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NASA NTRSDate not supplied

Introducing Tropical Geometric Approaches to Delay Tolerant Networking Optimization

Delay Tolerant Networking (DTN) is the standard approach to the networking of space systems with the goal of supporting the Solar System Internet (SSI). Current space networks have a small scale and often depend on rigorously scheduled (pre-determined) contact opportunities; this manual approach inhibits scalability. The goal of this paper is to recast these scheduling problems in order to apply the optimization machinery of tropical geometry. Contact opportunities in space are dependent on such factors as orbital mechanics and asset availability, which induce time-varying connectivity; indeed, end-to-end connectivity might never occur. Routing optimization within this structure is classically difficult and typically utilizes Dijkstra's algorithm as applied to contact graphs. Alternatively, we follow the successes of tropical geometry in train schedule optimization, job assignments, and even traditional networking, by extending this approach to this more general (i.e. disconnected) problem space. These successes imply tropical geometry provides a useful framework in the context of DTNs, starting with applications to queuing theory and long-haul links. Recently, tropical geometry has been applied to parametric path optimization on graphs with variable edge weights. In this work, we extend these advances to account for the problem of routing in a space network, and find that tropical geometry is well-suited to the challenges offered by this new setting, including contact schedules featuring probabilities. Our approach leverages the combinatorial nature of the problem to give feasible shortest path trees in the presence of variable channel conditions and latency, evolving topologies, and uncertainty inherent in space routing. We discuss our tropical approach to DTN for two Python implementations, a Verilog Tropical ALU implementation, tropical frameworks for other parametric graph problems, and solution stability. Lastly, a program for future work is included to illuminate the path ahead.

Delay Tolerant Networking↗

DOE OSTI2020

Machine learning enabled discovery of application dependent design principles for two-dimensional materials

Abstract The unique electronic and mechanical properties of two-dimensional (2D) materials make them promising next-generation candidates for a variety of applications. Large-scale searches for high-performing 2D materials are limited to calculating descriptors with computationally demanding first-principles density functional theory. In this work, we alleviate this issue by extending and generalizing crystal graph convolutional neural networks to systems with planar periodicity and train an ensemble of models to predict thermodynamic, mechanical and electronic properties. We carry out a screening of nearly 45,000 structures for two separate applications: mechanical strength and photovoltaics. By collecting statistics of the screened candidates, we investigate structural and compositional design principles that impact the properties of the structures surveyed. Our approach recovers some well-accepted design rules: hybrid organic-inorganic perovskites with lead and tin tend to be good candidates for solar cell applications and titanium based MXenes usually have high stiffness coefficients. Interestingly, other members of the group 4 elements also contribute to increasing the mechanical strength of MXenes. For all-inorganic perovskites, we discover some compositions that have not been deeply studied in the field of photovoltaics and thus open up paths for further investigation. We open-source the code-base to spur further development in this space.

Venturi, Victor (ORCID:0000000156727549)↗

DOE OSTI2021

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

A circular economy emphasizes the efficient use of all resources (e.g., materials, land, water). Despite anticipated overall benefits to society, the transition to a circular economy is likely to create regional differences in impacts. Current tools are unable to fully evaluate these potential externalities, which will be important for informing research prioritization and regional decision making. The Circular Economy Lifecycle Assessment and VIsualization (CELAVI) framework allows stakeholders to quantify and visualize potential regional and sectoral transfers of impacts that could result from transitioning to a circular economy, with particular focus on energy materials. The framework uses system dynamics to model material flows for multiple circular economy pathways and decisions are based on learning-by-doing and are implemented via cost and strategic value of different circular economy pathways. It uses network theory to track the spatial and sectoral flow of functional units across a graph and discrete event simulation to to step through time and evaluate lifecycle assessment data at each time step. The framework is designed to be flexible and scalable to accommodate multiple energy materials and multiple energy technologies. The primary goal of CELAVI is to help answer questions about how material flows and environmental and economic impacts of energy systems might change if the circularity of energy systems increases.

