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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

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↗
DOE OSTI2015

Systematic characterization of protein folding pathways using diffusion maps: Application to Trp-cage miniprotein

Understanding the mechanisms by which proteins fold from disordered amino-acid chains to spatially ordered structures remains an area of active inquiry. Molecular simulations can provide atomistic details of the folding dynamics which complement experimental findings. Conventional order parameters, such as root-mean-square deviation and radius of gyration, provide structural information but fail to capture the underlying dynamics of the protein folding process. It is therefore advantageous to adopt a method that can systematically analyze simulation data to extract relevant structural as well as dynamical information. The nonlinear dimensionality reduction technique known as diffusion maps automatically embeds the high-dimensional folding trajectories in a lower-dimensional space from which one can more easily visualize folding pathways, assuming the data lie approximately on a lower-dimensional manifold. The eigenvectors that parametrize the low-dimensional space, furthermore, are determined systematically, rather than chosen heuristically, as is done with phenomenological order parameters. We demonstrate that diffusion maps can effectively characterize the folding process of a Trp-cage miniprotein. By embedding molecular dynamics simulation trajectories of Trp-cage folding in diffusion maps space, we identify two folding pathways and intermediate structures that are consistent with the previous studies, demonstrating that this technique can be employed as an effective way of analyzing and constructing protein folding pathways from molecular simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Universal signatures of Dirac fermions in entanglement and charge fluctuations

We study the entanglement entropy (EE) and charge fluctuations in models where the low-energy physics is governed by massless Dirac fermions. We focus on the response to flux insertion which, for the EE, is widely assumed to be universal, i.e., independent of the microscopic details. We provide an analytical derivation of the EE and charge fluctuations for the seminal example of graphene, using the dimensional reduction of its tight-binding model to the one-dimensional Su-Schrieffer-Heeger model. Our asymptotic expression for the EE matches the conformal field theory prediction. We show that the charge variance has the same asymptotic behavior, up to a constant prefactor. To check the validity of universality arguments, we numerically consider several models, with different geometries and numbers of Dirac cones, and either for strictly two-dimensional models or for a gapless surface mode of three-dimensional topological insulators. We also show that the flux response does not depend on the entangling surface geometry as long as it encloses the flux. Finally we consider the universal corner contributions to the EE. We show that in the presence of corners, the Kitaev-Preskill subtraction scheme provides nonuniversal, geometry-dependent results.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2019

D1-D5-P superstrata in 5 and 6 dimensions: separable wave equations and prepotentials

We construct the most general single-mode superstrata in 5 dimensions with ambipolar, two centered Gibbons Hawking bases, via dimensional reduction of superstrata in 6 dimensions. Previously, asymptotically AdS 3 × $\mathbb{S}$ 2 5-dimensional superstrata have been produced, giving microstate geometries of black strings in 5 dimensions. Our construction produces asymptotically AdS 2 × $\mathbb{S}$ 3 geometries as well, the first instances of superstrata describing the microstate geometries of black holes in 5 dimensions. New examples of superstrata with separable massless wave equations in both 5 and 6 dimensions are uncovered. A $\mathbb{Z}$ 2 symmetry which identifies distinct 6-dimensional superstrata when reduced to 5 dimensions is found. Finally we use the mathematical structure of the underlying hyper-Kähler bases to produce prepotentials for the superstrata fluxes in 5 dimensions and uplift them to apply in 6 dimensions as well.l.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Deep learning for characterizing the self-assembly of three-dimensional colloidal systems

