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Results for “dimensionality reduction”

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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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Nonintrusive projection-based reduced order modeling using stable learned differential operators

Nonintrusive projection-based reduced order models (ROMs) are essential for dynamics prediction in multi-query applications where underlying governing equations are known but the access to the source of the underlying full order model (FOM) is unavailable; that is, FOM is a glass-box. This article proposes a learn-then-project approach for nonintrusive model reduction. In the first step of this approach, high-dimensional stable sparse learned differential operators (S-LDOs) are determined using the generated data. In the second step, the ordinary differential equations, comprising these S-LDOs, are used with suitable dimensionality reduction and low-dimensional subspace projection methods to provide equations for the evolution of reduced states. This approach allows easy integration into the existing intrusive ROM framework to enable nonintrusive model reduction while allowing the use of Petrov–Galerkin projections. The applicability of the proposed approach is demonstrated for Galerkin and LSPG projection-based ROMs through four numerical experiments: 1-D scalar advection, 1-D Burgers, 2-D scalar advection and 1-D scalar advection–diffusion–reaction equations. In conclusion, the results indicate that the proposed nonintrusive ROM strategy provides accurate and stable dynamics prediction.

42 ENGINEERING↗
DOE OSTI2025

Enhancing Interpretability in Generative Modeling: Statistically Disentangled Latent Spaces Guided by Generative Factors in Scientific Datasets

This study addresses the challenge of statistically extracting generative factors from complex, high-dimensional datasets in unsupervised or semi-supervised settings. We investigate encoder-decoder-based generative models for nonlinear dimensionality reduction, focusing on disentangling low-dimensional latent variables corresponding to independent physical factors. Introducing Aux-VAE, a novel architecture within the classical Variational Autoencoder framework, we achieve disentanglement with minimal modifications to the standard VAE loss function by leveraging prior statistical knowledge through auxiliary variables. These variables guide the shaping of the latent space by aligning latent factors with learned auxiliary variables. We validate the efficacy of Aux-VAE through comparative assessments on multiple datasets, including astronomical simulations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

An interactive machine learning platform for analyzing multi-particle coincidence data from cold target recoil ion momentum spectroscopy

We present SCULPT (Supervised Clustering and Uncovering Latent Patterns with Training), a comprehensive software platform for analyzing tabulated high-dimensional multi-particle coincidence data from Cold Target Recoil Ion Momentum Spectroscopy (COLTRIMS) experiments. The software addresses critical challenges in modern momentum spectroscopy by integrating advanced machine learning techniques with physics-informed analysis in an interactive web-based environment. SCULPT implements uniform manifold approximation and projection for non-linear dimensionality reduction to reveal correlations in high-dimensional data. We also discuss potential extensions to deep autoencoders for feature learning and genetic programming for automated discovery of physically meaningful observables. A novel adaptive confidence scoring system provides quantitative reliability assessments by evaluating user-selected clustering quality metrics with predefined weights that reflect each metric’s robustness. The platform features configurable molecular profiles for different experimental systems, interactive visualization with selection tools, and comprehensive data filtering capabilities. Utilizing a subset of SCULPT’s capabilities, we analyze photo-double-ionization data measured using the COLTRIMS method for three-body dissociation of the D 2 O molecule, revealing distinct fragmentation channels and their correlations with physics parameters. The software’s modular architecture and web-based implementation make it accessible to the broader atomic and molecular physics community, significantly reducing the time required for complex multi-dimensional analyses. This opens the door to finding and isolating rare events exhibiting non-linear correlations on the fly during experimental measurements, which can help steer exploration and improve the efficiency of experiments.