Eberle, Annika↗

DOE OSTI2022

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

Eberle, Annika↗

DOE OSTI2020

An Overview of the Circular Economy Lifecycle Assessment and VIsualization (CELAVI) Framework

A circular economy emphasizes the efficient use of all resources (e.g., materials, land, water). Despite anticipated overall benefits to society, the transition to a circular economy is likely to create regional differences in impacts. Current tools are unable to fully evaluate these potential externalities, which will be important for informing research prioritization and regional decision making. This presentation will review and contrast nine current impact assessment methods and describe their granularity, scope, data requirements, and capabilities within the context of identifying regional and sectoral transfers of impacts that could result from transitioning to a circular economy for energy systems. The review of current approaches highlights the need for a new hybrid circularity assessment framework that leverages multiple methods. We describe one such approach: the Circular Economy Lifecycle Assessment and VIsualization (CELAVI) framework. CELAVI uses system dynamics to model material flows for multiple circular economy pathways, network theory to track the spatial and sectoral flow of functional units across a graph, and discrete event simulation to to step through time and evaluate lifecycle assessment data at each time step. The framework is designed to be flexible and scalable enough to accommodate multiple energy materials and multiple energy technologies. CELAVI's hybridization of multiple existing methods yields additional capabilities, which may help answer questions about how flows between the technosphere and ecosphere may evolve if the circularity of energy systems is modified.

circular economy↗

DOE OSTI2023

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

Not Available

2D Materials↗

DOE OSTI2024

Landau singularities of the 7-point ziggurat. Part II

We solve the Landau equations to find the singularities of nine three-loop 7-point graphs that arise as relaxations of the graph studied in [22]. Along the way we establish that Y – Δ equivalence fails for certain branches of solutions to the Landau equations. We find two graphs with singularities outside the heptagon symbol alphabet; in particular they are not cluster variables of Gr(4, 7). We compare maximal residues of scalar graphs exhibiting these singularities to those in $\mathcal{N}$ = 4 super-Yang-Mills theory in order to probe their cancellation from its amplitudes.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Hypernetwork Science: From Multidimensional Networks to Computational Topology

As data structures and mathematical objects used for complex systems modeling, hypergraphs sit nicely poised between on the one hand the world of network models, and on the other that of higher-order mathematical abstractions from algebra, lattice theory, and topology. They are able to represent complex systems interactions more faithfully than graphs and networks, while also being some of the simplest classes of systems representing topological structures as collections of multidimensional objects connected in a particular pattern. In this paper we discuss the role of (undirected) hypergraphs in the science of complex networks, and provide a mathematical overview of the core concepts needed for hypernetwork modeling, including duality and the relationship to bicolored graphs, quantitative adjacency and incidence, the nature of walks in hypergraphs, and available topological relationships and properties. We close with a brief discussion of two example applications: biomedical databases for disease analysis, and domain-name system (DNS) analysis of cyber data.

Joslyn, Cliff A.↗

DOE OSTI2021

Deep-freeze graph training for latent learning

Scientific and engineering advances are primarily driven by multi-tier conceptual constructs and conditional theoretical frameworks. The theories allow predictions of hypothetical system responses, given a set of approximate conditions (ranges of applicability) imposed on latent parameters that cannot be measured directly. Learning to estimate the latent variables (Latent Learning) helps to pinpoint the anticipated range-edge anomalies and improves the confidence in interpretation, interpolation and extrapolation of limited experimental data. Due to high dimensionality and extreme non-linearity of the materials science problems, very large datasets are typically required for conventional data-driven model development. The vital experimental data collection, particularly on microstructural phases, is very challenging, which makes it difficult to compile a high-quality database. Incorporation of the domain knowledge into the computational graph structure, initialization and optimization processes presents a viable mechanism for developing accurate models, with limited datasets. Furthermore, this study successfully utilized the approach to build the Deep Freeze Graph (DeepFreG) by mapping known causality relationships and by digitizing empirical domain knowledge for Latent Learning (LL), with specific applications in materials science.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Spin-informed universal graph neural networks for simulating magnetic ordering