Creating a systematic framework to characterize the structural states of colloidal self-assembly systems is crucial for unraveling the fundamental understanding of these systems’ stochastic and non-linear behavior. The most accurate characterization methods create high-dimensional neighborhood graphs that may not provide useful information about structures unless these are well-defined reference crystalline structures. Dimensionality reduction methods are thus required to translate the neighborhood graphs into a low-dimensional space that can be easily interpreted and used to characterize non-reference structures. We investigate a framework for colloidal system state characterization that employs deep learning methods to reduce the dimensionality of neighborhood graphs. The framework next uses agglomerative hierarchical clustering techniques to partition the low-dimensional space and assign physically meaningful classifications to the resulting partitions. In this work, we first demonstrate the proposed colloidal self-assembly state characterization framework on a three-dimensional in silico system of 500 multi-flavored colloids that self-assemble under isothermal conditions. We next investigate the generalizability of the characterization framework by applying the framework to several independent self-assembly trajectories, including a three-dimensional in silico system of 2052 colloidal particles that undergo evaporation-induced self-assembly.

36 MATERIALS SCIENCE↗
DOE OSTI2025

A Class of Sparse Johnson–Lindenstrauss Transforms and Analysis of their Extreme Singular Values

The Johnson–Lindenstrauss (JL) lemma is a powerful tool for dimensionality reduction in modern algorithm design. The lemma states that any set of high-dimensional points in a Euclidean space can be projected into lower dimensions while approximately preserving pairwise Euclidean distances. Random matrices satisfying this lemma are called JL transforms (JLTs). Inspired by existing $s$-hashing JLTs with exactly $s$ nonzero elements on each column, the present work introduces an ensemble of sparse matrices encompassing so-called $s$-hashing-like matrices whose expected number of nonzero elements on each column is $s$. The independence of the sub-Gaussian entries of these matrices and the knowledge of their exact distribution play an important role in their analyses. Using properties of independent sub-Gaussian random variables, these matrices are demonstrated to be JLTs, and their smallest nontrivial singular values and largest singular values are estimated nonasymptotically using a technique from geometric functional analysis. As the dimensions of the matrix grow to infinity, these singular values are proved to converge almost surely to fixed quantities (by using the universal Bai–Yin law) and in distribution to the Gaussian orthogonal ensemble Tracy–Widom law after proper rescalings. Understanding the behaviors of extreme singular values is important in general because they are often used to define a measure of stability of matrix algorithms. For example, JLTs were recently used in derivative-free optimization algorithmic frameworks to select random subspaces in which are constructed random models or poll directions to achieve scalability, and hence estimating their smallest singular value in particular helps determine the dimension of these subspaces.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Pions as gluons in higher dimensions

We derive the nonlinear sigma model as a peculiar dimensional reduction of Yang-Mills theory. In this framework, pions are reformulated as higher-dimensional gluons arranged in a kinematic configuration that only probes cubic interactions. This procedure yields a purely cubic action for the nonlinear sigma model that exhibits a symmetry enforcing color-kinematics duality. Remarkably, the associated kinematic algebra originates directly from the Poincaré algebra in higher dimensions. Applying the same construction to gravity yields a new quartic action for Born-Infeld theory and, applied once more, a cubic action for the special Galileon theory. Since the nonlinear sigma model and special Galileon are subtly encoded in the cubic sectors of Yang-Mills theory and gravity, respectively, their double copy relationship is automatic.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2019

Visual Analytics for Deep Embeddings of Large Scale Molecular Dynamics Simulations

Molecular Dynamics (MD) simulation have been emerging as an excellent candidate for understanding complex atomic and molecular scale mechanism of bio-molecules that control essential bio-physical phenomenon in a living organism. But this MD technique produces large-size and long-timescale data that are inherently high-dimensional and occupies many terabytes of data. Processing this immense amount of data in a meaningful way is becoming increasingly difficult. Therefore, specific dimensionality reduction algorithm using deep learning technique has been employed here to embed the high-dimensional data in a lower-dimension latent space that still preserves the inherent molecular characteristics i.e. retains biologically meaningful information. Subsequently, the results of the embedding models are visualized for model evaluation and analysis of the extracted underlying features. However, most of the existing visualizations for embeddings have limitations in evaluating the embedding models and understanding the complex simulation data. We propose an interactive visual analytics system for embeddings of MD simulations to not only evaluate and explain an embedding model but also analyze various characteristics of the simulations. Our system enables exploration and discovery of meaningful and semantic embedding results and supports the understanding and evaluation of results by the quantitatively described features of the MD simulations (even without specific labels).

