS SCIENCE↗
A Graph Based Backtracking Algorithm for Solving General CSPs
Many AI tasks can be formalized as constraint satisfaction problems (CSPs), which involve finding values for variables subject to constraints. While solving a CSP is an NP-complete task in general, tractable classes of CSPs have been identified based on the structure of the underlying constraint graphs. Much effort has been spent on exploiting structural properties of the constraint graph to improve the efficiency of finding a solution. These efforts contributed to development of a class of CSP solving algorithms called decomposition algorithms. The strength of CSP decomposition is that its worst-case complexity depends on the structural properties of the constraint graph and is usually better than the worst-case complexity of search methods. Its practical application is limited, however, since it cannot be applied if the CSP is not decomposable. In this paper, we propose a graph based backtracking algorithm called omega-CDBT, which shares merits and overcomes the weaknesses of both decomposition and search approaches.
Pang, Wanlin↗
Impact-Driven Sampling Strategies for Hybrid Attack Graphs
Cyber-Physical Systems (CPSs) have a large input space, with discrete and continuous elements across multiple layers. Hybrid Attack Graph (HAG) provide a flexible and efficient approach to generate attack sequences for a CPS. Analysis and testing of large-scale HAGs are prohibitively costly. We propose a dimension reduction via property-preserving multi-layer graph sampling algorithms. Existing property-preserving graph sampling approaches generate a representative subgraph of an original large-sized graph while preserving the key properties, such as node and edge distribution, clustering coefficients, and betweenness. On the other hand, we propose impact-driven sampling strategies to transform the input data to a lower-dimensional representation while retaining key properties of the data.
Subasi, Omer↗
Model checking
Automatic formal verification methods for finite-state systems, also known as model-checking, successfully reduce labor costs since they are mostly automatic. Model checkers explicitly or implicitly enumerate the reachable state space of a system, whose behavior is described implicitly, perhaps by a program or a collection of finite automata. Simple properties, such as mutual exclusion or absence of deadlock, can be checked by inspecting individual states. More complex properties, such as lack of starvation, require search for cycles in the state graph with particular properties. Specifications to be checked may consist of built-in properties, such as deadlock or 'unspecified receptions' of messages, another program or implicit description, to be compared with a simulation, bisimulation, or language inclusion relation, or an assertion in one of several temporal logics. Finite-state verification tools are beginning to have a significant impact in commercial designs. There are many success stories of verification tools finding bugs in protocols or hardware controllers. In some cases, these tools have been incorporated into design methodology. Research in finite-state verification has been advancing rapidly, and is showing no signs of slowing down. Recent results include probabilistic algorithms for verification, exploitation of symmetry and independent events, and the use symbolic representations for Boolean functions and systems of linear inequalities. One of the most exciting areas for further research is the combination of model-checking with theorem-proving methods.
Dill, David L.↗
Multi-task graph neural networks for simultaneous prediction of global and atomic properties in ferromagnetic systems *
Abstract We introduce a multi-tasking graph convolutional neural network, HydraGNN, to simultaneously predict both global and atomic physical properties and demonstrate with ferromagnetic materials. We train HydraGNN on an open-source ab initio density functional theory (DFT) dataset for iron-platinum with a fixed body centered tetragonal lattice structure and fixed volume to simultaneously predict the mixing enthalpy (a global feature of the system), the atomic charge transfer, and the atomic magnetic moment across configurations that span the entire compositional range. By taking advantage of underlying physical correlations between material properties, multi-task learning (MTL) with HydraGNN provides effective training even with modest amounts of data. Moreover, this is achieved with just one architecture instead of three, as required by single-task learning (STL). The first convolutional layers of the HydraGNN architecture are shared by all learning tasks and extract features common to all material properties. The following layers discriminate the features of the different properties, the results of which are fed to the separate heads of the final layer to produce predictions. Numerical results show that HydraGNN effectively captures the relation between the configurational entropy and the material properties over the entire compositional range. Overall, the accuracy of simultaneous MTL predictions is comparable to the accuracy of the STL predictions. In addition, the computational cost of training HydraGNN for MTL is much lower than the original DFT calculations and also lower than training separate STL models for each property.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Scalable training of graph convolutional neural networks for fast and accurate predictions of HOMO-LUMO gap in molecules
Abstract Graph Convolutional Neural Network (GCNN) is a popular class of deep learning (DL) models in material science to predict material properties from the graph representation of molecular structures. Training an accurate and comprehensive GCNN surrogate for molecular design requires large-scale graph datasets and is usually a time-consuming process. Recent advances in GPUs and distributed computing open a path to reduce the computational cost for GCNN training effectively. However, efficient utilization of high performance computing (HPC) resources for training requires simultaneously optimizing large-scale data management and scalable stochastic batched optimization techniques. In this work, we focus on building GCNN models on HPC systems to predict material properties of millions of molecules. We use HydraGNN, our in-house library for large-scale GCNN training, leveraging distributed data parallelism in PyTorch. We use ADIOS, a high-performance data management framework for efficient storage and reading of large molecular graph data. We perform parallel training on two open-source large-scale graph datasets to build a GCNN predictor for an important quantum property known as the HOMO-LUMO gap. We measure the scalability, accuracy, and convergence of our approach on two DOE supercomputers: the Summit supercomputer at the Oak Ridge Leadership Computing Facility (OLCF) and the Perlmutter system at the National Energy Research Scientific Computing Center (NERSC). We present our experimental results with HydraGNN showing (i) reduction of data loading time up to 4.2 times compared with a conventional method and (ii) linear scaling performance for training up to 1024 GPUs on both Summit and Perlmutter.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Portable Parallel Algorithms and Frameworks for Exascale Graph Analytics