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

Xu, Wenbin↗

DOE OSTI2025

Differential equations for cosmological correlators

Cosmological fluctuations retain a memory of the physics that generated them in their spatial correlations. The strength of correlations varies smoothly as a function of external kinematics, which is encoded in differential equations satisfied by cosmological correlation functions. In this work, we provide a broader perspective on the origin and structure of these differential equations. As a concrete example, we study conformally coupled scalar fields in a power-law cosmology. The wavefunction coefficients in this model have integral representations, with the integrands being the product of the corresponding flat-space results and “twist factors” that depend on the cosmological evolution. Similar twisted integrals arise for loop amplitudes in dimensional regularization, and their recent study has led to the discovery of rich mathematical structures and powerful new tools for computing multi-loop Feynman integrals in quantum field theory. The integrals of interest in cosmology are also part of a finite-dimensional basis of master integrals, which satisfy a system of first-order differential equations. We develop a formalism to derive these differential equations for arbitrary tree graphs. The results can be represented in graphical form by associating the singularities of the differential equations with a set of graph tubings. Upon differentiation, these tubings grow in a local and predictive fashion. In fact, a few remarkably simple rules allow us to predict — by hand — the equations for all tree graphs. While the rules of this “kinematic flow” are defined purely in terms of data on the boundary of the spacetime, they reflect the physics of bulk time evolution. We also study the analogous structures in tr ϕ 3 theory, and see some glimpses of hidden structure in the sum over planar graphs. This suggests that there is an autonomous combinatorial or geometric construction from which cosmological correlations, and the associated spacetime, emerge.

Cosmological models↗

DOE OSTI2024

Non-Electricity Based Renewable Fuels: Theory and Computation for Solar Thermochemical Hydrogen

Dominated by photovoltaics and wind, current renewable energy sources generate mostly electricity, but 80% of the global final energy consumption occurs in form of fuels. Therefore, direct solar fuel generation would be a major breakthrough for the energy transition. Solar thermochemical hydrogen (STCH) is one of the very few potential routes towards scalable renewable fuels, but currently suffers from lack of an oxide working material that could optimally perform energy conversion within the thermodynamic boundary conditions. Theory and computation can contribute in two distinct ways, through materials search and discovery, but also by providing detailed mechanistic models for specific systems so to advance our understanding of possible design strategies. To enable high-throughput materials screening, we developed a defect graph neural network (dGNN) machine learning approach,[1] which accelerates the prediction of defect formation energies by replacing the tedious density functional theory (DFT) supercell calculations for all possible defect sites. This approach enables high-throughput database screening of oxides, which was integrated with thermodynamic modeling to extract the reduction entropies as additional selection criterion for STCH. Once potential candidate materials are identified, detailed models can guide materials design by predicting performance characteristics. One challenge is to quantitatively predict thermochemical equilibria at high concentrations when the redox active defects start to interact with each other, thereby impeding the formation of additional defects. Introducing a model for the free energy of defect interaction, parametrized on the basis of DFT data, we simulated the complete STCH redox cycle for (Sr,Ce)MnO3 alloys, achieving near-quantitative agreement with experimental data.[2] The analysis of these simulations reveals how defect interactions diminish the reduction entropy and H2 yield, suggesting to include these interactions in design considerations. Finally, we revisit the popular van't Hoff method for analyzing reduction enthalpies and entropies. This method is not ideal, as it involves a temperature-dependent convolution of gas-phase and solid-state entropies, causing uncertainties in the same order of magnitude as the physical quantities of interest. To avoid this problem, we suggest a simple alternative approach which can be applied to experimental and simulated data alike.

