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Chapter 4: Physically informed deep learning networks for simulating microstructure evolution of 3D polycrystals
As discussed in the previous chapter, high energy diffraction microscopy (HEDM) is used to study the micromechanical evolution of a material during in situ loading. HEDM experiments have been used to verify crystal plasticity (CP) simulations [119, 91, 90, 120], for experimental planning, material design, and to further analyze experimental results. However, Fast Fourier transform-based CP (CP-FFT) or finite element-based CP (CP-FE) methods are often too slow to be used in real-time during an experiment. CP-FFT is faster than CP-FE simulations due to the absence of meshing, but can still take hours to simulate the response of a single volume depending on the size and number of strain steps [127]. Reducing computation time would create a larger exploration space in planning and design, and enable faster analysis of experimental results and real-time feedback during an experiment. This research expands upon previous works to develop a workflow for predicting the full-field evolution of a 3D polycrystal. The workflow is simplified from previous works to predict only orientation and elastic strain tensors (from which stress tensors are calculated). The network is physically informed through loss functions and network architecture for a more robust model. The orientation predictions are informed about the cubic crystal symmetry of the material by incorporating disorientation and misorientation information into the network architecture and loss. The Von Mises stress is used to enforce the correct stress-strain trends in the strain tensor predictions. Additional total strain steps from the elastic and elastoplastic region are included to better capture the stress-strain evolution at smaller total strain steps. Material and hardening parameters are additional inputs into the networks to further inform the network and to study the network’s ability to predict different materials other than those used for training.
Bimetallic Ir x Pb nanowire networks with enhanced electrocatalytic activity for the oxygen evolution reaction
Metallic nanowire networks (MNNs) have attracted increasing attention due to their high surface area and tunable compositions. Although enormous efforts have been devoted to preparing noble metal MNNs with different compositions, the composition optimization and the formation mechanism of Ir-based MNNs have not been thoroughly investigated. Here, this work presents a facile method for synthesizing robust Ir-based bimetallic MNNs by chemical reduction. As unveiled by our characterization, the network structure is constructed by ultrafine nanowires evolved from aggregated nanoparticles. The element analysis confirms the even distribution of Pb and Ir elements. The introduction of Pb is found to be beneficial to the stable formation of Ir x Pb MNNs in the sol–gel process. By tuning the precursor ratio of Ir and Pb, the optimized Ir x Pb catalyst delivers an enhanced oxygen evolution reaction (OER) performance in acid media (307 mV at 10 mA cm −2 ), which is superior to that of the commercial IrO 2 catalyst. Besides, due to the robust structure of the Ir x Pb MNNs, excellent OER durability is observed in the accelerated durability test (ADT) (2000 cycles).
GrainNN: A neighbor-aware long short-term memory network for predicting microstructure evolution during polycrystalline grain formation
High fidelity simulations of grain formation in alloys are an indispensable tool for process-to-mechanical-properties characterization. Such simulations, however, can be computationally expensive as they require fine spatial and temporal discretizations. Their cost becomes an obstacle to parametric studies and ensemble runs and ultimately makes downstream tasks like optimal control and uncertainty quantification challenging. To enable such downstream tasks, we introduce GrainNN, an efficient and accurate reduced-order model for epitaxial grain growth in additive manufacturing conditions. GrainNN is a sequence-to-sequence long-short-term-memory (LSTM) deep neural network that evolves the dynamics of manually crafted features. Its innovations are (1) an attention mechanism with grain-microstructure-specific transformer architecture; and (2) an overlapping combination of several clones of the network to generalize to grain configurations that are different from those used for training. This design enables GrainNN to predict grain formation for unseen physical parameters, grain number, domain size and geometry. Furthermore, GrainNN not only reconstructs the quantities of interest but also can be pointwise accurate. In our numerical experiments, we use a polycrystalline phase field method to both generate the training data and assess GrainNN. For multiparametric, ensemble simulations with many grains, GrainNN can be orders of magnitude faster than phase field simulations, while delivering 5%–15% pointwise error. Additionally, this speedup includes the cost of the phase field simulations for generating training data.
