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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 613 records · Page 34

GrainGNN: A dynamic graph neural network for predicting 3D grain microstructure

We propose GrainGNN, a surrogate model for the evolution of polycrystalline grain structure under rapid solidification conditions in metal additive manufacturing. High fidelity simulations of solidification microstructures are typically performed using multicomponent partial differential equations (PDEs) with moving interfaces. The inherent randomness of the PDE initial conditions (grain seeds) necessitates ensemble simulations to predict microstructure statistics, e.g., grain size, aspect ratio, and crystallographic orientation. Here, currently such ensemble simulations are prohibitively expensive and surrogates are necessary.In GrainGNN, we use a dynamic graph to represent interface motion and topological changes due to grain coarsening. We use a reduced representation of the microstructure using hand-crafted features; we combine pattern finding and altering graph algorithms with two neural networks, a classifier (for topological changes) and a regressor (for interface motion). Both networks have an encoder-decoder architecture; the encoder has a multi-layer transformer long-short-term-memory architecture; the decoder is a single layer perceptron.We evaluate GrainGNN by comparing it to high-fidelity phase field simulations for in-distribution and out-of-distribution grain configurations for solidification under laser power bed fusion conditions. GrainGNN results in 80%–90% pointwise accuracy; and nearly identical distributions of scalar quantities of interest (QoI) between phase field and GrainGNN simulations compared using Kolmogorov-Smirnov test. GrainGNN's inference speedup (PyTorch on single x86 CPU) over a high-fidelity phase field simulation (CUDA on a single NVIDIA A100 GPU) is 150×–2000× for 100-initial grain problem. Further, using GrainGNN, we model the formation of 11,600 grains in 220 seconds on a single CPU core.

36 MATERIALS SCIENCE↗

Monitoring and flaw detection during wire-based directed energy deposition using in-situ acoustic sensing and wavelet graph signal analysis

The goal of this work is to detect flaw formation in the wire-based directed energy deposition (W-DED) process using in-situ sensor data. The W-DED studied in this work is analogous to metal inert gas electric arc welding. The adoption of W-DED in industry is limited because the process is susceptible to stochastic and environmental disturbances that cause instabilities in the electric arc, eventually leading to flaw formation, such as porosity and suboptimal geometric integrity. Moreover, due to the large size of W-DED parts, it is difficult to detect flaws post-process using non-destructive techniques, such as X-ray computed tomography. Accordingly, the objective of this work is to detect flaw formation in W-DED parts using data acquired from an acoustic (sound) sensor installed near the electric arc. To realize this objective, we develop and apply a novel wavelet integrated graph theory approach. The approach extracts a single feature called graph Laplacian Fiedler number from the noise-contaminated acoustic sensor data, which is subsequently tracked in a statistical control chart. Using this approach, the onset of various types of flaws are detected with a false alarm rate less-than 2%. This work demonstrates the potential of using advanced data analytics for in-situ monitoring of W-DED.

42 ENGINEERING↗

Graph neural networks for mechanical property prediction of 2D fiber composites

This work investigates the ability of graph neural networks (GNNs) to homogenize 2D fiber composite microstructures. We use different inhomogeneity and anisotropy indices to motivate and show that the Volume Elements (VEs) used in ML methods should ideally be far from their Representative Volume Element (RVE) size limit and, consequently, are notably anisotropic. Hence, training only the isotropic limit properties may not be acceptable. Another aspect is the need to normalize elastic stiffness values for ML, especially when high elastic contrast ratios are encountered between composite phases or in the material set. We introduce a normalization technique based on the mean-field method (MFM) to handle such high contrast ratios and train for the entire stiffness tensor. We show that the proposed GNN approaches exhibit high accuracy and efficiency compared to traditional methods and convolutional neural networks, utilizing unstructured graphs constructed from microstructure topology. Our model successfully predicts the stiffness tensor, peak strength under bulk damage, and brittle fracture initiation strength across diverse microstructure configurations while maintaining high accuracy even for extreme material contrasts and volume fractions. We also present a method to improve prediction accuracy for small dataset sizes using Voronoi partitioning.

