Search NASA⌕ Search

SEARCH · Search NASA

Results for “Problem structuring methods”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 325 records · Page 18

Data-driven based coordinated smart inverter control for distributed energy resources

Smart inverters (SI) for distributed energy resources (DER) are becoming popular since they have the ability to stabilize as well as restore the voltage and frequency of power systems. Aiming at establishing the mathematical models combined with SI control methods, multiple optimization methods are developed. However, the computational complexity of solving such a mathematical model with various uncertainties limits the real-time application of the SI control. To conquer this challenge, a data-driven-based SI control approach is developed to achieve coordinated control in the high penetration DER system. First, an optimization problem for maximizing the active power generation and minimizing the power loss is designed using the Volt/VAR control. To reduce the time consumption, the recurrent neural network (RNN) is proposed to model the relationship between the uncertainties and control actions during the offline site. The RNN with different sub-structures such as the long short-term memory cell and gated recurrent unit cell are included to enrich the diversity of features. In the last stage, different experiment comparisons, including multiple uncertainties maps and stateof- art machine learning methods, are conducted to verify the effectiveness of the proposed method based on the IEEE 123 bus power system. The results demonstrate that the proposed method can effectively achieve a rapid and coordinated control with a lower error rate.

Qiu, Wei↗

Extraction of mechanical properties of materials through deep learning from instrumented indentation

Instrumented indentation has been developed and widely utilized as one of the most versatile and practical means of extracting mechanical properties of materials. This method is particularly desirable for those applications where it is difficult to experimentally determine the mechanical properties using stress–strain data obtained from coupon specimens. Such applications include material processing and manufacturing of small and large engineering components and structures involving the following: three-dimensional (3D) printing, thin-film and multilayered structures, and integrated manufacturing of materials for coupled mechanical and functional properties. Here, we utilize the latest developments in neural networks, including a multifidelity approach whereby deep-learning algorithms are trained to extract elastoplastic properties of metals and alloys from instrumented indentation results using multiple datasets for desired levels of improved accuracy. We have established algorithms for solving inverse problems by recourse to single, dual, and multiple indentation and demonstrate that these algorithms significantly outperform traditional brute force computations and function-fitting methods. Moreover, we present several multifidelity approaches specifically for solving the inverse indentation problem which 1) significantly reduce the number of high-fidelity datasets required to achieve a given level of accuracy, 2) utilize known physical and scaling laws to improve training efficiency and accuracy, and 3) integrate simulation and experimental data for training disparate datasets to learn and minimize systematic errors. The predictive capabilities and advantages of these multifidelity methods have been assessed by direct comparisons with experimental results for indentation for different commercial alloys, including two wrought aluminum alloys and several 3D printed titanium alloys.

36 MATERIALS SCIENCE↗

Extraction of mechanical properties of materials through deep learning from instrumented indentation

Instrumented indentation has been developed and widely utilized as one of the most versatile and practical means of extracting mechanical properties of materials. This method is particularly desirable for those applications where it is difficult to experimentally determine the mechanical properties using stress–strain data obtained from coupon specimens. Such applications include material processing and manufacturing of small and large engineering components and structures involving the following: three dimensional (3D) printing, thin-film and multilayered structures, and integrated manufacturing of materials for coupled mechanical and functional properties. Here, we utilize the latest developments in neural networks, including a multifidelity approach whereby deep-learning algorithms are trained to extract elastoplastic properties of metals an d alloys from instrumented indentation results using multiple datasets for desired levels of improved accuracy. We have established algorithms for solving inverse problems by recourse to single, dual, and multiple indentation and demonstrate that these algorithms significantly outperform traditional brute force computations and function-fitting methods. Moreover, we present several multifidelity approaches specifically for solving the inverse indentation problem which 1) significantly reduce the number of high-fidelity datasets required to achieve a given level of accuracy, 2) utilize known physical and scaling laws to improve training efficiency and accuracy, and 3) integrate simulation and experimental data for training disparate datasets to learn and minimize systematic errors. The predictive capabilities and advantages of these multifidelity methods have been assessed by direct comparisons with experimental results for indentation for different commercial alloys, including two wrought aluminum alloys and several 3D printed titanium alloys.