Artificial neural networks↗
DOE OSTI2024

Lie-algebraic Kähler sigma models with U(1) isotropy

We discuss various questions that emerge in connection with the Lie-algebraic deformation of the sigma model in two dimensions. First, we supersymmetrize the original model endowing it with the minimal and extended supersymmetries. Then we derive the general hypercurrent anomaly in both cases. In the latter case this anomaly is one-loop but is somewhat different from the standard expressions one can find in the literature because the target manifold is nonsymmetric. We also show how to introduce the twisted masses and the term, and study the Bogomol’nyi–Prasad–Sommerfield equation for instantons, in particular the value of the topological charge. Then we demonstrate that the second loop in the function of the nonsupersymmetric Lie-algebraic sigma model is due to an infrared effect. To this end we use a supersymmetric regularization. We also conjecture that the above statement is valid for higher loops too, similar to the parallel phenomenon in four-dimensional super-Yang-Mills. In the second part of the paper we develop a special dimensional reduction—namely, starting from the two-dimensional Lie-algebraic model we arrive at a quasi-exactly solvable quantum-mechanical problem of the Lamé type.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

MOOSE ProbML: Parallelized probabilistic machine learning and uncertainty quantification for computational energy applications

Here, this paper presents the development and demonstration of massively parallel probabilistic machine learning (ML) and uncertainty quantification (UQ) capabilities within the Multiphysics Object-Oriented Simulation Environment (MOOSE), an open-source computational platform for parallel finite element and finite volume analyses. In addressing the computational expense and uncertainties inherent in complex multiphysics simulations, this paper integrates Gaussian process (GP) variants, active learning, Bayesian inverse UQ, adaptive forward UQ, Bayesian optimization, evolutionary optimization, and Markov chain Monte Carlo (MCMC) within MOOSE. It also elaborates on the interaction among key MOOSE systems — Sampler, MultiApp, Reporter, and Surrogate — in enabling these capabilities. The modularity offered by these systems enables development of a multitude of probabilistic ML and UQ algorithms in MOOSE. Example code demonstrations include parallel active learning and parallel Bayesian inference via active learning. The impact of these developments is illustrated through five applications relevant to computational energy applications: UQ of nuclear fuel fission product release, using parallel active learning Bayesian inference; very rare events analysis in nuclear microreactors using active learning; advanced manufacturing process modeling using multi-output GPs (MOGPs) and dimensionality reduction; fluid flow using deep GPs (DGPs); and tritium transport model parameter optimization for fusion energy, using batch Bayesian optimization. These capabilities are part of the MOOSE framework.

97 - MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Feedback Controllability Components Analysis (FCCA) v1.0

FCCA is a linear dimensionality reduction method that find subspaces of high-dimensional time-series data that are most feedback controllable. The key innovation is to formulate an objective function that quantifies the joint cost of state reconstruction and state regulation that can be evaluated from purely observational data. To do this, it leverages the duality between controllability and observability. We provide analytic results demonstrating the validity of the cost function. We evaluated this method in both synthetic and real neural data (from multiple organisms and brain areas).

Kumar, Ankit↗
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 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 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 OSTI2025

Experimental Realization of One-Dimensional Helium

Abstract As the spatial dimension is lowered, locally stabilizing interactions are reduced, leading to the emergence of strongly fluctuating phases of matter without classical analogues. Realizing 1D platforms has been elusive, due to their inherent lack of stability, with a few notable exceptions such as spin chains and ultracold low-density gasses. The inability of such systems to exhibit long range order is essential to their universal description in terms of the Tomonaga-Luttinger liquid theory. Here we report on the experimental observation of a one-dimensional quantum liquid of $$^4$$ 4 He using nanoengineering to confine it within a porous material preplated with a noble gas to enhance dimensional reduction. The resulting excitations of the confined $$^4$$ 4 He, confirmed by neutron scattering, are qualitatively different than three- and two-dimensional superfluid helium, and consistent with Quantum Monte Carlo calculations. The results can be analyzed in terms of a mobile impurity in an otherwise linear Luttinger liquid allowing for the extraction of the microscopic parameters describing the emergent quantum liquid.