Brittle strength↗

Street-level temperature estimation using graph neural networks: Performance, feature embedding and interpretability

Estimating street-level air temperature is a challenging task due to the highly heterogeneous urban surfaces, canyon-like street morphology, and the diverse physical processes in the built environment. Though pioneering studies have embarked on investigations via data-driven approaches, many questions remain to be answered. Here, in this study, we leveraged an innovative framework and redefined the street-level temperature estimation problem using Graph Neural Networks (GNN) with spatial embedding techniques. The results showed that GNN models are more capable and consistent of estimating street-level temperature among tested locations, benefiting from its unique strength in handling extensive data over unstructured graph topology. In addition, we conducted in-depth analysis of feature importance to enhance the model interpretability. Among the urban features analyzed in this study, the time-variant canopy density and meter-level land use data emerge as crucial factors. Our findings highlight GNN 's high potential in capturing the complex dynamics between urban elements and their impacts on microclimate, thus offering valuable insights for comprehensive urban data collection and urban climate modeling in general. Collectively, this study also contributes to urban planning and policy by providing avenues to enhance city resilience against climate change, thereby advancing the agenda for environmental stewardship and urban sustainability.

54 ENVIRONMENTAL SCIENCES↗

Multilevel Monte Carlo Predictions of First Passage Times in Three-Dimensional Discrete Fracture Networks: A Graph-Based Approach

In this paper, we present a method combining multilevel Monte Carlo (MLMC) and a graph-based primary subnetwork identification algorithm to provide estimates of the mean and variance of the distribution of first passage times in fracture media at significantly lower computational cost than standard Monte Carlo (MC) methods. Simulations of solute transport are performed using a discrete fracture network (DFN), and instead of using various grid resolutions for levels in the MLMC, which is standard practice in MLMC, we identify a hierarchy of subnetworks in the DFN based on the shortest topological paths through the network using a graph-based method. While the mean of these ensembles is of critical importance, the variance is also essential in fractured media where uncertainty is an overarching theme, and understanding variability across an ensemble is a requirement for safety assessments. The method provides good estimates of the mean and variance at two orders of magnitude lower computational cost than MC.

54 ENVIRONMENTAL SCIENCES↗

On the absence of absolutely continuous spectra for Schroedinger operators on radial tree graphs

The subject of the paper is Schroedinger operators on tree graphs which are radial, having the branching number b{sub n} at all the vertices at the distance t{sub n} from the root. We consider a family of coupling conditions at the vertices characterized by (b{sub n}-1){sup 2}+4 real parameters. We prove that if the graph is sparse so that there is a subsequence of {l_brace}t{sub n+1}-t{sub n{r_brace}} growing to infinity, in the absence of the potential the absolutely continuous spectrum is empty for a large subset of these vertex couplings, but on the the other hand, there are cases when the spectrum of such a Schroedinger operator can be purely absolutely continuous.

97 MATHEMATICS AND COMPUTING↗

The problem of deficiency indices for discrete Schroedinger operators on locally finite graphs

The number of self-adjoint extensions of a symmetric operator acting on a complex Hilbert space is characterized by its deficiency indices. Given a locally finite unoriented simple tree, we prove that the deficiency indices of any discrete Schroedinger operator are either null or infinite. We also prove that all deterministic discrete Schroedinger operators which act on a random tree are almost surely self-adjoint. Furthermore, we provide several criteria of essential self-adjointness. We also address some importance to the case of the adjacency matrix and conjecture that, given a locally finite unoriented simple graph, its deficiency indices are either null or infinite. Besides that, we consider some generalizations of trees and weighted graphs.