3D printed materials, stress-strain behavior, mult↗

Toward a QUBO-Based Density Matrix Electronic Structure Method

Density matrix electronic structure theory is used in many quantum chemistry methods to “alleviate” the computational cost that arises from directly using wave functions. Although density matrix based methods are computationally more efficient than wave function based methods, significant computational effort is involved. Because the Schrödinger equation needs to be solved as an eigenvalue problem, the time-to-solution scales cubically with the system size in mean-field type approaches such as Hartree–Fock and density functional theory and is solved as many times in order to reach charge or field self-consistency. We hereby propose and study a method to compute the density matrix by using a quadratic unconstrained binary optimization (QUBO) solver. This method could be useful to solve the problem with quantum computers and, more specifically, quantum annealers. Our proposed approach is based on a direct construction of the density matrix using a QUBO eigensolver. We explore the main parameters of the algorithm focusing on precision and efficiency. We show that, while direct construction of the density matrix using a QUBO formulation is possible, the efficiency and precision have room for improvement. Moreover, calculations performed with quantum annealing on D-Wave’s new Advantage quantum computer are compared with results obtained with classical simulated annealing, further highlighting some problems of the proposed method. Finally, we also suggest alternative methods that could lead to a more efficient QUBO-based density matrix construction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

PT symmetry, pattern formation, and finite-density QCD

A longstanding issue in the study of quantum chromodynamics (QCD) is its behavior at nonzero baryon density, which has implications for many areas of physics. The path integral has a complex integrand when the quark chemical potential is nonzero and therefore has a sign problem, but it also has a generalized ${\mathscr{PT}}$ symmetry. We review some new approaches to ${\mathscr{PT}}$-symmetric field theories, including both analytical techniques and methods for lattice simulation. We show that ${\mathscr{PT}}$-symmetric field theories with more than one field generally have a much richer phase structure than their Hermitian counterparts, including stable phases with patterning behavior. The case of a ${\mathscr{PT}}$-symmetric extension of a φ 4 model is explained in detail. The relevance of these results to finite density QCD is explained, and we show that a simple model of finite density QCD exhibits a patterned phase in its critical region.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Efficient mapping between void shapes and stress fields using Deep Convolutional Neural Networks with sparse data

Establishing fast and accurate structure-to-property relationships is an important component in the design and discovery of advanced materials. Physics-based simulation models like the finite element method (FEM) are often used to predict deformation, stress, and strain fields as a function of material microstructure in material and structural systems. Such models may be computationally expensive and time intensive if the underlying physics of the system is complex. This limits their application to solve inverse design problems and identify structures that maximize performance. In such scenarios, surrogate models are employed to make the forward mapping computationally efficient to evaluate. However, the high dimensionality of the input microstructure and the output field of interest often renders such surrogate models inefficient, especially when dealing with sparse data. Deep convolutional neural network (CNN) based surrogate models have shown great promise in handling such high-dimensional problems. In this paper, a single ellipsoidal void structure under a uniaxial tensile load represented by a linear elastic, high-dimensional and expensive-to-query, FEM model. We consider two deep CNN architectures, a modified convolutional autoencoder framework with a fully connected bottleneck and a UNet CNN, and compare their accuracy in predicting the von Mises stress field for any given input void shape in the FEM model. Additionally, a sensitivity analysis study is performed using the two approaches, where the variation in the prediction accuracy on unseen test data is studied through numerical experiments by varying the number of training samples from 20 to 100.

surrogate modeling; convolutional neural networks;↗

Image feature extraction and galaxy classification: a novel and efficient approach with automated machine learning

ABSTRACT In this work, we explore the possibility of applying machine learning methods designed for 1D problems to the task of galaxy image classification. The algorithms used for image classification typically rely on multiple costly steps, such as the point spread function deconvolution and the training and application of complex Convolutional Neural Networks of thousands or even millions of parameters. In our approach, we extract features from the galaxy images by analysing the elliptical isophotes in their light distribution and collect the information in a sequence. The sequences obtained with this method present definite features allowing a direct distinction between galaxy types. Then, we train and classify the sequences with machine learning algorithms, designed through the platform Modulos AutoML. As a demonstration of this method, we use the second public release of the Dark Energy Survey (DES DR2). We show that we are able to successfully distinguish between early-type and late-type galaxies, for images with signal-to-noise ratio greater than 300. This yields an accuracy of $86{{\ \rm per\ cent}}$ for the early-type galaxies and $93{{\ \rm per\ cent}}$ for the late-type galaxies, which is on par with most contemporary automated image classification approaches. The data dimensionality reduction of our novel method implies a significant lowering in computational cost of classification. In the perspective of future data sets obtained with e.g. Euclid and the Vera Rubin Observatory, this work represents a path towards using a well-tested and widely used platform from industry in efficiently tackling galaxy classification problems at the peta-byte scale.

