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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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DOE OSTI2024

Facial Named Entity Recognition by Attention-Based Graph Convolutional Neural Network

In the realm of facial recognition and analysis, the ability to accurately cluster large datasets of facial images stands as a cornerstone for various applications, ranging from security surveillance to user biometric identification. This project evolves a novel approach to facial data clustering by embedding facial images into a high-dimensional vector space using an advanced embedding model trained on separate data and assumes a graph-like structure on the high-dimensional vectors. We find our method works significantly better than common shallow methods.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1972

Lie theory and control systems defined on spheres

It is shown that in constructing a theory for the most elementary class of control problems defined on spheres, some results from the Lie theory play a natural role. To understand controllability, optimal control, and certain properties of stochastic equations, Lie theoretic ideas are needed. The framework considered here is the most natural departure from the usual linear system/vector space problems which have dominated control systems literature. For this reason results are compared with those previously available for the finite dimensional vector space case.

Brockett, R. W.↗

DOE OSTI2020

The structural information filtered features (SIFF) potential: Maximizing information stored in machine-learning descriptors for materials prediction

Machine learning inspired potentials continue to improve the ability for predicting structures of materials. However, many challenges still exist, particularly when calculating structures of disordered systems. These challenges are primarily due to the rapidly increasing dimensionality of the feature-vector space which in most machine-learning algorithms is dependent on the size of the structure. In this article, we present a feature-engineered approach that establishes a set of principles for representing potentials of physical structures (crystals, molecules, and clusters) in a feature space rather than a physically motivated space. Our goal in this work is to define guiding principles that optimize information storage of the physical parameters within the feature representations. In this manner, we focus on keeping the dimensionality of the feature space independent of the number of atoms in the structure. Our Structural Information Filtered Features (SIFF) potential represents structures by utilizing a feature vector of low-correlated descriptors, which correspondingly maximizes information within the descriptor. We present results of our SIFF potential on datasets composed of disordered (carbon and carbon–oxygen) clusters, molecules with C 7 O 2 H 2 stoichiometry in the GDB9-14B dataset, and crystal structures of the form (Al x Ga y In z ) 2 O 3 as proposed in the NOMAD Kaggle competition. Our potential's performance is at least comparable, sometimes significantly more accurate, and often more efficient than other well-known machine-learning potentials for structure prediction. However, primarily, we offer a different perspective on how researchers should consider opportunities in maximizing information storage for features.

36 MATERIALS SCIENCE↗

NASA NTRS2009

Hybrid NN/SVM Computational System for Optimizing Designs

A computational method and system based on a hybrid of an artificial neural network (NN) and a support vector machine (SVM) (see figure) has been conceived as a means of maximizing or minimizing an objective function, optionally subject to one or more constraints. Such maximization or minimization could be performed, for example, to optimize solve a data-regression or data-classification problem or to optimize a design associated with a response function. A response function can be considered as a subset of a response surface, which is a surface in a vector space of design and performance parameters. A typical example of a design problem that the method and system can be used to solve is that of an airfoil, for which a response function could be the spatial distribution of pressure over the airfoil. In this example, the response surface would describe the pressure distribution as a function of the operating conditions and the geometric parameters of the airfoil. The use of NNs to analyze physical objects in order to optimize their responses under specified physical conditions is well known. NN analysis is suitable for multidimensional interpolation of data that lack structure and enables the representation and optimization of a succession of numerical solutions of increasing complexity or increasing fidelity to the real world. NN analysis is especially useful in helping to satisfy multiple design objectives. Feedforward NNs can be used to make estimates based on nonlinear mathematical models. One difficulty associated with use of a feedforward NN arises from the need for nonlinear optimization to determine connection weights among input, intermediate, and output variables. It can be very expensive to train an NN in cases in which it is necessary to model large amounts of information. Less widely known (in comparison with NNs) are support vector machines (SVMs), which were originally applied in statistical learning theory. In terms that are necessarily oversimplified to fit the scope of this article, an SVM can be characterized as an algorithm that (1) effects a nonlinear mapping of input vectors into a higher-dimensional feature space and (2) involves a dual formulation of governing equations and constraints. One advantageous feature of the SVM approach is that an objective function (which one seeks to minimize to obtain coefficients that define an SVM mathematical model) is convex, so that unlike in the cases of many NN models, any local minimum of an SVM model is also a global minimum.