97 MATHEMATICS AND COMPUTING↗

Quantum graph as a quantum spectral filter

We study the transmission of a quantum particle along a straight input-output line to which a graph {Gamma} is attached at a point. In the point of contact we impose a singularity represented by a certain properly chosen scale-invariant coupling with a coupling parameter {alpha}. We show that the probability of transmission along the line as a function of the particle energy tends to the indicator function of the energy spectrum of {Gamma} as {alpha}{yields}{infinity}. This effect can be used for a spectral analysis of the given graph {Gamma}. Its applications include a control of a transmission along the line and spectral filtering. The result is illustrated with an example where {Gamma} is a loop exposed to a magnetic field. Two more quantum devices are designed using other special scale-invariant vertex couplings. They can serve as a band-stop filter and as a spectral separator, respectively.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Synchronizability of random rectangular graphs

Random rectangular graphs (RRGs) represent a generalization of the random geometric graphs in which the nodes are embedded into hyperrectangles instead of on hypercubes. The synchronizability of RRG model is studied. Both upper and lower bounds of the eigenratio of the network Laplacian matrix are determined analytically. It is proven that as the rectangular network is more elongated, the network becomes harder to synchronize. The synchronization processing behavior of a RRG network of chaotic Lorenz system nodes is numerically investigated, showing complete consistence with the theoretical results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Domain configurations in dislocations embedded hexagonal manganite systems: From the view of graph theory

Topological defects and their interactions often arouse multiple types of emerging phenomena from edge states in Skyrmions to disclination pairs in liquid crystals. In hexagonal manganites, partial edge dislocations, a prototype topological defect, are ubiquitous and they significantly alter the topologically protected domains and their behaviors. In this work, combining electron microscopy experiment and graph theory analysis, we report a systematic study of the connections and configurations of domains in this dislocation embedded system. Rules for domain arrangement are established. The dividing line between domains, which can be attributed by the strain field of dislocations, is accurately described by a genus model from a higher dimension in the graph theory. In conclusion, our results open a door for the understanding of domain patterns in topologically protected multiferroic systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Classification of dynamical Lie algebras generated by spin interactions on undirected graphs

Dynamical Lie algebras (DLAs) are a versatile tool for various topics that span from the expressibility-trainability of variational quantum algorithms (VQAs), to simulation of many body Hamiltonians. Quantum gates and most of the Hamiltonians of interest consist of local interactions; therefore, the analysis of all possible DLAs generated by 1- and 2-local operators is crucial for quantum simulation and VQAs on current hardware. Previously in [R. Wiersema et al ., npj Quantum Inf. 10 , 110 (2024)], we analyzed the DLAs on linear, circular and all-to-all topologies, and obtained results about their dimensions and algebraic structure. Here, in this work, we extend our analysis into any possible hardware topology and provide a classification of all DLAs generated by Pauli strings on any undirected interaction graph. Our results indicate that the DLAs depend solely on whether the connectivity or interaction graph is bipartite or not. In addition, we find that the non-trivial polynomially scaling DLAs appear only on 1D line or circle topologies, and all other DLAs have dimensions scaling exponentially with the system size. Together with the current VQA literature, our results imply that either the majority of VQAs are non-trainable, or we are yet to understand the role of DLAs on the trainability of VQAs.

Algebraic structures↗

Embeddings of graphs into Euclidean space under which the number of points that belong to a hyperplane is minimal

The paper is devoted to the characteristic of a graph that is the minimal (over all embeddings of the graph into a space of given dimension) number of points that belong to the same hyperplane. Upper and lower estimates for this number are given that linearly depend on the dimension of the space. For trees a more precise upper estimate is obtained, which asymptotically coincides with the lower one for large dimension of the space. Bibliography: 9 titles.

97 MATHEMATICS AND COMPUTING↗

A three-colour graph as a complete topological invariant for gradient-like diffeomorphisms of surfaces

In a paper of Oshemkov and Sharko, three-colour graphs were used to make the topological equivalence of Morse-Smale flows on surfaces obtained by Peixoto more precise. In the present paper, in the language of three-colour graphs equipped with automorphisms, we obtain a complete (including realization) topological classification of gradient-like cascades on surfaces. Bibliography: 25 titles.