Sokol, Paul E.↗
DOE OSTI2025

In Situ Data Analysis Through Physics-informed Tensor Decompositions (LDRD Final Report)

We introduce a new low-dimensional model of high-dimensional numerical simulation data based on low-rank tensor decompositions. Our new model aims to minimize differences between the model data and simulation data as well as functions of the model data and functions of the simulation data. This novel approach to dimensionality reduction of simulation data provides a means of directly incorporating quantities of interests and invariants associated with conservation principles associated with the simulation data into the low-dimensional model, thus enabling more accurate analysis of the simulation without requiring access to the full set of high-dimensional data. Computational results of applying this approach to two standard low-rank tensor decompositions of data arising from simulation of combustion and plasma physics are presented.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Blueprints for Training Information Bottlenecks for Collider Analyses

Dimensionality reduction is a crucial aspect of data analysis in high energy physics, even if accompanied by information loss. Several methods, including histogram- and kernel-based analyses, are only computationally feasible for low-dimensional data. Furthermore, simulation models used in HEP can often only be validated for low-dimensional data. We provide several blueprints for using machine learning to create low-dimensional data representations (continuous event variables and discrete classification labels) for use in signal discovery and parameter estimation tasks. We also describe how to design the learned representation to facilitate a) searches with unknown model parameters and b) validation of simulation models in data control regions.

43 PARTICLE ACCELERATORS↗
DOE OSTI2026

A two-stage optical fusion framework for wildfire severity mapping across the conterminous United States

Accurate wildfire severity mapping (WSM) is essential for post-fire recovery planning, erosion risk assessment, ecosystem monitoring, and disaster risk reduction. Although Landsat and Sentinel optical imagery have been widely used for burn severity assessment, the added value of fusing multiple optical sensors has not been sufficiently quantified across diverse fire events, particularly since the launch of Landsat-9. This study evaluates whether multisensor optical fusion improves wildfire severity mapping relative to single-sensor baselines using Sentinel-2, Landsat-8, and Landsat-9 imagery across 40 wildfire events in the conterminous United States. We tested a two-stage fusion framework that combines feature-level fusion with pixel-level dimensionality reduction. First, feature-level fused datasets were created through early fusion by combining standardized post-fire bands from each sensor into a single predictor stack. Both raw reflectance bands and pairwise spectral transforms were retained to capture within- and cross-sensor spectral interactions. Second, Linear Discriminant Analysis was applied to both single-sensor and fused datasets to produce comparable low-dimensional feature spaces. Six machine-learning classifiers were then used to benchmark model performance with repeated spatially buffered train–test splits. Results show that Landsat-9 was the strongest single-sensor baseline. Among the fusion strategies, Sentinel-2 + Landsat-9 produced the most consistent improvement and reduced performance variability. Landscape-condition analysis further showed that this fusion was most beneficial in shrubland-dominated and high-terrain fires, where it achieved the highest overall mean accuracy and the fewest failures. In contrast, its benefits were less reliable in evergreen forests, mixed vegetation, and low- to moderate-elevation terrain. In operational settings, the Sentinel-2 + Landsat-9 configuration offers a practical solution for post-fire recovery planning, erosion-risk assessment, watershed management, and ecological monitoring when field observations are available and timely satellite-based information is needed.

Landsat↗
DOE OSTI2024

Layered and Low-Dimensional Lead, Silver, and Bismuth Halide Perovskites Directed by Halogen-Substituted Spacer Cations