Rai, Man Mohan↗

NASA NTRS1985

On the convergence of an iterative formulation of the electromagnetic scattering from an infinite grating of thin wires

Contraction theory is applied to an iterative formulation of electromagnetic scattering from periodic structures and a computational method for insuring convergence is developed. A short history of spectral (or k-space) formulation is presented with an emphasis on application to periodic surfaces. The mathematical background for formulating an iterative equation is covered using straightforward single variable examples including an extension to vector spaces. To insure a convergent solution of the iterative equation, a process called the contraction corrector method is developed. Convergence properties of previously presented iterative solutions to one-dimensional problems are examined utilizing contraction theory and the general conditions for achieving a convergent solution are explored. The contraction corrector method is then applied to several scattering problems including an infinite grating of thin wires with the solution data compared to previous works.

Brand, J. C.↗

DOE OSTI2018

A simple procedure for construction of the orthonormal basis vectors of irreducible representations of O(5) in the O T ( 3 ) Ⓧ O N ( 2 ) basis

We report a simple and effective algebraic isospin projection procedure for constructing orthonormal basis vectors of irreducible representations of O(5) ⊃ OT(3) Ⓧ O$_\mathscr{N}$ (2) from those in the canonical O(5) ⊃ SU Λ (2) Ⓧ SU I (2) basis is outlined. The expansion coefficients are components of null space vectors of the projection matrix with four nonzero elements in each row in general. Explicit formulae for evaluating O T (3)-reduced matrix elements of O(5) generators are derived.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2018

Stability of solution mappings for parametric bilevel vector equilibrium problems

In this paper, we first revisit the parametric bilevel vector equilibrium problems in Hausdorff topological vector spaces. Then we study the stability conditions such as (Hausdorff) upper semicontinuity, (Hausdorff) lower semicontinuity, outer-continuity and outer-openness of solutions for such problems. Many examples are provided to illustrate the essentialness of the imposed assumptions. For the applications, we obtain the stability results for the parametric vector variational inequality problems with equilibrium constraints and parametric vector optimization problems with equilibrium constraints.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1979

Investigations on the hierarchy of reference frames in geodesy and geodynamics

Problems related to reference directions were investigated. Space and time variant angular parameters are illustrated in hierarchic structures or towers. Using least squares techniques, model towers of triads are presented which allow the formation of linear observation equations. Translational and rotational degrees of freedom (origin and orientation) are discussed along with and the notion of length and scale degrees of freedom. According to the notion of scale parallelism, scale factors with respect to a unit length are given. Three-dimensional geodesy was constructed from the set of three base vectors (gravity, earth-rotation and the ecliptic normal vector). Space and time variations are given with respect to a polar and singular value decomposition or in terms of changes in translation, rotation, deformation (shear, dilatation or angular and scale distortions).