79 ASTRONOMY AND ASTROPHYSICS↗

Neural-network quantum states for the nuclear many-body problem

A long-standing goal of nuclear theory is to explain how the structure and dynamics of atomic nuclei and neutron-star matter emerge from the underlying interactions among protons and neutrons. Achieving this goal requires solving the nuclear quantum many-body problem with high accuracy across a wide range of length scales and density regimes. In this review, we discuss how artificial neural network representations of the nuclear many-body wave function have significantly extended the capabilities of continuum quantum Monte Carlo methods. In particular, neural network quantum states enable calculations of larger systems than were previously accessible and provide a flexible framework for capturing phenomena that challenge conventional approaches, including the emergence of nuclear clusters and superfluid phases in dense matter. We highlight recent applications to finite nuclei, infinite nuclear and neutron matter, and dynamical processes relevant to lepton-nucleus and nucleus-nucleus scattering. We also discuss conceptual and methodological connections with condensed matter physics, emphasizing developments in neural network quantum states that bridge strongly correlated systems across disciplines. Together, these developments demonstrate how neural-network methods open new avenues toward unified and accurate descriptions of nuclear structure, matter, and reactions.

Lovato, Alessandro [Argonne; TIFPA-INFN, Trento; V↗

SCONCE : a cosmic web finder for spherical and conic geometries

The latticework structure known as the cosmic web provides a valuable insight into the assembly history of large-scale structures. Despite the variety of methods to identify the cosmic web structures, they mostly rely on the assumption that galaxies are embedded in a Euclidean geometric space. Here, we present a novel cosmic web identifier called SCONCE (Spherical and CONic Cosmic wEb finder) that inherently considers the 2D (RA, DEC) spherical or the 3D (RA, DEC, z) conic geometry. The proposed algorithms in sconce generalize the well-known subspace constrained mean shift (SCMS) method and primarily address the predominant filament detection problem. They are intrinsic to the spherical/conic geometry and invariant to data rotations. We further test the efficacy of our method with an artificial cross-shaped filament example and apply it to the SDSS galaxy catalogue, revealing that the 2D spherical version of our algorithms is robust even in regions of high declination. Finally, using N-body simulations from Illustris, we show that the 3D conic version of our algorithms is more robust in detecting filaments than the standard SCMS method under the redshift distortions caused by the peculiar velocities of haloes. Our cosmic web finder is packaged in python as SCONCE-SCMS and has been made publicly available.

79 ASTRONOMY AND ASTROPHYSICS↗

Special Issue: Geostatistics and Machine Learning

Abstract Recent years have seen a steady growth in the number of papers that apply machine learning methods to problems in the earth sciences. Although they have different origins, machine learning and geostatistics share concepts and methods. For example, the kriging formalism can be cast in the machine learning framework of Gaussian process regression. Machine learning, with its focus on algorithms and ability to seek, identify, and exploit hidden structures in big data sets, is providing new tools for exploration and prediction in the earth sciences. Geostatistics, on the other hand, offers interpretable models of spatial (and spatiotemporal) dependence. This special issue on Geostatistics and Machine Learning aims to investigate applications of machine learning methods as well as hybrid approaches combining machine learning and geostatistics which advance our understanding and predictive ability of spatial processes.

58 GEOSCIENCES↗

Multi-head physics-informed neural networks for learning functional priors and uncertainty quantification

In numerous applications, the integration of prior knowledge and historical information is essential, particularly for tasks requiring the solution of ordinary or partial differential equations (ODEs/PDEs) in data-sparse or noisy environments. For instance, achieving accurate solutions to time-dependent PDEs with limited initial condition measurements necessitates an effective strategy for embedding prior knowledge. Hard-parameter sharing architectures in neural networks (NNs) have demonstrated success in both traditional and scientific machine learning domains, facilitating the learning of informative representations. Here, in this study, we introduce a novel, yet efficient, method to enhance physics-informed neural networks (PINNs) by incorporating a multi-head structure that enables the learning of functional priors from both empirical data and governing physical laws. This prior information can then be used to address data sparsity and high-level noise in solving ODE/PDE problems with uncertainty quantification (UQ). The approach, termed Multi-Head PINN (MH-PINN), consists of a shared body NN and multiple head NNs, each corresponding to an individual PINN instance. Our framework for functional prior learning is carried out in two stages: (1) training the MH-PINNs to develop a shared body NN alongside multiple head NNs, and (2) employing these trained head NNs to estimate a prior distribution through a normalizing flow-based density estimator. The learned functional prior can then be applied as a regularization mechanism in deterministic contexts or as an informative prior within a Bayesian inference framework, aiding in the resolution of subsequent ODE/PDE tasks. We evaluate the efficacy of MH-PINNs across five benchmark problems, including a high-dimensional parametric PDE, all characterized by data sparsity or substantial noise levels. Our findings reveal that MH-PINNs deliver accurate solutions and robust UQ, demonstrating adaptability across a range of complex and challenging scenarios.