Evolution of Robustness in Growing Random Networks
Networks are widely used to model the interaction between individual dynamic systems. In many instances, the total number of units and interaction coupling are not fixed in time, and instead constantly evolve. In networks, this means that the number of nodes and edges both change over time. Various properties of coupled dynamic systems, such as their robustness against noise, essentially depend on the structure of the interaction network. Therefore, it is of considerable interest to predict how these properties are affected when the network grows as well as their relationship to the growth mechanism. Here, we focus on the time evolution of a network’s Kirchhoff index. We derive closed-form expressions for its variation in various scenarios, including the addition of both edges and nodes. For the latter case, we investigate the evolution where single nodes with one or two edges connecting to existing nodes are added recursively to a network. In both cases, we derive the relations between the properties of the nodes to which the new node connects along with the global evolution of network robustness. In particular, we show how different scalings of the Kirchhoff index can be obtained as a function of the number of nodes. We illustrate and confirm this theory via numerical simulations of randomly growing networks.
Object Detection and Recognition with PointPillars in LiDAR Point Clouds – Comparisions
In the field of autonomous systems, neural networks have been leveraged for object detection and recognition in 2-dimensional images captured by cameras. Other types of sensors are available for sensing surroundings, including LiDAR sensors, and corresponding networks have been developed to perform detection and recognition in the point clouds generated by these sensors. The approaches are similar, both perform convolutions, but have distinct characteristics and challenges. In designing and configuring autonomous systems, a variety of LiDAR sensors are available, along with configurable deep neural networks to leverage their data. This work presents a review of the PointPillars network, an evolution of the seminal PointNet, comparing accuracy and training time relative to different LiDAR sensors, network and training parameters, CPU and GPU hardware, and the criticality of the use of reflective intensity as a feature. The value of using reflectivity as a predictive feature is explored and quantified to determine if it makes a significant difference in accuracy of the PointPillars network. Two separate LiDAR sensors are utilized, a 16-plane and a 32-plane, and corresponding accuracies and training times with the PointPillars network are evaluated.
Accelerate microstructure evolution simulation using graph neural networks with adaptive spatiotemporal resolution
Abstract Surrogate models driven by sizeable datasets and scientific machine-learning methods have emerged as an attractive microstructure simulation tool with the potential to deliver predictive microstructure evolution dynamics with huge savings in computational costs. Taking 2D and 3D grain growth simulations as an example, we present a completely overhauled computational framework based on graph neural networks with not only excellent agreement to both the ground truth phase-field methods and theoretical predictions, but enhanced accuracy and efficiency compared to previous works based on convolutional neural networks. These improvements can be attributed to the graph representation, both improved predictive power and a more flexible data structure amenable to adaptive mesh refinement. As the simulated microstructures coarsen, our method can adaptively adopt remeshed grids and larger timesteps to achieve further speedup. The data-to-model pipeline with training procedures together with the source codes are provided.
Mesoscale Modeling of Dislocation Cell Structure Evolution and Radiation-Induced Segregation in Additively Manufactured Austenitic Stainless Steel
Structural alloys under irradiation develop radiation-induced segregation (RIS) at point defect sinks, which lead to undesired changes in the alloy's properties. Additively manufactured austenitic stainless steels are expected to yield a distinct response to irradiation damage owing to their unique as-printed dislocation cell structure. In this talk, we present the development of a mesoscale model for dislocation cell structure evolution coupled with RIS using the MOOSE framework. The evolution of network dislocations within spatially distinct cells and cell walls are modeled using climb-mediated edge annihilation and generation processes. Starting with initial microstructures of as-printed non-equilibrium segregations at dislocation cell walls, our 2D and 3D simulations explore the effects of irradiation temperature, dose rate, dislocation sink bias, and specimen thickness on microstructure evolution. The results will be compared against experimental characterizations of in-situ and ex-situ ion-irradiated samples, and the implications of evolving cell structure on irradiation damage response will be discussed.