Chae, Junghoon↗
DOE OSTI2023

Comparing storm resolving models and climates via unsupervised machine learning

Global storm-resolving models (GSRMs) have gained widespread interest because of the unprecedented detail with which they resolve the global climate. However, it remains difficult to quantify objective differences in how GSRMs resolve complex atmospheric formations. This lack of comprehensive tools for comparing model similarities is a problem in many disparate fields that involve simulation tools for complex data. To address this challenge we develop methods to estimate distributional distances based on both nonlinear dimensionality reduction and vector quantization. Our approach automatically learns physically meaningful notions of similarity from low-dimensional latent data representations that the different models produce. This enables an intercomparison of nine GSRMs based on their high-dimensional simulation data (2D vertical velocity snapshots) and reveals that only six are similar in their representation of atmospheric dynamics. Furthermore, we uncover signatures of the convective response to global warming in a fully unsupervised way. Our study provides a path toward evaluating future high-resolution simulation data more objectively.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Uncertainty propagation and sensitivity analysis for constrained optimization of nuclear waste vitrification

Abstract The vitrification of high‐level waste (HLW) by heating a mixture of glass‐forming chemicals (GFCs) with the waste can be improved using a constrained optimization problem. This study explores how different uncertainty propagation (UP) methods implemented with the optimization process can affect the glass formulation of nuclear waste glasses. UP is the effort of propagating uncertain inputs through a system to understand and quantify output distributions. Uncertainty intervals are crafted from output distributions to inform the optimization algorithm. UP is often implemented with Monte Carlo (MC) sampling for large nonlinear systems, which can be difficult to implement within a constrained optimization algorithm that requires derivative information. Other UP methods often used for optimization under uncertainty (OUU) can be designed to work within an established constrained optimization framework. Methods of UP are evaluated in this study including iterative sampling approaches, first‐order approximations, and surrogate modeling with machine learning (ML). A method of dimensional reduction based on global sensitivity analysis is introduced to support the UP methods for the large dimensionality of the problem. Analytical UP methods able to achieve similar optimums 10 times faster than the baseline MC approach, and produce 93.9% similar output distributions are reported.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2019

Unitarization from geometry

We study the perturbative unitarity of scattering amplitudes in general dimensional reductions of Yang–Mills theories and general relativity on closed internal manifolds. For the tree amplitudes of the dimensionally reduced theory to have the expected high-energy behavior of the higher-dimensional theory, the masses and cubic couplings of the Kaluza–Klein states must satisfy certain sum rules that ensure there are nontrivial cancellations between Feynman diagrams. These sum rules give constraints on the spectra and triple overlap integrals of eigenfunctions of Laplacian operators on the internal manifold and can be proven directly using Hodge and eigenfunction decompositions. One consequence of these constraints is that there is an upper bound on the ratio of consecutive eigenvalues of the scalar Laplacian on closed Ricci-flat manifolds with special holonomy. This gives a sharp bound on the allowed gaps between Kaluza–Klein excitations of the graviton that also applies to Calabi–Yau compactifications of string theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Cost function for low-dimensional manifold topology assessment

Abstract In reduced-order modeling, complex systems that exhibit high state-space dimensionality are described and evolved using a small number of parameters. These parameters can be obtained in a data-driven way, where a high-dimensional dataset is projected onto a lower-dimensional basis. A complex system is then restricted to states on a low-dimensional manifold where it can be efficiently modeled. While this approach brings computational benefits, obtaining a good quality of the manifold topology becomes a crucial aspect when models, such as nonlinear regression, are built on top of the manifold. Here, we present a quantitative metric for characterizing manifold topologies. Our metric pays attention to non-uniqueness and spatial gradients in physical quantities of interest, and can be applied to manifolds of arbitrary dimensionality. Using the metric as a cost function in optimization algorithms, we show that optimized low-dimensional projections can be found. We delineate a few applications of the cost function to datasets representing argon plasma, reacting flows and atmospheric pollutant dispersion. We demonstrate how the cost function can assess various dimensionality reduction and manifold learning techniques as well as data preprocessing strategies in their capacity to yield quality low-dimensional projections. We show that improved manifold topologies can facilitate building nonlinear regression models.

