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Results for “differentiable manifold”

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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68 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Time-series forecasting using manifold learning, radial basis function interpolation, and geometric harmonics

We address a three-tier numerical framework based on nonlinear manifold learning for the forecasting of high-dimensional time series, relaxing the “curse of dimensionality” related to the training phase of surrogate/machine learning models. At the first step, we embed the high-dimensional time series into a reduced low-dimensional space using nonlinear manifold learning (local linear embedding and parsimonious diffusion maps). Then, we construct reduced-order surrogate models on the manifold (here, for our illustrations, we used multivariate autoregressive and Gaussian process regression models) to forecast the embedded dynamics. Finally, we solve the pre-image problem, thus lifting the embedded time series back to the original high-dimensional space using radial basis function interpolation and geometric harmonics. The proposed numerical data-driven scheme can also be applied as a reduced-order model procedure for the numerical solution/propagation of the (transient) dynamics of partial differential equations (PDEs). In conclusion, we assess the performance of the proposed scheme via three different families of problems: (a) the forecasting of synthetic time series generated by three simplistic linear and weakly nonlinear stochastic models resembling electroencephalography signals, (b) the prediction/propagation of the solution profiles of a linear parabolic PDE and the Brusselator model (a set of two nonlinear parabolic PDEs), and (c) the forecasting of a real-world data set containing daily time series of ten key foreign exchange rates spanning the time period 3 September 2001–29 October 2020.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Data-driven Whitney forms for structure-preserving control volume analysis

Control volume analysis models physics via the exchange of generalized fluxes between subdomains. Here, we introduce a scientific machine learning framework adopting a partition of unity architecture to identify physically-relevant control volumes, with generalized fluxes between subdomains encoded via Whitney forms. The approach provides a differentiable parameterization of geometry which may be trained in an end-to-end fashion to extract reduced models from full field data while exactly preserving physics. The architecture admits a data-driven finite element exterior calculus allowing discovery of mixed finite element spaces with closed form quadrature rules. An equivalence between Whitney forms and graph networks reveals that the geometric problem of control volume learning is equivalent to an unsupervised graph discovery problem. The framework is developed for manifolds in arbitrary dimension, with examples provided for H(div) problems in $\mathbb{R}$ establishing convergence and structure preservation properties. Finally, we consider a lithium-ion battery problem where we discover a reduced finite element space encoding transport pathways from high-fidelity microstructure resolved simulations. The approach reduces the 5.89M finite element simulation to 136 elements while reproducing pressure to under 0.1% error and preserving conservation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Decorated TQFTs and their Hilbert spaces

We discuss topological quantum field theories that compute topological invariants which depend on additional structures (or decorations) on three-manifolds. The q-series invariant $\hat{Z}$(q) proposed by Gukov, Pei, Putrov, and Vafa is an example of such an invariant. We describe how to obtain these decorated invariants by cutting and gluing and make a proposal for Hilbert spaces that are assigned to two-dimensional surfaces in the $\hat{Z}$-TQFT.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Short-Wave Infrared Upconverting Nanoparticles

Optical technologies enable real-time, noninvasive analysis of complex systems but are limited to discrete regions of the optical spectrum. While wavelengths in the short-wave infrared (SWIR) window (typically, 1700-3000 nm) should enable deep subsurface penetration and reduced photodamage, there are few luminescent probes that can be excited in this region. Here, we report the discovery of lanthanide-based upconverting nanoparticles (UCNPs) that efficiently convert 1740 or 1950 nm excitation to wavelengths compatible with conventional silicon detectors. Screening of Ln3+ ion combinations by differential rate equation modeling identifies Ho3+/Tm3+ or Tm3+ dopants with strong visible or NIR-I emission following SWIR excitation. Experimental upconverted photoluminescence excitation (U-PLE) spectra find that 10% Tm3+-doped NaYF4 core/shell UCNPs have the strongest 800 nm emission from SWIR wavelengths, while UCNPs with an added 2% or 10% Ho3+ show the strongest red emission when excited at 1740 or 1950 nm. Mechanistic modeling shows that addition of a low percentage of Ho3+ to Tm3+-doped UCNPs shifts their emission from 800 to 652 nm by acting as a hub of efficient SWIR energy acceptance and redistribution up to visible emission manifolds. Parallel experimental and computational analysis shows rate equation models are able to predict compositions for specific wavelengths of both excitation and emission. These SWIR-responsive probes open a new IR bioimaging window, and are responsive at wavelengths important for vision technologies.