Bayesian inference↗

Affinity propagation clustering of full-field, high-spatial-dimensional measurements for robust output-only modal identification: A proof-of-concept study

Determination of the model order is a challenging problem in system identification, especially in output-only or operational modal identification where some modes are weakly excited. While existing methods such as the stabilization diagram method (spectral information) are effective, they do not scale to high-dimensional data, which is usually needed for high-fidelity characterization of structural dynamics and has been made available in the emerging full-field measurement techniques using optical methods such as photogrammetry and laser vibrometers. In this proof-of-concept study we present a new non-parametric, data-driven approach for robust output-only identification of high-spatial-dimensional modal parameters of basic structures by efficiently processing and interactively exploiting the full-field measurement (i.e., very dense spatial measurement points). Specifically, we first over-estimate the system model once, producing a pool of candidate modes associated with their modal frequencies and full-field, high-spatial-dimensional mode shapes. This is accomplished by a data-driven method termed affinity propagation clustering (APC), where the active clusters, which are the active modes in our formulations, emerge from the "message-passing" procedure and does not require a pre-determination of the cluster number (mode or model order). Next, rather than using the spectral information to distinguish the physical and spurious modes in the stabilization diagram method, we exploit and visualize the spatial, full-field mode shape associated with each candidate mode to do so. We conduct extensive experiments on basic structural models with comparisons to a few existing methods. The results indicate that the new method is computationally efficient for identifying high-spatial-dimensional modal parameters, and robust to identify weak modes by exploiting the full-field measurement. We also discuss its applicability and limitations for structures with complex geometry (shapes).

42 ENGINEERING↗

Inversion of Many-Beam Bragg Intensities for Phasing by Iterated Projections: Removal of Multiple Scattering Artifacts from Diffraction Data

An iterated projection algorithm (N-Phaser) is developed that reconstructs a scattering potential from N-beam multiple Bragg scattered intensities. The method may be used to eliminate multiple scattering artifacts from electron diffraction data, solving the phase problem and increasing the thicknesses of samples used in materials science, solid-state chemistry, and small molecule crystallography. For high-energy transmission electron diffraction, we show that the algorithm recovers accurate complex structure factors from a wide range of thicknesses, orientations, and relativistic beam energies, and does not require known thickness or atomic-resolution data if sufficient multiple scattering occurs. Furthermore, extensions to Cryo-electron microscopy and Micro-electron diffraction are suggested.

36 MATERIALS SCIENCE↗

Management of Risks Associated with Application of Novel Materials in Novel Operating Environments in Novel Reactor Designs

There is currently no widely agreed, detailed general method for licensing a novel plant incorporating novel materials (or materials being deployed in novel environments); in many such situations, there are no directly applicable engineering code cases for decision-makers (including regulators) to rely on. This paper discusses a framework for solving this problem that is based on the Reliability and Integrity Management (RIM) approach delineated in ASME BPVC Section XI Division 2. NRC Regulatory Guide 1.246, Rev. 0, endorses, with conditions, the subject portion of the ASME Code. The proposed framework is meant to support development of a licensing case by addressing certain technical challenges. The framework discussed here is compatible with the Licensing Modernization Project, but applying it in a specific case will call for advances in the state of practice, if not the state of the art. The RIM approach calls for applicants to (a) allocate reliability targets to plant structures, systems, and components (SSCs), (b) show that they are able to relate the currently observed physical condition of each SSC in the program to its failure probability well enough to determine whether the target reliability allocations are being satisfied, allowing for uncertainty related to the novelty of the materials/designs/operating environments, and (c) be able to demonstrate that the proposed program of surveillances will reliably detect unacceptable degradation of an SSC before SSC failure occurs. These challenges are discussed in the paper, and a potentially applicable modeling approach based on cumulative damage rather than failure rates is briefly illustrated.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Data-driven reduced-order models for port-Hamiltonian systems with operator inference

