Leveraging Physics-based Surrogates for Efficient Density Estimation of Sparse Observable Data on Low-dimensional Manifolds.
Abstract not provided.
Yen, Tian Yu↗
SEARCH · Search NASA
Results for “low dimensional”
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.
Spin Effects in Low Dimensional Correlated Systems (Final Technical Report)
Our program focuses on the behavior of two-dimensional superconducting systems that have been placed in high magnetic fields and/or in contact with magnetic materials. Our specific research agenda is organized into two separate but related areas. The first is a study of disorder and correlation effects in extremely thin superconducting aluminum, beryllium, and rhenium films that have been subjected to very high magnetic fields. We are particularly interested in understanding how the coupling between the applied field and the electron spins affects the system’s ability to form superconducting state. We now have good evidence that as the electron spins in these superconductors attempt to align to the magnetic field, a new superconducting phase emerges near the critical field transition and that this phase has a significant influence on the character of the transition. Thus, the spin behavior near the transition is much more complex than expected. The second class of systems is proximity structures comprised of superconducting/ferromagnetic (SC/FM) and superconducting/heavy metal (SC/HM) bilayers. We have developed spin-resolved tunneling probes that give us a direct measure of the proximity-induced exchange field in the SC/FM structures, as well as the spin-orbit scattering rate in SC/HM structures. Recently we have demonstrated that the magnitude of the exchange field can be modulated with an external gate, thereby producing a magneto-electric response in the bilayers. We plan to optimize this magneto-electric effect by getting a better understanding of the microscopic mechanism of the interface-induce exchange field, as well as improving the gate barriers and/or the bilayer interface quality. The ultimate goal is to develop a device such as a voltage-controlled superconducting switch or a spin- polarized electron source with a voltage-tunable Zeeman splitting.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Uncertainty Quantification and Sensitivity Analysis of Low-Dimensional Manifold via Co-Kurtosis PCA in Combustion Modeling
For multi-scale multi-physics applications e.g., the turbulent combustion code Pele, robust and accurate dimensionality reduction is crucial to solving problems at exascale and beyond. A recently developed technique, Co-Kurtosis based Principal Component Analysis (CoK-PCA) which leverages principal vectors of co-kurtosis, is a promising alternative to traditional PCA for complex chemical systems. To improve the effectiveness of this approach, we employ Artificial Neural Networks for reconstructing thermo-chemical scalars, species production rates, and overall heat release rates corresponding to the full state space. Our focus is on bolstering confidence in this deep learning based non-linear reconstruction through Uncertainty Quantification (UQ) and Sensitivity Analysis (SA). UQ involves quantifying uncertainties in inputs and outputs, while SA identifies influential inputs. One of the noteworthy challenges is the computational expense inherent in both endeavors. To address this, we employ the Monte Carlo methods to effectively quantify and propagate uncertainties in our reduced spaces while managing computational demands. Our research carries profound implications not only for the realm of combustion modeling but also for a broader audience in UQ. By showcasing the reliability and robustness of CoK-PCA in dimensionality reduction and deep learning predictions, we empower researchers and decision-makers to navigate complex combustion systems with greater confidence.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Low‐dimensional manifold learning for uncertainty quantification in complex multi‐scale stochastic systems
Broadly speaking, the goals of the project are to develop techniques to use manifold learning to develop reduced‐order and surrogate models for "hyper‐reduction" of very high‐dimensional complex multi‐scale systems. This is being achieved by employing a newly proposed form of manifold projection and learning that leverages recent advancements in computational geometry and data‐driven modeling. In particular, we are applying a manifold projection technique to project the solutions of very high‐dimensional systems onto the so‐called Grassmannmanifold, a Reimannian manifold comprised of orthonormal matrices. We then apply data‐driven machine learning techniques to classify the solutions on the manifold (e.g. clustering techniques) according to their proximity on the manifold and leverage a further nonlinear dimension reduction to organize the structured data on the manifold. Finally, we are developing novel techniques that enable us to directly interpolate the hyper‐reduced data such that we can predict the solution of the complex, high‐ dimensional system without need to call the full expensive computational model. Given their adherence to the underlying structure of the solution of the physical system, it is expected that these approximate solutions will be sufficiently constrained so as to (approximately) adhere to physical principles.