Qi, Xiao↗
DOE OSTI2022

A survey of unsupervised learning methods for high-dimensional uncertainty quantification in black-box-type problems

Constructing surrogate models for uncertainty quantification (UQ) on complex partial differential equations (PDEs) having inherently high-dimensional O(10 n ), n ≥ 2, stochastic inputs (e.g., forcing terms, boundary conditions, initial conditions) poses tremendous challenges. The “curse of dimensionality” can be addressed with suitable unsupervised learning techniques used as a pre-processing tool to encode inputs onto lower-dimensional subspaces while retaining its structural information and meaningful properties. In this work, we review and investigate thirteen dimension reduction methods including linear and nonlinear, spectral, blind source separation, convex and non-convex methods and utilize the resulting embeddings to construct a mapping to quantities of interest via polynomial chaos expansions (PCE). Here, we refer to the general proposed approach as manifold PCE (m-PCE), where manifold corresponds to the latent space resulting from any of the studied dimension reduction methods. To investigate the capabilities and limitations of these methods we conduct numerical tests for three physics-based systems (treated as black-boxes) having high-dimensional stochastic inputs of varying complexity modeled as both Gaussian and non-Gaussian random fields to investigate the effect of the intrinsic dimensionality of input data. We demonstrate both the advantages and limitations of the unsupervised learning methods and we conclude that a suitable m-PCE model provides a cost-effective approach compared to alternative algorithms proposed in the literature, including recently proposed expensive deep neural network-based surrogates and can be readily applied for high-dimensional UQ in stochastic PDEs.

42 ENGINEERING↗
DOE OSTI2025

Inverse Trans Influence and Uranium-Arene σ-Bonding Drive Molecular Geometry: Ligand Modification from Hard to Soft Flips the Oxide from Axial to Equatorial

A rare example of an equatorially bound terminal uranium(V) oxo complex in a chelating sulfur-based ligand environment, namely [(mes( Me,Ad ArS) 3 )U V (O eq )(THF)] (2), is presented. Octahedrally coordinated 2 is obtained by reaction of the mesitylene-anchored tris-thiophenolate-coordinated uranium(III) complex [U III ((SAr Ad,Me ) 3 mes)] (1) with the oxygen-atom transfer reagent N 2 O. The observed, equatorially bound oxo ligand in 2 is in stark contrast to its known tris-aryloxide analog, [(mes( Me,Ad ArO) 3 )U V (O ax )(THF)] (A), where the oxo ligand occupies the typically observed axial coordination site. Complexes 1 and 2 are characterized by single-crystal X-ray diffraction analyses and spectroscopic and magnetochemical methods, including 1 H NMR, UV/vis/NIR electronic absorption, as well as EPR spectroscopy and SQUID magnetometry, thus confirming the C S symmetry and the pentavalent oxidation state of 2. Encompassing quantum chemical calculations (DFT and CASPT2) on 2 and its tris-phenolate analog A, support and rationalize the structural and electronic differences. The molecular orbital pictures show that a stabilizing σ-bonding interaction arising from the U–O eq inverse trans influence (ITI) is present in 2 but missing in A. In 2, the sulfur 3p orbitals are closer in energy to the uranium 5f manifold than the arene π-system, leading to an ITI, while U–arene σ- or δ-bonding is not observed. Although the arene orbitals remain separated from the uranium 5f orbitals in A, the absence of an ITI allows the arene a 2u orbital to engage in a σ-type interaction with the metal. Thus, incorporating a tris-thiophenolate to an arene anchor introduces a new design concept in molecular f-element chemistry. This approach stabilizes an equatorially bound U(V) oxo center, contrasting with its tris-phenolate counterpart, where oxo coordination is axial. The observed geometric divergence, driven by competing ITI and U–arene interactions, not only tunes electronic structure but also leads to differentiated reactivity: only the phenolate analogs activate H 2 O, while the thiolates do not.