Graphs (or networks) are a tool used to model the interactions among various entities. Efficiently processing large graphs has recently attracted significant attention due to the applications of graphs in various domains, such as biology, chemistry, and cyber-security. Analyzing the structure and properties of these graphs is an important component of many scientific computing pipelines. With the explosion in the volume of data, graphs have become very large and can contain hundreds of billions of vertices and trillions of edges. Therefore, it is crucial to develop high-performance methods to enable graph analysis to be done quickly and energy-efficiently. Furthermore, these solutions should be highly parallel in order to take advantage of modern parallel machines. However, designing efficient solutions is not enough. With the wide variety of computing environments available, each with different programmability and performance characteristics, it is necessary to develop solutions that are portable in terms of both performance (i.e., provide theoretical guarantees) and programmability (i.e., provide high level abstractions).
97 MATHEMATICS AND COMPUTING↗
Generation of precedence relations for mechanical assemblies
Planning of assembly sequences is essential to the manufacturing system design process. Several methodologies have been proposed to represent all the feasible assembly sequences. In this thesis, three algorithms are presented to generate three sets of precedence relations based on all the infeasible assembly tasks, all the infeasible assembly states, and all the feasible assembly sequences, respectively. The equivalence of the resulting sets of precedence relations to the AND/OR graph is established. A new property, the real time property, of a representation of assembly sequences is defined and discussed. A representation of assembly sequences is said to have the real time property, if it is possible to generate the next assembly task by testing locally in the representation, and it will guarantee that the generated assembly task will not lead the assembly sequence to a dead end situation, in which no feasible assembly task can be performed any more. It is shown that the correctness and completeness of one representation can not guarantee the real time property of the representation. It is proven that the directed graph representation and the set of precedence relations based on all the infeasible assembly states have the real time property, while the AND/OR graph representation and the set of precedence relations based on all the infeasible assembly tasks do not have the real time property. Finally in the thesis, the PLEIDEAS system, a PLanning Environment for Integrated DEsign of Assembly Systems, is described and illustrated by an example.
Zhang, Hui↗
Prediction of fiber composite mechanical behavior made simple
The elastic properties and failure stresses of angleplied fiber composite laminates were determined using a pocket calculator. The procedure uses simple equations and appropriate graphs of elastic properties versus angle plies, and can handle all types of fiber composites including hybrids. The versatility and generality of the method is illustrated in several step-by-step numerical examples.
Chamis, C. C.↗
Task scheduling in dataflow computer architectures
Dataflow computers provide a platform for the solution of a large class of computational problems, which includes digital signal processing and image processing. Many typical applications are represented by a set of tasks which can be repetitively executed in parallel as specified by an associated dataflow graph. Research in this area aims to model these architectures, develop scheduling procedures, and predict the transient and steady state performance. Researchers at NASA have created a model and developed associated software tools which are capable of analyzing a dataflow graph and predicting its runtime performance under various resource and timing constraints. These models and tools were extended and used in this work. Experiments using these tools revealed certain properties of such graphs that require further study. Specifically, the transient behavior at the beginning of the execution of a graph can have a significant effect on the steady state performance. Transformation and retiming of the application algorithm and its initial conditions can produce a different transient behavior and consequently different steady state performance. The effect of such transformations on the resource requirements or under resource constraints requires extensive study. Task scheduling to obtain maximum performance (based on user-defined criteria), or to satisfy a set of resource constraints, can also be significantly affected by a transformation of the application algorithm. Since task scheduling is performed by heuristic algorithms, further research is needed to determine if new scheduling heuristics can be developed that can exploit such transformations. This work has provided the initial development for further long-term research efforts. A simulation tool was completed to provide insight into the transient and steady state execution of a dataflow graph. A set of scheduling algorithms was completed which can operate in conjunction with the modeling and performance tools previously developed. Initial studies on the performance of these algorithms were done to examine the effects of application algorithm transformations as measured by such quantities as number of processors, time between outputs, time between input and output, communication time, and memory size.