97 MATHEMATICS AND COMPUTING↗
Low‐dimensional manifold learning for uncertainty quantification in complex multi‐scale stochastic systems
This report presents the final conclusions, achievements, and other details from the Department of Energy sponsored research. It is structured to follow standard DOE annual reports as submitted through the Portfolio Analysis and Management System (PAMS).
97 MATHEMATICS AND COMPUTING↗
Low-dimensional electronic systems on a silicon platform
Explore the source record for details and available documents.
Lu, Tzu-Ming↗
Deciphering and Manipulating Low Dimensional Magnetism
This program investigates the electronic structure and collective quantum phenomena of correlated magnetic materials using advanced angle-resolved photoemission spectroscopy (ARPES) and complementary probes, with a focus on three interrelated material families: (i) the semiconducting van der Waals magnet Cr₂Ge₂Te₆, (ii) metallic Fe-based van der Waals magnets including Fe₃GeTe₂ Fe₃GaTe₂, and Fe5GeTe₂, and (iii) kagome magnets such as FeGe, FeSn, and CsV₃Sb₅/CsCr₃Sb₅. In Cr₂Ge₂Te₆, our work established how spin excitations develop across a dimensional crossover as spins establish correlation to form long range order, providing a clean platform to isolate correlation effects. In metallic Fe-based magnets, we uncovered the dichotomy between flat and dispersive bands, revealed momentum-dependent electronic reconstructions tied to magnetic order, and demonstrated reversible, non-volatile electronic switching near room temperature, highlighting the strong coupling among spin, charge, and lattice degrees of freedom in metallic ferromagnets. In kagome magnets, we identified charge density wave formation, symmetry breaking, flat-band renormalization, and field-induced momentum-dependent electronic anisotropy, elucidating how geometric frustration and electronic correlations conspire to generate emergent quantum states. Collectively, these results establish a unified microscopic framework for understanding correlation-driven electronic reconstruction, symmetry breaking, and collective order across semiconducting and metallic magnetic systems, advancing DOE mission goals in quantum materials discovery and control.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Grassmannian Diffusion Maps--Based Dimension Reduction and Classification for High-Dimensional Data
This work introduces the Grassmannian diffusion maps (GDMaps), a novel nonlinear dimensionality reduction technique that defines the affinity between points through their representation as low-dimensional subspaces corresponding to points on the Grassmann manifold. Here, the method is designed for applications, such as image recognition and data-based classification of constrained high-dimensional data where each data point itself is a high-dimensional object (i.e., a large matrix) that can be compactly represented in a lower-dimensional subspace. The GDMaps is composed of two stages. The first is a pointwise linear dimensionality reduction wherein each high-dimensional object is mapped onto the Grassmann manifold representing the low-dimensional subspace on which it resides. The second stage is a multipoint nonlinear kernel-based dimension reduction using diffusion maps to identify the subspace structure of the points on the Grassmann manifold. To this end, an appropriate Grassmannian kernel is used to construct the transition matrix of a random walk on a graph connecting points on the Grassmann manifold. Spectral analysis of the transition matrix yields low-dimensional Grassmannian diffusion coordinates embedding the data into a low-dimensional reproducing kernel Hilbert space. Further, a novel data classification/recognition technique is developed based on the construction of an overcomplete dictionary of reduced dimension whose atoms are given by the Grassmannian diffusion coordinates. Three examples are considered. First, a "toy" example shows that the GDMaps can identify an appropriate parametrization of structured points on the unit sphere. The second example demonstrates the ability of the GDMaps to revealing the intrinsic subspace structure of high-dimensional random field data. In the last ex- ample, a face recognition problem is solved considering face images subject to varying illumination conditions, changes in face expressions, and occurrence of occlusions. The technique presented high recognition rates (i.e., 95% in the best case) using a fraction of the data required by conventional methods.