Hydrocarbons↗
DOE OSTI2021

4-manifolds and topological modular forms

We build a connection between topology of smooth 4-manifolds and the theory of topological modular forms by considering topologically twisted compactification of 6d (1, 0) theories on 4-manifolds with flavor symmetry backgrounds. The effective 2d theory has (0, 1) supersymmetry and, possibly, a residual flavor symmetry. The equivariant topological Witten genus of this 2d theory then produces a new invariant of the 4-manifold equipped with a principle bundle, valued in the ring of equivariant weakly holomorphic (topological) modular forms. We describe basic properties of this map and present a few simple examples. As a byproduct, we obtain some new results on ’t Hooft anomalies of 6d (1, 0) theories and a better understanding of the relation between 2d (0, 1) theories and TMF spectra.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Excerpt from Oxygen Monitor Clean Testing Report Performed in 2010

The Rosemount X-STREAM Series X2GP is a paramagnetic oxygen analyzer with a 0-25% oxygen measurement range. It claims a drift less than 2% of span (0.10% volume oxygen) per week, and a response time of less than 5 seconds (for the analyzer to report 90% of a step change). Our test equipment was set-up such that the same gas was running through each oxygen analyzer at the same time. This allowed Calibration Error, Calibration Drift, and Loss of Power Testing to be run on all monitors at the same time, eliminating any variability between the analyzers from tolerances in the gas cylinder, ambient temperature, ambient pressure, test duration, etc. An APTech pressure regulator was placed on the gas cylinder manifold and a 23 psia Paroscientific pressure transducer measured the regulator’s outlet pressure. This did not give the inlet pressure on any one analyzer but outlet pressure from the manifold before the stream was split. The APTech pressure regulator was used to keep operating conditions consistent. A DWYER rotameter was installed on each oxygen monitor’s outlet piping. With the exception of Variation of Flow Rate Testing, the rotameter was left fully open for all testing. The flow rate through each oxygen monitor was controlled by a Swagelok needle valve that was installed on each analyzer’s inlet piping. Additionally, a filter was installed in the each monitor’s inlet piping to keep particles from the measurement cells and a Swagelok ball valve was installed on each monitor’s outlet piping to isolate each monitor between tests. No pumps were installed. Each of the cylinders used was at a pressure greater than ambient room barometric pressure. This pressure differential was used to move gas through the testing equipment. The flow rate through each analyzer was controlled by the Swagelok needle valve installed on each analyzer’s inlet piping. Finally, for all tests, a Paroscientific Digiquartz Barometer was used to measure ambient room barometric pressure and a Fluke Thermo-hygrometer was used to measure ambient room temperature.

47 OTHER INSTRUMENTATION↗
DOE OSTI2024

Learning physics-based reduced-order models from data using nonlinear manifolds

Here we present a novel method for learning reduced-order models of dynamical systems using nonlinear manifolds. First, we learn the manifold by identifying nonlinear structure in the data through a general representation learning problem. The proposed approach is driven by embeddings of low-order polynomial form. A projection onto the nonlinear manifold reveals the algebraic structure of the reduced-space system that governs the problem of interest. The matrix operators of the reduced-order model are then inferred from the data using operator inference. Numerical experiments on a number of nonlinear problems demonstrate the generalizability of the methodology and the increase in accuracy that can be obtained over reduced-order modeling methods that employ a linear subspace approximation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Task-oriented machine learning surrogates for tipping points of agent-based models

We present a machine learning framework bridging manifold learning, neural networks, Gaussian processes, and Equation-Free multiscale approach, for the construction of different types of effective reduced order models from detailed agent-based simulators and the systematic multiscale numerical analysis of their emergent dynamics. The specific tasks of interest here include the detection of tipping points, and the uncertainty quantification of rare events near them. Our illustrative examples are an event-driven, stochastic financial market model describing the mimetic behavior of traders, and a compartmental stochastic epidemic model on an Erdös-Rényi network. We contrast the pros and cons of the different types of surrogate models and the effort involved in learning them. Importantly, the proposed framework reveals that, around the tipping points, the emergent dynamics of both benchmark examples can be effectively described by a one-dimensional stochastic differential equation, thus revealing the intrinsic dimensionality of the normal form of the specific type of the tipping point. This allows a significant reduction in the computational cost of the tasks of interest.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Effective field theories as Lagrange spaces