Hybrid organic–inorganic metal halides provide a diverse parameter space in which the optoelectronic properties can be tuned through the composition. The compositional tunability extends to the metal site, which can be expanded from single valent metals (e.g., Pb 2+ ) to multivalent metals (e.g., Ag + and Bi 3+ ), and the dimension (2D, 1D, or 0D). However, a deeper understanding of how the organic cations template these metal halide structures is needed. Here, we synthesize and study the structures of a series of new layered and low-dimensional metal (Pb, Ag, and Bi) halides templated by the halogenated aryl spacer cations 2-chlorobenzylammonium (2ClBZ) and 3-chloro-2-fluorobenzylammonium (3Cl2FBZ). We report new lead perovskites, (3Cl2FBZ) 2 PbBr 4 , (2ClBZ) 3 PbI 5 , and (3Cl2FBZ) 2 PbI 4 , and compare them to their silver and/or bismuth analogs (2ClBZ) 4 AgBiBr 8 , (3Cl2FBZ) 4 AgBiBr 8 , (2ClBZ) 3 Bi 2 I 9 , and (3Cl2FBZ) 4 Bi 2 I 10 . In all structures, the halogen-substituted cations result in 2D or “pseudo-2D” layering, but the different halogen substituents introduce different distortions (tilting, octahedral distortion) and dimensional reduction to 1D or 0D depending on the metal and halide compositions. Optical absorption measurements reveal the bandgaps are tunable through metal sites, dimension, and cations to different extents. Furthermore, the 1D (3Cl2FBZ) 4 Bi 2 I 10 crystallizes in the noncentrosymmetric space group Cmc2 1 and exhibits second-harmonic generation (SHG). Furthermore, the organic–inorganic interactions and resultant structural distortions examined here provide insights toward the engineering of noncentrosymmetry and dimensional control in hybrid metal halide perovskites.

Cations↗
DOE OSTI2024

Co-orchestration of multiple instruments to uncover structure–property relationships in combinatorial libraries

The rapid growth of automated and autonomous instrumentation brings forth opportunities for the co-orchestration of multimodal tools that are equipped with multiple sequential detection methods or several characterization techniques to explore identical samples. This is exemplified by combinatorial libraries that can be explored in multiple locations via multiple tools simultaneously or downstream characterization in automated synthesis systems. In co-orchestration approaches, information gained in one modality should accelerate the discovery of other modalities. Correspondingly, an orchestrating agent should select the measurement modality based on the anticipated knowledge gain and measurement cost. Herein, we propose and implement a co-orchestration approach for conducting measurements with complex observables, such as spectra or images. The method relies on combining dimensionality reduction by variational autoencoders with representation learning for control over the latent space structure and integration into an iterative workflow via multi-task Gaussian Processes (GPs). This approach further allows for the native incorporation of the system's physics via a probabilistic model as a mean function of the GPs. We illustrate this method for different modes of piezoresponse force microscopy and micro-Raman spectroscopy on a combinatorial Sm-BiFeO3 library. However, the proposed framework is general and can be extended to multiple measurement modalities and arbitrary dimensionality of the measured signals.

47 OTHER INSTRUMENTATION↗
DOE OSTI2024

Machine-learned closure of URANS for stably stratified turbulence: connecting physical timescales & data hyperparameters of deep time-series models

Stably stratified turbulence (SST), a model that is representative of the turbulence found in the oceans and atmosphere, is strongly affected by fine balances between forces and becomes more anisotropic in time for decaying scenarios. Moreover, there is a limited understanding of the physical phenomena described by some of the terms in the Unsteady Reynolds-Averaged Navier–Stokes (URANS) equations—used to numerically simulate approximate solutions for such turbulent flows. Rather than attempting to model each term in URANS separately, it is attractive to explore the capability of machine learning (ML) to model groups of terms, i.e. to directly model the force balances. We develop deep time-series ML for closure modeling of the URANS equations applied to SST. We consider decaying SST which are homogeneous and stably stratified by a uniform density gradient, enabling dimensionality reduction. We consider two time-series ML models: long short-term memory and neural ordinary differential equation. Both models perform accurately and are numerically stable in a posteriori (online) tests. Furthermore, we explore the data requirements of the time-series ML models by extracting physically relevant timescales of the complex system. We find that the ratio of the timescales of the minimum information required by the ML models to accurately capture the dynamics of the SST corresponds to the Reynolds number of the flow. The current framework provides the backbone to explore the capability of such models to capture the dynamics of high-dimensional complex dynamical system like SST flows.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Understanding latent timescales in neural ordinary differential equation models of advection-dominated dynamical systems