Hamiltonian operator inference has been developed in Sharma et al. (2022) to learn structure-preserving reduced-order models (ROMs) for Hamiltonian systems. The method constructs a low-dimensional model using only data and knowledge of the functional form of the Hamiltonian. The resulting ROMs preserve the intrinsic structure of the system, ensuring that the mechanical and physical properties of the system are maintained. In this work, we extend this approach to port-Hamiltonian systems, which generalize Hamiltonian systems by including energy dissipation, external input, and output. Based on snapshots of the system’s state and output, together with the information about the functional form of the Hamiltonian, reduced operators are inferred through optimization and are then used to construct data-driven ROMs. To further alleviate the complexity of evaluating nonlinear terms in the ROMs, a hyper-reduction method via discrete empirical interpolation is applied. Accordingly, we derive error estimates for the ROM approximations of the state and output. Lastly, we demonstrate the structure preservation, as well as the accuracy of the proposed port-Hamiltonian operator inference framework, through numerical experiments on a linear mass–spring-damper problem and a nonlinear Toda lattice problem.

97 MATHEMATICS AND COMPUTING↗

Recent Advances toward Efficient Calculation of Higher Nuclear Derivatives in Quantum Chemistry

In this article, we provide an overview of state-of-the-art techniques that are being developed for efficient calculation of second and higher nuclear derivatives of quantum mechanical (QM) energy. Calculations of nuclear Hessians and anharmonic terms incur high costs and memory and scale poorly with system size. Three emerging classes of methods—machine learning (ML), automatic differentiation (AD), and matrix completion (MC)—have demonstrated promise in overcoming these challenges. We illustrate studies that employ unsupervised ML methods to reduce the need for multiple Hessian calculations in dynamics simulations and those that utilize supervised ML to construct approximate potential energy surfaces and estimate Hessians and anharmonic terms at reduced cost. By extension, if electronic structure operations could be written in a manner similar to functions underlying ML methods, rapid differentiation or AD routines can be employed to inexpensively calculate higher arbitrary-order derivatives. While ML approaches are typically black-box, we describe methods such as compressed sensing (CS) and MC, which explicitly leverage problem-specific mathematical properties of higher derivatives such as sparsity and low-rank, to complete higher derivative information using only a small, incomplete sample. The three classes of methods facilitate reliable predictions of observables ranging from infrared spectra to thermal conductivity and constitute a promising way forward in accurately capturing otherwise intractable higher-order responses of QM energy to nuclear perturbations.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

SO(3)-invariant PCA with application to molecular data

Principal component analysis (PCA) is a fundamental technique for dimensionality reduction and denoising; however, its application to three-dimensional data with arbitrary orientations -- common in structural biology -- presents significant challenges. A naive approach requires augmenting the dataset with many rotated copies of each sample, incurring prohibitive computational costs. In this paper, we extend PCA to 3D volumetric datasets with unknown orientations by developing an efficient and principled framework for SO(3)-invariant PCA that implicitly accounts for all rotations without explicit data augmentation. By exploiting underlying algebraic structure, we demonstrate that the computation involves only the square root of the total number of covariance entries, resulting in a substantial reduction in complexity. We validate the method on real-world molecular datasets, demonstrating its effectiveness and opening up new possibilities for large-scale, high-dimensional reconstruction problems.

Fraiman, Michael [Tel Aviv Univ., Tel Aviv (Israel↗

To image, or not to image: class-specific diffractive cameras with all-optical erasure of undesired objects

Abstract Privacy protection is a growing concern in the digital era, with machine vision techniques widely used throughout public and private settings. Existing methods address this growing problem by, e.g., encrypting camera images or obscuring/blurring the imaged information through digital algorithms. Here, we demonstrate a camera design that performs class-specific imaging of target objects with instantaneous all-optical erasure of other classes of objects. This diffractive camera consists of transmissive surfaces structured using deep learning to perform selective imaging of target classes of objects positioned at its input field-of-view. After their fabrication, the thin diffractive layers collectively perform optical mode filtering to accurately form images of the objects that belong to a target data class or group of classes, while instantaneously erasing objects of the other data classes at the output field-of-view. Using the same framework, we also demonstrate the design of class-specific permutation and class-specific linear transformation cameras, where the objects of a target data class are pixel-wise permuted or linearly transformed following an arbitrarily selected transformation matrix for all-optical class-specific encryption, while the other classes of objects are irreversibly erased from the output image. The success of class-specific diffractive cameras was experimentally demonstrated using terahertz (THz) waves and 3D-printed diffractive layers that selectively imaged only one class of the MNIST handwritten digit dataset, all-optically erasing the other handwritten digits. This diffractive camera design can be scaled to different parts of the electromagnetic spectrum, including, e.g., the visible and infrared wavelengths, to provide transformative opportunities for privacy-preserving digital cameras and task-specific data-efficient imaging.

47 OTHER INSTRUMENTATION↗