The Evolution of the Peridynamics Co-Authorship Network
We report peridynamics is a relatively new field in continuum mechanics that has developed over the past 20 years. This paper studies the evolution of collaborations in the field of peridynamics since its inception using social network analysis. For this purpose, we construct a network for each year from 2000 to 2019 describing co-authorship between scientists in peridynamics. In these networks, each node represents a scientist and each link connects two co-authoring scientists with a link weight representing the frequency and strength of their collaboration; each network as a whole can be thought of as a graph representation of the peridynamics community for the given year. By constructing a network for each year, we are able to analyze the evolution of the network in time and discuss the implications of this evolution for the peridynamics community. Our study demonstrates that the peridynamics community has been growing exponentially in size in recent years. Centrality metrics are also used to identify the most collaborative scientists in the community. Moreover, we compute link recommendations based on both elevating a scientist’s position in the network with respect to certain centrality metrics or closing structural holes in the network identified with persistent homology. We further extend the analysis to higher-order networks whose nodes represent groups of scientists in the community and whose links connect collaborating groups. In some sense, our work studies the past, present, and future of the peridynamics community.
Exact block encoding of imaginary time evolution with universal quantum neural networks
We develop a constructive approach to generate quantum neural networks capable of representing the exact thermal states of all many-body qubit Hamiltonians. The Trotter expansion of the imaginary time propagator is implemented through an exact block encoding by means of a unitary, restricted Boltzmann machine architecture. Marginalization over the hidden-layer neurons (auxiliary qubits) creates the nonunitary action on the visible layer. Then, we introduce a unitary deep Boltzmann machine architecture in which the hidden-layer qubits are allowed to couple laterally to other hidden qubits. We prove that this wave-function is closed under the action of the imaginary time propagator and, more generally, can represent the action of a universal set of quantum gate operations. We provide analytic expressions for the coefficients for both architectures, thus enabling exact network representations of thermal states without stochastic optimization of the network parameters. In the limit of large imaginary time, the yields the ground state of the system. The number of qubits grows linearly with the number of interactions and total imaginary time for a fixed interaction order. Both networks can be readily implemented on quantum hardware via midcircuit measurements of auxiliary qubits. If only one auxiliary qubit is measured and reset, the circuit depth scales linearly with imaginary time and number of interactions, while the width is constant. Alternatively, one can employ a number of auxiliary qubits linearly proportional to the number of interactions, and circuit depth grows linearly with imaginary time only. Every midcircuit measurement has a postselection success probability, and the overall success probability is equal to the product of the probabilities of the midcircuit measurements.
Multifold Insights for Power System Dynamics From Data Assimilation: Meeting Current Challenges
The world’s electric power grids have evolved over the last 120 years from a single power line to today’s large networks. The evolution will continue at an accelerated rate with extensive smart grid development worldwide. Here for example, the U.S. government has set a goal of reaching 100 percent carbon pollution-free electricity by 2035, while the Department of Energy (DOE) shared a goal to deploy 30 GW and 110 GW of offshore wind by 2030 and 2050, respectively. To meet such ambitious goals, in the years to come, a significant percentage of electricity will come from intermittent renewable sources, electric vehicles (EVs), and be supplied to a vast number of loads that will actively respond to grid conditions and incentive signals. This development is largely driven by environmental and economic factors, such as reducing carbon emissions and saving electricity cost for consumers. These energy resources lead to new uncertain behaviors and dynamics which the grid has never seen and were not considered in its design. Operating such a dynamic grid with sufficient reliability and efficiency is a monumental challenge.