Grafarend, E. W.↗

NASA NTRS2017

Automation of POST Cases via External Optimizer and "Artificial p2" Calculation

During early conceptual design of complex systems, speed and accuracy are often at odds with one another. While many characteristics of the design are fluctuating rapidly during this phase there is nonetheless a need to acquire accurate data from which to down-select designs as these decisions will have a large impact upon program life-cycle cost. Therefore enabling the conceptual designer to produce accurate data in a timely manner is tantamount to program viability. For conceptual design of launch vehicles, trajectory analysis and optimization is a large hurdle. Tools such as the industry standard Program to Optimize Simulated Trajectories (POST) have traditionally required an expert in the loop for setting up inputs, running the program, and analyzing the output. The solution space for trajectory analysis is in general non-linear and multi-modal requiring an experienced analyst to weed out sub-optimal designs in pursuit of the global optimum. While an experienced analyst presented with a vehicle similar to one which they have already worked on can likely produce optimal performance figures in a timely manner, as soon as the "experienced" or "similar" adjectives are invalid the process can become lengthy. In addition, an experienced analyst working on a similar vehicle may go into the analysis with preconceived ideas about what the vehicle's trajectory should look like which can result in sub-optimal performance being recorded. Thus, in any case but the ideal either time or accuracy can be sacrificed. In the authors' previous work a tool called multiPOST was created which captures the heuristics of a human analyst over the process of executing trajectory analysis with POST. However without the instincts of a human in the loop, this method relied upon Monte Carlo simulation to find successful trajectories. Overall the method has mixed results, and in the context of optimizing multiple vehicles it is inefficient in comparison to the method presented POST's internal optimizer functions like any other gradient-based optimizer. It has a specified variable to optimize whose value is represented as optval, a set of dependent constraints to meet with associated forms and tolerances whose value is represented as p2, and a set of independent variables known as the u-vector to modify in pursuit of optimality. Each of these quantities are calculated or manipulated at a certain phase within the trajectory. The optimizer is further constrained by the requirement that the input u-vector must result in a trajectory which proceeds through each of the prescribed events in the input file. For example, if the input u-vector causes the vehicle to crash before it can achieve the orbital parameters required for a parking orbit, then the run will fail without engaging the optimizer, and a p2 value of exactly zero is returned. This poses a problem, as this "non-connecting" region of the u-vector space is far larger than the "connecting" region which returns a non-zero value of p2 and can be worked on by the internal optimizer. Finding this connecting region and more specifically the global optimum within this region has traditionally required the use of an expert analyst.

Dees, Patrick D.↗

DOE OSTI2018

Algebraic multigrid for directed graph Laplacian linear systems (NS‐LAMG)

Summary We propose nonsymmetric lean algebraic multigrid (NS‐LAMG), a new algebraic multigrid algorithm for directed graph Laplacian systems that combines ideas from undirected graph Laplacian multigrid solvers and multigrid algorithms for Markov chain stationary distribution systems. Low‐degree elimination, proposed in LAMG for undirected graphs, is generalized to directed graphs and is a key component of NS‐LAMG. In the setup phase, we propose a simple stationary‐aggregation multigrid algorithms for Markov chain stationary distribution systems solver enhanced by low‐degree elimination to find the right null‐space vector that is used for the intergrid transfer operators. Numerical results show that low‐degree elimination improves performance and that NS‐LAMG outperforms generalized minimal residual method with restart and stable bi‐conjugate gradient method for real‐world, directed graph Laplacian linear systems.

Fox, Alyson↗

DOE OSTI2025

A Type II Hamiltonian Variational Principle and Adjoint Systems for Lie Groups

We present a novel Type II variational principle on the cotangent bundle of a Lie group which enforces Type II boundary conditions, i.e., fixed initial position and final momentum. In general, such Type II variational principles are only globally defined on vector spaces or locally defined on general manifolds; however, by left translation, we are able to define this variational principle globally on cotangent bundles of Lie groups. Type II boundary conditions are particularly important for adjoint sensitivity analysis, which is our motivating application. As such, we additionally discuss adjoint systems on Lie groups, their properties, and how they can be used to solve optimization problems subject to dynamics on Lie groups.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Leveraging operator learning to accelerate convergence of the preconditioned conjugate gradient method

We propose a new deflation strategy to accelerate the convergence of the preconditioned conjugate gradient (PCG) method for solving parametric large-scale linear systems of equations. Unlike traditional deflation techniques that rely on eigenvector approximations or recycled Krylov subspaces, we generate the deflation subspaces using operator learning, specifically the Deep Operator Network (DeepONet). To this aim, we introduce two complementary approaches for assembling the deflation operators. The first approach approximates near-null space vectors of the discrete PDE operator using the basis functions learned by the DeepONet. The second approach directly leverages solutions predicted by the DeepONet. To further enhance convergence, we also propose several strategies for prescribing the sparsity pattern of the deflation operator. Here, a comprehensive set of numerical experiments encompassing steady-state, time-dependent, scalar, and vector-valued problems posed on both structured and unstructured geometries is presented and demonstrates the effectiveness of the proposed DeepONet-based deflated PCG method, as well as its generalization across a wide range of model parameters and problem resolutions.