first-principles calculations↗

DOE OSTI2023

Efficient 3D Molecular Design with an E(3) Invariant Transformer VAE

This work introduces a three-dimensional (3D) invariant graph-to-string transformer variational autoencoders (VAE) (Vagrant) for generating molecules with accurate density functional theory (DFT)-level properties. Vagrant learns to model the joint probability distribution of a 3D molecular structure and its properties by encoding molecular structures into a 3D-aware latent space. Directed navigation through this latent space implicitly optimizes the 3D structure of a molecule, and the latent embedding can be used to condition a generative transformer to predict the candidate structure as a one-dimensional (1D) sequence. Additionally, we introduce two novel sampling methods that exploit the latent characteristics of a VAE to improve performance. Here, we show that our method outperforms comparable 3D autoregressive and diffusion methods for predicting quantum chemical property values of novel molecules in terms of both sample quality and computational efficiency.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Structural constraint integration in a generative model for the discovery of quantum materials

Billions of organic molecules have been computationally generated, yet functional inorganic materials remain scarce due to limited data and structural complexity. Here, in this work, we introduce Structural Constraint Integration in a GENerative model (SCIGEN), a framework that enforces geometric constraints, such as honeycomb and kagome lattices, within diffusion-based generative models to discover stable quantum materials candidates. SCIGEN enables conditional sampling from the original distribution, preserving output validity while guiding structural motifs. This approach generates ten million inorganic compounds with Archimedean and Lieb lattices, over 10% of which pass multistage stability screening. High-throughput density functional theory calculations on 26,000 candidates shows over 95% convergence and 53% structural stability. A graph neural network classifier detects magnetic ordering in 41% of relaxed structures. Furthermore, we synthesize and characterize two predicted materials, TiPd 0.22 Bi 0.88 and Ti 0.5 Pd 1.5 Sb, which display paramagnetic and diamagnetic behaviour, respectively. Our results indicate that SCIGEN provides a scalable path for generating quantum materials guided by lattice geometry.

36 MATERIALS SCIENCE↗

NASA NTRSDate not supplied

Toward Time Synchronization in Delay Tolerant Network based Solar System Internetworking

The expanding presence in space will place an increased dependency on networked communications– a scalable communications infrastructure; that is, the Solar System Internet (SSI). Upcoming developments towards a SSI include NASA’s upcoming LunaNet, or lunar Internet, which provides multi-hop multi-path communications using Delay Tolerant Networking (DTN). DTN has been an active area of research and development, particularly in routing, security, and optimization. DTNs are marked by mobility, disconnection, and a wide variance of latencies (propagation and processing delays). In this paper, we outline progress towards a theory of time synchronization across such a network. An underlying assumption of DTN is that the network is time synchronized already, rather than synchronization being provided as a service. While this is necessary for schedule-based routing, which is necessarily prevalent in DTNs, it is so deeply ingrained as to be built into the primary unit of data in DTNs– the bundle. Indeed, a bundle’s creation timestamp and its time to live (called the lifetime) are based on time, and there are special recommendations for systems that lack accurate clocks. The assumption of time synchronization makes sense when limiting considerations to smaller-scale and more traditional space communication. However, just as end-to-end connectivity cannot be guaranteed in DTNs, neither can access to a reference or authoritative clock. In this more general case, it might be necessary to synchronize over time-varying meshes, and perhaps even to consider relativistic effects. Moreover, by imposing synchronization restrictions in order to sustain a network, the effectiveness of the network to achieve scalability will be necessarily muted. To work towards a time synchronization theory for DTNs, we build upon past successes in modeling DTNs using time-varying graphs and sheaves. This includes error and limitation estimation, which allows one to define domains over which schedule-based routing is possible, up to some threshold sensitivity. Despite the theoretical nature of these results, the approaches taken are also algorithmic, and hence lend themselves to practical implementations. The paper concludes with comparisons of the various methods along with suggestions for future work.