42 ENGINEERING↗
Widespread Negative Longitudinal Piezoelectric Responses in Ferroelectric Crystals with Layered Structures
In this study, we investigate the underlying mechanisms of the universal negative piezoelectricity in low-dimensional layered materials by carrying out first-principles calculations. Two-dimensional layered ferroelectric CuInP 2 S 6 is analyzed in detail as a typical example, but the theory can be applied to any other low-dimensional layered piezoelectrics. Consistent with the theory proposed in [Phys. Rev. Lett. 119, 207601 (2017), the anomalous negative piezoelectricity in CuInP 2 S 6 also results from its negative clamped-ion term, which cannot be compensated by the positive internal-strain part. Here, we focus on a more general rule by proposing that having a negative clamped-ion term should be universal among piezoelectric materials, which is attributed to the “lag of Wannier center” effect. The internal-strain term, which is the change in polarization due to structural relaxation in response to strain, is mostly determined by the spatial structure and chemical bonding of the material. In a low-dimensional layered piezoelectric material such as CuInP 2 S 6 , the internal-strain term is approximately zero. This is because the internal structure of the molecular layers, which are bonded by the weak van der Waals interaction, responds little to the strain. As a result, the magnitude of the dipole, which depends strongly on the dimension and structure of the molecular layer, also has a small response with respect to strain. An equation bridging the internal strain responses in low-dimensional and three-dimensional piezoelectrics is also derived to analytically express this point. This work aims to deepen our understanding about this anomalous piezoelectric effect, especially in low-dimensional layered materials, and provide strategies for discovering materials with novel electromechanical properties.
2-dimensional systems↗
Detecting thermodynamic phase transition via explainable machine learning of photoemission spectroscopy
Identifying thermodynamic signatures of electronic phases, such as superconductivity, is challenging in low-dimensional materials due to strong fluctuations and low probing volume. Spectroscopic methods are often used to identify new bulk phases, but their main measurable quantity—electronic energy gaps—is no longer an effective order parameter in low-dimensional and fluctuating systems. Combining angle-resolved photoemission with a domain-adversarial neural network, we report a data-driven method to identify thermodynamic phase transitions solely based on single-particle spectra. We demonstrate 97.6% accuracy in cuprate superconductor Bi 2 Sr 2 CaCu 2 O 8+δ with strong superconducting fluctuations. This model notably compensates for the scarcity of experimental data by leveraging virtually inexhaustible simulated data. Further, its explainability reveals the crucial role of in-gap spectral weight in detecting phase fluctuations and thermodynamic transitions. Our work pinpoints the spectroscopic signatures of fluctuating orders and enables using spectroscopy for machine-learning-assisted material discovery for low-dimensional and strong coupling systems.
2D materials↗
Perovskite superlattices with efficient carrier dynamics
Compared with their three-dimensional (3D) counterparts, low-dimensional metal halide perovskites (2D and quasi-2D; B 2 A n-1 M n X 3n+1 , such as B = R-NH 3 + , A = HC(NH 2 ) 2 + , Cs + ; M = Pb 2+ , Sn 2+ ; X = Cl - , Br - , I - ) with periodic inorganic-organic structures have shown promising stability and hysteresis-free electrical performance. However, their unique multiple-quantum-well structure limits the device efficiencies because of the grain boundaries and randomly oriented quantum wells in polycrystals. In single crystals, the carrier transport through the thickness direction is hindered by the layered insulating organic spacers. Furthermore, the strong quantum confinement from the organic spacers limits the generation and transport of free carriers. Also, lead-free metal halide perovskites have been developed but their device performance is limited by their low crystallinity and structural instability 11 . Here, in this paper, we report a low-dimensional metal halide perovskite BA 2 MA n-1 Sn n I 3n+1 (BA, butylammonium; MA, methylammonium; n = 1, 3, 5) superlattice by chemical epitaxy. The inorganic slabs are aligned vertical to the substrate and interconnected in a criss-cross 2D network parallel to the substrate, leading to efficient carrier transport in three dimensions. A lattice-mismatched substrate compresses the organic spacers, which weakens the quantum confinement. The performance of a superlattice solar cell has been certified under the quasi-steady state, showing a stable 12.36% photoelectric conversion efficiency. Moreover, an intraband exciton relaxation process may have yielded an unusually high open-circuit voltage (V OC ).