Deflation↗

DOE OSTI2023

Scalable Bayesian optimization with randomized prior networks

Several fundamental problems in science and engineering consist of global optimization tasks involving unknown high-dimensional (black-box) functions that map a set of controllable variables to the outcomes of an expensive experiment. Bayesian Optimization (BO) techniques are known to be effective in tackling global optimization problems using a relatively small number objective function evaluations, but their performance suffers when dealing with high-dimensional outputs. To overcome the major challenge of dimensionality, here we propose a deep learning framework for BO and sequential decision making based on bootstrapped ensembles of neural architectures with randomized priors. Using appropriate architecture choices, we show that the proposed framework can approximate functional relationships between design variables and quantities of interest, even in cases where the latter take values in high-dimensional vector spaces or even infinite-dimensional function spaces. In the context of BO, we augmented the proposed probabilistic surrogates with re-parameterized Monte Carlo approximations of multiple-point (parallel) acquisition functions, as well as methodological extensions for accommodating black-box constraints and multi-fidelity information sources. We test the proposed framework against state-of-the-art methods for BO and demonstrate superior performance across several challenging tasks with high-dimensional outputs, including a constrained multi-fidelity optimization task involving shape optimization of rotor blades in turbo-machinery.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Importance of Engineered and Learned Molecular Representations in Predicting Organic Reactivity, Selectivity, and Chemical Properties

Machine-readable chemical structure representations are foundational in all attempts to harness machine learning for the prediction of reactivities, selectivities, and chemical properties directly from molecular structure. The featurization of discrete chemical structures into a continuous vector space is a critical phase undertaken before model selection, and the development of new ways to quantitatively encode molecules is an active area of research. Here, we highlight the application and suitability of different representations, from expert-guided “engineered” descriptors to automatically “learned” features, in different prediction tasks relevant to organic and organometallic chemistry, where differing amounts of training data are available. These tasks include statistical models of stereo- and enantioselectivity, thermochemistry, and kinetics developed using experimental and quantum chemical data. The use of expert-guided molecular descriptors provides an opportunity to incorporate chemical knowledge, domain expertise, and physical constraints into statistical modeling. In applications to stereoselective organic and organometallic catalysis, where data sets may be relatively small and 3D-geometries and conformations play an important role, mechanistically informed features can be used successfully to obtain predictive statistical models that are also chemically interpretable. We provide an overview of several recent applications of this approach to obtain quantitative models for reactivity and selectivity, where topological descriptors, quantum mechanical calculations of electronic and steric properties, along with conformational ensembles, all feature as essential ingredients of the molecular representations used. Alternatively, more flexible, general-purpose molecular representations such as attributed molecular graphs can be used with machine learning approaches to learn the complex relationship between a structure and prediction target. This approach has the potential to out-perform more traditional representation methods such as “hand-crafted” molecular descriptors, particularly as data set sizes grow. One area where this is particularly relevant is in the use of large sets of quantum mechanical data to train quantitative structure–property relationships. A general approach toward curating useful data sets and training highly accurate graph neural network models is discussed in the context of organic bond dissociation enthalpies, where this strategy outperforms regression using precomputed descriptors. Finally, we describe how graph neural network predictions can be incorporated into mechanistically informed statistical models of chemical reactivity and selectivity. Once trained, this approach avoids the expensive computational overhead associated with quantum mechanical calculations, while maintaining chemical interpretability. We illustrate examples for which fast predictions of bond dissociation enthalpy and of the identities of radicals formed through cleavage of a molecule’s weakest bond are used in simple physical models of site-selectivity and reactivity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Deep Koopman operators for causal discovery