97 MATHEMATICS AND COMPUTING↗

Small covers of graph-associahedra and realization of cycles

An oriented connected closed manifold M{sup n} is called a URC- manifold if for any oriented connected closed manifold N{sup n} of the same dimension there exists a nonzero-degree mapping of a finite-fold covering M-hat {sup n} of M{sup n} onto N{sup n}. This condition is equivalent to the following: for any n-dimensional integral homology class of any topological space X, a multiple of it can be realized as the image of the fundamental class of a finite-fold covering M-hat {sup n} of M{sup n} under a continuous mapping f: M-hat {sup n}→X. In 2007 the author gave a constructive proof of Thom's classical result that a multiple of any integral homology class can be realized as an image of the fundamental class of an oriented smooth manifold. This construction yields the existence of URC-manifolds of all dimensions. For an important class of manifolds, the so-called small covers of graph-associahedra corresponding to connected graphs, we prove that either they or their two-fold orientation coverings are URC-manifolds. In particular, we obtain that the two-fold covering of the small cover of the usual Stasheff associahedron is a URC-manifold. In dimensions 4 and higher, this manifold is simpler than all the previously known URC-manifolds. Bibliography: 39 titles. (paper)

97 MATHEMATICS AND COMPUTING↗

Peculiar spectral statistics of ensembles of trees and star-like graphs

In this paper we investigate the eigenvalue statistics of exponentially weighted ensembles of full binary trees and p-branching star graphs. We show that spectral densities of corresponding adjacency matrices demonstrate peculiar ultrametric structure inherent to sparse systems. In particular, the tails of the distribution for binary trees share the \Lifshitz singularity" emerging in the onedimensional localization, while the spectral statistics of p-branching star-like graphs is less universal, being strongly dependent on p. The hierarchical structure of spectra of adjacency matrices is interpreted as sets of resonance frequencies, that emerge in ensembles of fully branched tree-like systems, known as dendrimers. However, the relaxational spectrum is not determined by the cluster topology, but has rather the number-theoretic origin, re ecting the peculiarities of the rare-event statistics typical for one-dimensional systems with a quenched structural disorder. The similarity of spectral densities of an individual dendrimer and of ensemble of linear chains with exponential distribution in lengths, demonstrates that dendrimers could be served as simple disorder-less toy models of one-dimensional systems with quenched disorder.

97 MATHEMATICS AND COMPUTING↗

Construction of equally entangled bases in arbitrary dimensions via quadratic Gauss sums and graph states

Recently, Karimipour and Memarzadeh [Phys. Rev. A 73, 012329 (2006)] studied the problem of finding a family of orthonormal bases in a bipartite space, each of dimension D, with the following properties: (i) The family continuously interpolates between a product basis and a maximally entangled basis as some parameter t is varied, and (ii) for a fixed t, all basis states have the same amount of entanglement. The authors derived a necessary condition and provided explicit solutions for D{<=}5, but the existence of a solution for arbitrary dimensions remained an open problem. We prove that such families exist in arbitrary dimensions by providing two simple solutions, one that employs the properties of quadratic Gauss sums and the other that uses graph states. The latter can be generalized to more than two parties--we can construct equally entangled families that vary continuously between a product basis and a graph-state basis.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Bell inequality tests of four-photon six-qubit graph states

We now experimentally demonstrate a Y-shaped graph state with photons' polarization and spatial modes as qubits. Based on this state and a linear-type graph state, we report on the experimental realization of two different Bell inequality tests, which represent higher violation than previous Bell tests.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Graph-state basis for Pauli channels

Quantum capacities of Pauli channels are not additive, a degenerate quantum code may improve the hashing bound of the capacity. The difficulty in approaching the capacity is how to calculate the coherent information of a generic degenerate quantum code. Using graph state basis, we greatly reduce the problem for the input of quantum error-correcting code. We show that for a graph diagonal state passing through a Pauli channel the output state is diagonalizable and the joint output state of the system and ancilla is block diagonalizable. When the input state is an equal probable mixture of codewords of a stabilizer code, the coherent information can be analytically obtained.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