36 MATERIALS SCIENCE↗
Fast Computational Algorithms for Partial Differential Equations and Uncertainty Quantifications
This project concerned the construction, testing and analysis of computational algorithms for solving parameterized and stochastic partial differential equations. The study and understanding of equations of this type is of fundamental importance in numerous engineering and scientific applications. Examples include simulation of plasma dynamics in models of electric propulsion and nuclear fusion, simulation of multiphase flows, such as the flow of water, gas and oil in reservoirs, and structural analysis of the dependence of structures on materials. Parametrization is used in such settings when properties of the models such as viscosity of fluids or electric resistivity of materials are not precisely understood and instead are treated as random variables. The resulting solutions are themselves random, and having such solutions will enable engineers to use probabilistic methods to assess the likelihood of events, for example, whether a pollutant in a liquid will exceed a limit, and to use such analyses to develop ways to ensure positive outcomes. Construction of accurate (high resolution) computational solutions is expensive, requiring significant computer time and computational resources, and there is need to reduce computational cost to make simulation useful and effective. The aim of the project was to construct algorithms to efficiently compute surrogate solutions to parameterized problems to allow for efficient and accurate simulation. The technical approach used focused on two related strategies, based on rank-reduction methods and reduced-order models. These methods construct surrogate solutions of parameter-dependent models by projection or interpolation into low-dimensional approximation spaces. Cost savings are achieved if the low-dimensional spaces can be identified and constructed efficiently and if the resulting low-dimensional algebraic systems can be solved cheaply. Accomplishments include: Theoretical and empirical demonstration of the effectiveness of fast multigrid solution strategies for computing low-rank representations of parameter-dependent solutions to discrete partial differential equations, including the first proof establishing so-called textbook convergence properties for low-rank methods. Development of efficient solution algorithms for solving nonlinear parameter-dependent partial differential equations used in models of fluid dynamics. Developent of efficient algorithms for low-rank representation of solutions of time-dependent simulations of fluid dynamics using multi-dimensional tensor representations of solutions.
97 MATHEMATICS AND COMPUTING↗
Reaching 90% Photoluminescence Quantum Yield in One-Dimensional Metal Halide C 4 N 2 H 14 PbBr 4 by Pressure-Suppressed Nonradiative Loss
Low-dimensional perovskite-related metal halides have emerged as a new class of light-emitting materials with tunable broadband emission from self-trapped excitons (STEs). Although various types of low-dimensional structures have been developed, fundamental understating of the structure–property relationships for this class of materials is still very limited, and further improvement of their optical properties remains greatly important. Here, we report a significant pressure-induced photoluminescence (PL) enhancement in a one-dimensional hybrid metal halide C 4 N 2 H 14 PbBr 4 , and the underlying mechanisms are investigated using in situ experimental characterization and first-principles calculations. Under a gigapascal pressure scale, the PL quantum yields (PLQYs) were quantitatively determined to show a dramatic increase from the initial value of 20% at ambient conditions to over 90% at 2.8 GPa. With in situ characterization of photophysical properties and theoretical analysis, we found that the PLQY enhancement was mainly attributed to the greatly suppressed nonradiative decay. Pressure can effectively tune the energy level of self-trapped states and increase the exciton binding energy, which leads to a larger Stokes shift. The resulting highly localized excitons with stronger binding reduce the probability for carrier scattering, to result in the significantly suppressed nonradiative decay. Overall, our findings clearly show that the characteristics of STEs in low-dimensional metal halides can be well-tuned by external pressure, and enhanced optical properties can be achieved.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Stability and magnetic behavior of exfoliable nanowire one-dimensional materials
Low-dimensional materials can display enhanced electronic, magnetic, and quantum properties. Here we use the topological scaling algorithm to identify all sufficiently metastable materials in the Materials Project database to identify bulk crystals with one-dimensional (1D) structural motifs: Five hundred fifty-one crystals that are within 50 meV atom –1 of the thermodynamic hull display 1D motifs, where 293 of these contain d-valence elements, which we focus on in this work. After exfoliating nanowires from 263 of these materials and calculating their thermodynamic stability using density functional theory, 103 nanowires meet per-atom and per-Ångström thermodynamic stability criteria. We illustrate for three nanowire systems that a variety of local minima can be present in these systems, demonstrating one case of a Peierls distortion. The wires display a broad diversity of electronic and magnetic properties of these nanowires, with 14 metals, 7 half-metals, and 82 semiconductors and insulators, and 41 nanowires displaying magnetic moments ranging from 0.1 to 5μ B per d-valence species when assuming ferromagnetic order. A subset of these chains are investigated for the impact of magnetic ordering, identifying 1D FeCl 3 to be most stable in an antiferromagnetic state. The electronic and magnetic properties of the identified 1D materials could enable applications in spintronic and quantum devices.