Causal discovery aims to identify cause-effect mechanisms for better scientific understanding, explainable decision-making, and more accurate modeling. Standard statistical frameworks, such as Granger causality, lack the ability to quantify causal relationships in nonlinear dynamics due to the presence of complex feedback mechanisms, timescale mixing, and nonstationarity. Thus, applying these methods to study causal dynamics in real-world systems, such as the Earth, is a major challenge. Addressing this shortcoming, we leverage deep learning and a Koopman operator-theoretic formalism to present a class of causal discovery algorithms. Kausal uses deep Koopman operator methods to approximate nonlinear dynamics in a linearized vector space in which traditional causal inference methods such as Granger causality can be more easily applied. Our idealized experiments demonstrate Kausal’s superior ability in discovering and characterizing causal signals compared to existing deep learning and non-deep learning state-of-the-art approaches. Finally, the successful identification of major El Niño and La Niña events in observations showcases Kausal’s skill to handle real-world applications.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Evaluating the gradients of localized diabatic state energies and couplings at minimum cost

We calculate the gradients of Boys diabatic state energies and couplings when the electronic vector space is generated by configuration interaction singles. Our approach follows the Lagrangian approach of Paz and Glover (rather than direct differentiation of the adiabatic-to-diabatic approaches that have been published previously). The result is that we achieve a dramatic increase in savings over previous approaches, and the present approach should be immediately useful to scientists focused on electronic relaxation, especially chemists studying electron transfer who wish to go beyond the Condon approximation. Here, a future extension to time-dependent density functional theory in the Tamm–Dancoff approximation is clear.

Chemical physics↗

DOE OSTI2025

CSGL: chemical synthesis graph learning for molecule representation

Abstract Motivation Molecule representation learning (MRL) translates molecules into a real vector space, serving as input to downstream tasks in biology, chemistry, and computer science. This article introduces a chemical synthesis graph learning (CSGL) framework, which enhances MRL by considering both the atomic structures of molecules and their roles in chemical reactions through a hierarchical graph representation. Specifically, molecules are first modeled based on their molecular graphs, which capture atomic-level structural information. They are then further refined using a chemical synthesis graph, where nodes represent reactant and product molecule sets, and edges encode chemical transformations between reactants and products (e.g. changes in molecular structures). CSGL optimizes molecular embeddings of reactant and product nodes in a fashion that ensures the embeddings conform to a chemical balance constraint. Results Experimental results show that our method CSGL achieves strong performance on a variety of tasks, including product prediction, reaction classification, and molecular property prediction. Availability and implementation https://github.com/li-2023/CSGL.

Biochemistry & Molecular Biology↗

DOE OSTI2024

Detecting damage in composites using volume decomposition analysis of tomographic data

Detection of damage in a single tow ceramic matrix composite specimen has been achieved using orthogonal decomposition of volumetric tomographic datasets collected at four tensile loads. This decomposition approach has been applied at two different length scales: (i) individual fibres and (ii) bulk volumes containing fibres and matrix material. Volumes were first decomposed to feature vectors, orders of magnitude smaller than the original volume they describe, and then comparisons between datasets at different load levels were made in feature vector space. The results show quantitative measurements of damage location, damage morphology and the relative growth of this damage with increased load when compared with a dataset with less or no damage. No prior knowledge of the dataset or training of algorithms is required for damage to be detected, it is only necessary that at least two datasets are available for comparison, e.g. from in situ or repeated scanning measurements. Results are generated on significantly shorter timescales when compared with previous automated approaches to tomography data processing. This approach has the potential to be applied to damage detection in a range of materials through comparisons of volumetric datasets from a range of measurement or computational techniques.

Middleton, Ceri A.↗