Development of Mechanistic Fission Gas Release and Swelling Models for UN Fuels in BISON
This report describes the work in NEAMS (Nuclear Energy Advanced Modeling and Simulation) to develop a mechanistic fission gas model for uranium nitride fuels in BISON. The existing Sifgrs (Simple integrated fission gas release and swelling) model tracks the average properties of two bubble populations in the bulk and at the grain boundaries. It was recognized that dislocations play a crucial role in the fission gas swelling of UN, and an irradiation-induced dislocation density model was needed, as well as a model describing how fission gas interacts with dislocations creating a third population of bubbles along dislocations. A mechanistic model that tracks dislocation bubbles was implemented in Sifgrs. This model was used to simulate fission gas swelling and release in UN. Lower-length-scale calculations and experimental observations from carbide fuel were leveraged to help populate the model with essential parameters. As a placeholder, an empirical function was formulated for the evolution of the dislocation network. Because of the difference in evolution of this network at different temperatures, the dislocation bubbles are able to capture behavior that the bulk intragranular bubbles cannot. It was found that the bulk bubbles dominate microscopic swelling at low temperatures, and the dislocation bubbles dominate at higher temperatures. Based on this model, the transition between the two bubble types is the main factor behind the breakaway swelling phenomenon in UN. In order to test the model, a couple of assessments were run. For the lower temperature JOYO pins, the model produces reasonable fission gas release and swelling values. For the higher temperature SP1 pin, the model dramatically underestimates the fission gas release. This issue is attributed to the gas being trapped inside dislocation bubbles, unable to escape to grain boundaries to cause fission gas release, and could be remedied by a mechanistic dislocation model that allows the dislocation density to decrease at very high temperatures. A preliminary mechanistic dislocation model was developed supported by first-principle calculations. These calculations provided valuable insight into how interstitial defects cluster in UN in the {110} orientation, and may eventually form dislocation loops, leading to the conclusion that dislocation loops may nucleate from these clusters. An estimate of the dislocation line energy in UN was obtained and will be improved in future work. The free-energy cluster dynamics code Centipede was used to track interstitial and vacancy absorption at dislocation loops and calculate their growth. In addition, improvements to Centipede were made including new convergence criteria for transient simulations and sink driving force updates.
A Distributed Trust Model Simulator for Energy Grid of Things Distributed Energy Resource Management System
The evolution of networks into more distributed, self-reliant nodes has mitigated single-point failures that plagued traditional centralized networks. Applied to power grids, distributed systems can increase the integrity and availability of grid services while also offering a power management solution. However, while distributed networks provide scalability, security, and sustainability compared to centralized networks, their distributed nature makes them harder for anomaly detection and prevention. Incorporating a Distributed Trust Model (DTM) System into an Energy Grid of Things Distributed Energy Resource Management System (EGOT DERMS) allows grid participants to be characterized and their communication to be analyzed for possible attacks. A Trust Model simulator is needed to evaluate and improve the DTM System.Trustworthiness is calculated using a Trust Model. While many trust models exist, most only consider 2-3 matrices to evaluate trust. The TM proposed in this thesis uses a Metric Vector of Trust (MVoT) monitoring 17 parameters when assessing trust. Moreover, unlike standard trust models, the proposed trust model establishes a method to test the trust between various actors within the network and probe the trust model itself. Using a Trust Model Simulator, MVoT calaculations, initial values, and parameters are fine-tuned to achieve high-confidence message classifications and minimize false positives. The DTM System and Trust Mode Simulation Suite allow for distributed trust evaluation with a real-time classification of EGOT DERMS actors, providing additional security for distributed systems.
Evolution of Intent and Social Influence Networks and Their Significance in Detecting COVID-19 Disinformation Actors on Social Media
Online disinformation actors are those individuals or bots who disseminate false or misleading information over social media, with the intent to sway public opinion in the information domain towards harmful social outcomes. Quantification of the degree to which users post or respond intentionally versus under social influence, remains a challenge, as individuals or organizations operating the profile are foreshadowed by their online persona. However, social influence has been shown to be measurable in the paradigm of information theory. In this paper, we introduce an information theoretic measure to quantify social media user intent, and then investigate the corroboration of intent with evolution of the social network and detection of disinformation actors related to COVID-19 discussions on Twitter. Our measurement of user intent utilizes an existing time series analysis technique for estimation of social influence using transfer entropy among the considered users. We have analyzed 4.7 million tweets originating from several countries of interest, during a 5 month period when the arrival of the first dose of COVID vaccinations were announced. Our key findings include evidence that: (i) a significant correspondence between intent and social influence; (ii) ranking over users by intent and social influence is unstable over time with evidence of shifts in the hierarchical structure; and (iii) both user intent and social influence are important when distinguishing disinformation actors from non-disinformation actors.