We present a formulation of scalar effective field theories in terms of the geometry of Lagrange spaces. The horizontal geometry of the Lagrange space generalizes the Riemannian geometry on the scalar field manifold, inducing a broad class of affine connections that can be used to covariantly express and simplify tree-level scattering amplitudes. Meanwhile, the vertical geometry of the Lagrange space characterizes the physical validity of the effective field theory, as a torsion component comprises strictly higher-point Wilson coefficients. Imposing analyticity, unitarity, and symmetry on the theory then constrains the signs and sizes of derivatives of the torsion component, implying that physical theories correspond to a special class of vertical geometry.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Data-driven recovery of hidden physics in reduced order modeling of fluid flows

In this article, we introduce a modular hybrid analysis and modeling (HAM) approach to account for hidden physics in reduced order modeling (ROM) of parameterized systems relevant to fluid dynamics. The hybrid ROM framework is based on using first principles to model the known physics in conjunction with utilizing the data-driven machine learning tools to model the remaining residual that is hidden in data. This framework employs proper orthogonal decomposition as a compression tool to construct orthonormal bases and Galerkin projection (GP) as a model to build the dynamical core of the system. Our proposed methodology hence compensates structural or epistemic uncertainties in models and utilizes the observed data snapshots to compute true modal coefficients spanned by these bases. The GP model is then corrected at every time step with a data-driven rectification using a long short-term memory (LSTM) neural network architecture to incorporate hidden physics. A Grassmannian manifold approach is also adopted for interpolating basis functions to unseen parametric conditions. The control parameter governing the system's behavior is thus implicitly considered through true modal coefficients as input features to the LSTM network. The effectiveness of the HAM approach is then discussed through illustrative examples that are generated synthetically to take hidden physics into account. Furthermore, our approach thus provides insights addressing a fundamental limitation of the physics-based models when the governing equations are incomplete to represent underlying physical processes.

42 ENGINEERING↗
DOE OSTI2020

Gradient-based constrained optimization using a database of linear reduced-order models

A methodology grounded in model reduction is presented for accelerating the gradient-based solution of a family of linear or nonlinear constrained optimization problems where the constraints include at least one linear Partial Differential Equation (PDE). A key component of this methodology is the construction, during an offline phase, of a database of pointwise, linear, Projection-based Reduced-Order Models (PROM)s associated with a design parameter space and the linear PDE(s). A parameter sampling procedure based on an appropriate saturation assumption is proposed to maximize the efficiency of such a database of PROMs. A real-time method is also presented for interpolating at any queried but unsampled parameter vector in the design parameter space the relevant sensitivities of a PROM. The practical feasibility, computational advantages, and performance of the proposed methodology are demonstrated for several realistic, nonlinear, aerodynamic shape optimization problems governed by linear aeroelastic constraints.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Asymptotic vacuum solution at tokamak X-point tip

In the H-mode regime of diverted tokamaks, the presence of strong pressure gradients in the pedestal gives rise to a sizable bootstrap current, together with the Ohmic and Pfirsch–Schlueter currents, close to the separatrix. For such equilibria, the presence of finite current density close to the separatrix requires the reexamination of equilibrium properties. It is almost universally assumed that the two branches of the separatrix (the stable and unstable manifolds) are straight as they cross at the X-point. However, the opposite angles of the plasma-filled segment and vacuum one cannot be equal if the current density does not vanish at the separatrix on the plasma side. We solve this difficulty by chipping off a thin layer of plasma edge so that the sharp corner of the plasma-filled segment becomes a hyperbola. Using the conformal transformation, we found that in the assumption of a hyperbolic boundary, the X point moves beyond the plasma boundary to fall in the vacuum region. An acute angle of the plasma-filled segment leads to an obtuse opposite angle of vacuum segment and vice versa. In the case of an acute angle of the plasma-filled segment, the new X point shifts inside the X point formed by the asymptotes of a hyperbolic boundary; in the case of an obtuse angle of the plasma-filled segment, the new X point shifts outside the X point formed by the asymptotes of a hyperbolic plasma boundary. Furthermore, the results are important for understanding the X point features, which affect the tokamak edge stability and transport.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