The neural ordinary differential equation (ODE) framework has shown considerable promise in recent years in developing highly accelerated surrogate models for complex physical systems characterized by partial differential equations (PDEs). For PDE-based systems, state-of-the-art neural ODE strategies leverage a two-step procedure to achieve this acceleration: a nonlinear dimensionality reduction step provided by an autoencoder, and a time integration step provided by a neural-network based model for the resultant latent space dynamics (the neural ODE). This work explores the applicability of such autoencoder-based neural ODE strategies for PDEs in which advection terms play a critical role. More specifically, alongside predictive demonstrations, physical insight into the sources of model acceleration (i.e., how the neural ODE achieves its acceleration) is the scope of the current study. Such investigations are performed by quantifying the effects of both autoencoder and neural ODE components on latent system time-scales using eigenvalue analysis of dynamical system Jacobians. To this end, the sensitivity of various critical training parameters – de-coupled versus end-to-end training, latent space dimensionality, and the role of training trajectory length, for example – to both model accuracy and the discovered latent system timescales is quantified. Furthermore, this work specifically uncovers the key role played by the training trajectory length (the number of rollout steps in the loss function during training) on the latent system timescales: larger trajectory lengths correlate with an increase in limiting neural ODE time-scales, and optimal neural ODEs are found to recover the largest time-scales of the full-order (ground-truth) system. Demonstrations are performed across fundamentally different unsteady fluid dynamics configurations influenced by advection: (1) the Kuramoto–Sivashinsky equations (2) Hydrogen-Air channel detonations (the compressible reacting Navier–Stokes equations with detailed chemistry), and (3) 2D Atmospheric flow.

Advection-dominated dynamical systems↗
DOE OSTI2025

Generative learning for slow manifolds and bifurcation diagrams

In dynamical systems characterized by separation of time scales, the approximation of so called “slow manifolds”, on which the long term dynamics lie, is a useful step for model reduction. Initializing on such slow manifolds is a useful step in modeling, since it circumvents fast transients, and is crucial in multiscale algorithms (like the equation-free approach) alternating between fine scale (fast) and coarser scale (slow) simulations. In a similar spirit, when one studies the infinite time dynamics of systems depending on parameters, the system attractors (e.g., its steady states) lie on bifurcation diagrams (curves for one-parameter continuation, and more generally, on manifolds in state parameter space. Sampling these manifolds gives us representative attractors (here, steady states of ODEs or PDEs) at different parameter values. Algorithms for the systematic construction of these manifolds (slow manifolds, bifurcation diagrams) are required parts of the “traditional” numerical nonlinear dynamics toolkit. In more recent years, as the field of Machine Learning develops, conditional score-based generative models (cSGMs) have been demonstrated to exhibit remarkable capabilities in generating plausible data from target distributions that are conditioned on some given label. It is tempting to exploit such generative models to produce samples of data distributions (points on a slow manifold, steady states on a bifurcation surface) conditioned on (consistent with) some quantity of interest (QoI, observable). In this work, we present a framework for using cSGMs to quickly (a) initialize on a low-dimensional (reduced-order) slow manifold of a multi-time-scale system consistent with desired value(s) of a QoI (a “label”) on the manifold, and (b) approximate steady states in a bifurcation diagram consistent with a (new, out-of-sample) parameter value. This conditional sampling can help uncover the geometry of the reduced slow-manifold and/or approximately “fill in” missing segments of steady states in a bifurcation diagram. Finally, the quantity of interest, which determines how the sampling is conditioned, is either known a priori or identified using manifold learning-based dimensionality reduction techniques applied to the training data.

Dynamical systems↗