36 MATERIALS SCIENCE↗
Colloidal Quantum Shells: An Emerging 2D Semiconductor for Energy Applications
Low-dimensional semiconductors hold strong promise for future energy applications. These nanomaterials are inexpensive to process and offer a broad spectrum of attractive quantum-mechanical properties. The notorious problem of low-dimensional nanostructures, however, lies in their limited performance under high energetic loads, when more than one exciton per particle is created. Multiple excitons undergo fast annihilation, causing efficiently roll-off in energy-intensive applications, including high-brightness LEDs, X-ray scintillators, and solar cells. In this prospective, we will highlight an emerging type of low-dimensional semiconductors that allows avoiding such multi-exciton (MX) energy losses. Recently demonstrated colloidal quantum shells benefit from the spatial separation of multiple excitons, which leads to extraordinary improvements to MX lifetimes and MX quantum yield. This makes quantum shell morphology an attractive candidate for solution-processed optical and electrical devices. In this Focus Review, we compare the optoelectronic properties of quantum shells against other low-dimensional semiconductors and discuss their emerging opportunities in solid-state lighting and energy-harvesting applications.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Deep nonparametric estimation of intrinsic data structures by chart autoencoders: Generalization error and robustness
Autoencoders have demonstrated remarkable success in learning low-dimensional latent features of high-dimensional data across various applications. Assuming that data are sampled near a low-dimensional manifold, we employ chart autoencoders, which encode data into low-dimensional latent features on a collection of charts, preserving the topology and geometry of the data manifold. Our paper establishes statistical guarantees on the generalization error of chart autoencoders, and we demonstrate their denoising capabilities by considering n noisy training samples, along with their noise-free counterparts, on a d-dimensional manifold. By training autoencoders, we show that chart autoencoders can effectively denoise the input data with normal noise. We prove that, under proper network architectures, chart autoencoders achieve a squared generalization error in the order of n–$\frac{2}{d+2}$log 4 n, which depends on the intrinsic dimension of the manifold and only weakly depends on the ambient dimension and noise level. We further extend our theory on data with noise containing both normal and tangential components, where chart autoencoders still exhibit a denoising effect for the normal component. As a special case, our theory also applies to classical autoencoders, as long as the data manifold has a global parametrization. Furthermore, our results provide a solid theoretical foundation for the effectiveness of autoencoders, which is further validated through several numerical experiments.
97 MATHEMATICS AND COMPUTING↗
Quasi-One-Dimensional Metallicity in Compressed CsSnI 3
Low-dimensional metal halides exhibit strong structural and electronic anisotropies, making them candidates for accessing unusual electronic properties. Here, in this work, we demonstrate pressure-induced quasi-one-dimensional (quasi-1D) metallicity in δ-CsSnI 3 . With the application of pressure up to 40 GPa, the initially insulating δ-CsSnI 3 transforms to a metallic state. Synchrotron X-ray diffraction and Raman spectroscopy indicate that the starting 1D chain structure of edge-sharing Sn–I octahedra in δ-CsSnI 3 is maintained in the high-pressure metallic phase while the SnI 6 octahedral chains are distorted. Our experiments combined with first-principles density functional theory calculations reveal that pressure induces Sn–Sn hybridization and enhances Sn–I coupling within the chain, leading to band gap closure and formation of conductive SnI 6 distorted octahedral chains. In contrast, the interchain I...I interactions remain minimal, resulting in a highly anisotropic electronic structure and quasi-1D metallicity. Our study offers a high-pressure approach for achieving diverse electronic platforms in the broad family of low-dimensional metal halides.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Operator inference for non-intrusive model reduction with quadratic manifolds
This paper proposes a novel approach for learning a data-driven quadratic manifold from high-dimensional data, then employing this quadratic manifold to derive efficient physics-based reduced-order models. The key ingredient of the approach is a polynomial mapping between high-dimensional states and a low-dimensional embedding. This mapping consists of two parts: a representation in a linear subspace (computed in this work using the proper orthogonal decomposition) and a quadratic component. The approach can be viewed as a form of data-driven closure modeling, since the quadratic component introduces directions into the approximation that lie in the orthogonal complement of the linear subspace, but without introducing any additional degrees of freedom to the low-dimensional representation. Combining the quadratic manifold approximation with the operator inference method for projection-based model reduction leads to a scalable non-intrusive approach for learning reduced-order models of dynamical systems. Further, applying the new approach to transport-dominated systems of partial differential equations illustrates the gains in efficiency that can be achieved over approximation in a linear subspace.
42 ENGINEERING↗