Delay Tolerant Networking↗

NASA NTRS1990

A VLSI decomposition of the deBruijn graph

A new Viterbi decoder for convolutional codes with constraint lengths up to 15, called the Big Viterbi Decoder, is under development for the Deep Space Network. It will be demonstrated by decoding data from the Galileo spacecraft, which has a rate 1/4, constraint-length 15 convolutional encoder on board. Here, the mathematical theory underlying the design of the very-large-scale-integrated (VLSI) chips that are being used to build this decoder is explained. The deBruijn graph B sub n describes the topology of a fully parallel, rate 1/v, constraint length n+2 Viterbi decoder, and it is shown that B sub n can be built by appropriately wiring together (i.e., connecting together with extra edges) many isomorphic copies of a fixed graph called a B sub n building block. The efficiency of such a building block is defined as the fraction of the edges in B sub n that are present in the copies of the building block. It is shown, among other things, that for any alpha less than 1, there exists a graph G which is a B sub n building block of efficiency greater than alpha for all sufficiently large n. These results are illustrated by describing a special hierarchical family of deBruijn building blocks, which has led to the design of the gate-array chips being used in the Big Viterbi Decoder.

Collins, O.↗

DOE OSTI2025

Kinematic flow from the flow of cuts

The wavefunction coefficients of conformally coupled scalars in power-law FRW cosmologies satisfy differential equations governed by a set of simple combinatorial rules known as the kinematic flow. In this paper we derive the kinematic flow, expressed using a set of differential forms referred to as the cut basis, from a geometric perspective, relying solely on the cosmological hyperplane arrangement and without invoking bulk physics. Each element of the cut basis corresponds to the positive geometry associated to an independent cut of the physical FRW-form and can be labeled by decorating (minors of) the truncated Feynman graph with an acyclic orientation. We provide a straightforward prescription to associate a logarithmic differential form to each element of the cut basis by considering its corresponding decorated graph. Moreover, we show that the residues of the physical FRW-form are canonical forms of certain graphical zonotopes labeled by the same set of decorated graphs. These zonotopes control the cut combinatorics -- flow of cuts -- of the physical FRW-form and the cut basis (by construction). Using the theory of relative twisted cohomology and intersection theory, we derive a closed form formula for the differential equations of the cut basis. We also introduce combinatorial rules that compute the kinematic differential of any basis element without explicit calculation. The combinatorics of our differential equations is a natural consequence of the flow of cuts and is equivalent (up to rescaling) to the kinematic flow for the recently studied time integral basis. In particular, our differential equations decouple into exponentially many sectors, one for each way of cutting a subset of edges of the graph.

General Relativity and Quantum Cosmology↗

DOE OSTI2022

Accurate Prediction of Voltage of Battery Electrode Materials Using Attention-Based Graph Neural Networks

Performing first-principles calculations to discover electrodes’ properties in the large chemical space is a challenging task. While machine learning (ML) has been applied to effectively accelerate those discoveries, most of the applied methods ignore the materials’ spatial information and only use predefined features: based only on chemical compositions. Here, we propose two attention-based graph convolutional neural network techniques to learn the average voltage of electrodes. Our proposed methods, which combine both atomic composition and atomic coordinates in 3D-space, improve the accuracy in voltage prediction significantly when compared to composition-based ML models. The first model directly learns the chemical reaction of electrodes and metal ions to predict their average voltage, whereas the second model combines electrodes’ ML predicted formation energy (E form ) to compute their average voltage. Our E form -based model demonstrates improved accuracy in transferability from our subset of learned Li ions to Na ions. Moreover, we predicted the theoretical voltage of 10 Na x MPO 4 F (M = Ti, Cr, Fe, Cu, Mn, Co, and Ni) fluorophosphate battery frameworks, which are unavailable in the Material Project database. It could be shown that we can expect average voltages higher than 3.1 V from those Na battery frameworks except from the NaTiPO 4 F and TiPO 4 F pair of electrodes, which offer an average voltage of 1.32 V.

25 ENERGY STORAGE↗