42 ENGINEERING↗
DOE OSTI2023

Online data-driven changepoint detection for high-dimensional dynamical systems

In this study, the detection of anomalies or transitions in complex dynamical systems is of critical importance to various applications. In this study, we propose the use of machine learning to detect changepoints for high-dimensional dynamical systems. Here, changepoints indicate instances in time when the underlying dynamical system has a fundamentally different characteristic—which may be due to a change in the model parameters or due to intermittent phenomena arising from the same model. We propose two complementary approaches to achieve this, with the first devised using arguments from probabilistic unsupervised learning and the latter devised using supervised deep learning. To accelerate the deployment of transition detection algorithms in high-dimensional dynamical systems, we introduce dimensionality reduction techniques. Our experiments demonstrate that transitions can be detected efficiently, in real-time, for the two-dimensional forced Kolmogorov flow and the Rössler dynamical system, which are characterized by anomalous regimes in phase space where dynamics are perturbed off the attractor at potentially uneven intervals. Finally, we also demonstrate how variations in the frequency of detected changepoints may be utilized to detect a significant modification to the underlying model parameters by utilizing the Lorenz-63 dynamical system.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Double copy for massive scalar field theories

We explore extensions of the double copy to massive theories and find a new cubic theory with a local double copy. We consider the nonlinear sigma model and the special galileon theory, massless versions of which are known to be related through the double copy. We show that by performing a Kaluza-Klein reduction of these theories from five dimensions down to four, a double copy relation exists between the resulting massive four-dimensional scalar field theories. This requires the vanishing contribution of new galileon terms arising in high dimensions. We further explore if other interactions that do not arise from a dimensional reduction of the nonlinear sigma model could be double copied and find a new cubic interaction which satisfies the BCJ relations up to 5-point amplitudes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Categorical Dimensions of Human Odor Descriptor Space Revealed by Non-Negative Matrix Factorization

In contrast to most other sensory modalities, the basic perceptual dimensions of olfaction remain unclear. Here, we use nonnegative matrix factorization (NMF) – a dimensionality reduction technique – to uncover structure in a panel of odor profiles, with each odor defined as a point in multi-dimensional descriptor space. The properties of NMF are favorable for the analysis of such lexical and perceptual data, and lead to a high-dimensional account of odor space. We further provide evidence that odor dimensions apply categorically. That is, odor space is not occupied homogenously, but rather in a discrete and intrinsically clustered manner. We discuss the potential implications of these results for the neural coding of odors, as well as for developing classifiers on larger datasets that may be useful for predicting perceptual qualities from chemical structures.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2013

Categorical dimensions of human odor descriptor space revealed by non-negative matrix factorization

In contrast to most other sensory modalities, the basic perceptual dimensions of olfaction remain un- clear. Here, we use non-negative matrix factorization (NMF) - a dimensionality reduction technique - to uncover structure in a panel of odor profiles, with each odor defined as a point in multi-dimensional descriptor space. The properties of NMF are favorable for the analysis of such lexical and perceptual data, and lead to a high-dimensional account of odor space. We further provide evidence that odor di- mensions apply categorically. That is, odor space is not occupied homogenously, but rather in a discrete and intrinsically clustered manner. We discuss the potential implications of these results for the neural coding of odors, as well as for developing classifiers on larger datasets that may be useful for predicting perceptual qualities from chemical structures.

Chennubhotla, Chakra↗