The State of the Art in Visualizing Dynamic Multivariate Networks
Abstract Most real‐world networks are both dynamic and multivariate in nature, meaning that the network is associated with various attributes and both the network structure and attributes evolve over time. Visualizing dynamic multivariate networks is of great significance to the visualization community because of their wide applications across multiple domains. However, it remains challenging because the techniques should focus on representing the network structure, attributes and their evolution concurrently. Many real‐world network analysis tasks require the concurrent usage of the three aspects of the dynamic multivariate networks. In this paper, we analyze current techniques and present a taxonomy to classify the existing visualization techniques based on three aspects: temporal encoding, topology encoding, and attribute encoding. Finally, we survey application areas and evaluation methods; and discuss challenges for future research.
ITeM: Independent temporal motifs to summarize and compare temporal networks
We report networks are a fundamental and flexible way of representing various complex systems. Many domains such as communication, citation, procurement, biology, social media, and transportation can be modeled as a set of entities and their relationships. Temporal networks are a specialization of general networks where every relationship occurs at a discrete time. The temporal evolution of such networks is as important to understand as the structure of the entities and relationships. We present the Independent Temporal Motif (ITeM) to characterize temporal graphs from different domains. ITeMs can be used to model the structure and the evolution of the graph. In contrast to existing work, ITeMs are edge-disjoint directed motifs that measure the temporal evolution of ordered edges within the motif. For a given temporal graph, we produce a feature vector of ITeM frequencies and the time it takes to form the ITeM instances. We apply this distribution to measure the similarity of temporal graphs. We show that ITeM has higher accuracy than other motif frequency-based approaches. We define various ITeM-based metrics that reveal salient properties of a temporal network. We also present importance sampling as a method to efficiently estimate the ITeM counts. We present a distributed implementation of the ITeM discovery algorithm using Apache Spark and GraphFrame. We evaluate our approach on both synthetic and real temporal networks.
Benefits and Limits of Phasing Alleles for Network Inference of Allopolyploid Complexes
Abstract Accurately reconstructing the reticulate histories of polyploids remains a central challenge for understanding plant evolution. Although phylogenetic networks can provide insights into relationships among polyploid lineages, inferring networks may be hindered by the complexities of homology determination in polyploid taxa. We use simulations to show that phasing alleles from allopolyploid individuals can improve phylogenetic network inference under the multispecies coalescent by obtaining the true network with fewer loci compared with haplotype consensus sequences or sequences with heterozygous bases represented as ambiguity codes. Phased allelic data can also improve divergence time estimates for networks, which is helpful for evaluating allopolyploid speciation hypotheses and proposing mechanisms of speciation. To achieve these outcomes in empirical data, we present a novel pipeline that leverages a recently developed phasing algorithm to reliably phase alleles from polyploids. This pipeline is especially appropriate for target enrichment data, where the depth of coverage is typically high enough to phase entire loci. We provide an empirical example in the North American Dryopteris fern complex that demonstrates insights from phased data as well as the challenges of network inference. We establish that our pipeline (PATÉ: Phased Alleles from Target Enrichment data) is capable of recovering a high proportion of phased loci from both diploids and polyploids. These data may improve network estimates compared with using haplotype consensus assemblies by accurately inferring the direction of gene flow, but statistical nonidentifiability of phylogenetic networks poses a barrier to inferring the evolutionary history of reticulate complexes.