Katsinis, Constantine↗
Image-based model of the spectrin cytoskeleton for red blood cell simulation
We simulate deformable red blood cells in the microcirculation using the immersed boundary method with a cytoskeletal model that incorporates structural details revealed by tomographic images. The elasticity of red blood cells is known to be supplied by both their lipid bilayer membranes, which resist bending and local changes in area, and their cytoskeletons, which resist in-plane shear. The cytoskeleton consists of spectrin tetramers that are tethered to the lipid bilayer by ankyrin and by actin-based junctional complexes. We model the cytoskeleton as a random geometric graph, with nodes corresponding to junctional complexes and with edges corresponding to spectrin tetramers such that the edge lengths are given by the end-to-end distances between nodes. The statistical properties of this graph are based on distributions gathered from three-dimensional tomographic images of the cytoskeleton by a segmentation algorithm. We show that the elastic response of our model cytoskeleton, in which the spectrin polymers are treated as entropic springs, is in good agreement with the experimentally measured shear modulus. By simulating red blood cells in flow with the immersed boundary method, we compare this discrete cytoskeletal model to an existing continuum model and predict the extent to which dynamic spectrin network connectivity can protect against failure in the case of a red cell subjected to an applied strain. As a result, the methods presented here could form the basis of disease- and patient-specific computational studies of hereditary diseases affecting the red cell cytoskeleton.
59 BASIC BIOLOGICAL SCIENCES↗
Quantifying Graph Uncertainty from Communication Data
Graphs are a widely used abstraction for representing a variety of important real-world problems including emulating cyber networks for situational awareness, or studying social networks to understand human interactions or pandemic spread. Communication data is often converted into graphs to help understand social and technical patterns in the underlying communication data. However, prior to this project, little work had been performed analyzing how best to develop graphs from such data. Thus, many critical, national security problems were being performed against graph representations of questionable quality. Herein, we describe our analyses that were precursors to our final statistically grounded technique for creating static graph snapshots from a stream of communication events. The first analyzes the statistical distribution properties of a variety of real-world communication datasets generally fit best by Pareto, log normal, and extreme value distributions. The second derives graph properties that can be estimated given the expected statistical distribution for communication events and the communication interval to be viewed node observability, edge observability, and expected accuracy of node degree. Unfortunately, as that final process is under review for publication, we can't publish it here at this time.
97 MATHEMATICS AND COMPUTING↗
Cayley fuzzy graphs on the fuzzy groups
Given non-trivial group G and a non-empty subset S of G such that not containing the identity element of G and S=S{sup −1}:={s"−"1∣s∈S}, the Cayley graph Γ=Cay(G,S) is the graph whose vertex set V(Γ) is G, and edge set E(Γ) is {{g,sg}∣g∈G,s∈S}. The Cayley graphs are presently being considered as models architecture for interconnection networks. When there is an uncertainty on vertices or edges, fuzzy graph has special importance. In this paper, we develop the concept of Cayley fuzzy graphs on the fuzzy groups and investigate some basic properties of Cayley fuzzy graphs. We introduce some sufficient conditions on the fuzzy graphs that under it’s, a fuzzy graph is a Cayley fuzzy graph and discuss some operations of the fuzzy graphs on the Cayley fuzzy graphs, prove that the product of two Cayley fuzzy graphs is a Cayley fuzzy graph, for some products. Also we provide an application of Cayley fuzzy graphs, and use Dijkstra’s Algorithm for finding the fuzzy shortest path in a Cayley fuzzy graph.
97 MATHEMATICS AND COMPUTING↗
Topological properties of the limited penetrable horizontal visibility graph family
Not Available
Wang, Minggang↗
Predicting magnetic properties of van der Waals magnets using graph neural networks
Not Available
Minch, Peter (ORCID:0009000274941252)↗
The fully indecomposable matrix and its associated bipartite graph - An investigation of combinatorial and structural properties
Combinatorial properties of classes of nonnegative matrices
Roberts, E. J.↗