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DOE OSTI2025

Information theory optimization of signals from small-angle scattering measurements

Small-angle X-ray scattering (SAXS) of particles in solution informs on the conformational states and assemblies of biological macromolecules (bioSAXS) outside of cryo- and solid-state conditions. In bioSAXS, the SAXS measurement under dilute conditions is resolution limited, and through an inverse Fourier transform, the measured SAXS intensities directly relate to the physical space occupied by the particles via the P (r)-distribution. Yet, this inverse transform of SAXS data has been historically cast as an ill-posed, ill-conditioned problem requiring an indirect approach. Here, we show that through the applications of matrix and information theories, the inverse transform of SAXS intensity data is a well-conditioned problem. The so-called ill-conditioning of the inverse problem is directly related to the Shannon number. By exploiting the oversampling enabled by modern detectors, a direct inverse Fourier transform of the SAXS data is possible, provided the recovered information does not exceed the Shannon number. The Shannon limit corresponds to the maximum number of significant singular values that can be recovered in a SAXS experiment, suggesting this relationship is a fundamental property of band-limited inverse integral transform problems. This correspondence reduces the complexity of the inverse problem to the Shannon limit and maximum dimension. We propose a hybrid scoring function using an information theory framework that assesses both the quality of the model-data fit as well as the quality of the recovered P (r)-distribution. The hybrid score utilizes the Akaike information criteria and Durbin-Watson statistic that considers parameter-model complexity, i.e., degrees of freedom, and the randomness of the model-data residuals. The described tests and findings extend the boundaries for bioSAXS by completing the information theory formalism initiated by Peter B. Moore to enable a quantitative measure of resolution in SAXS, robustly determine maximum dimension, and more precisely define the best parameter model appropriately representing the observed scattering data.

Rambo, Robert P. [Science and Technology Facilitie↗

DOE OSTI2020

Boosting the Performance of Plug-and-Play Priors via Denoiser Scaling

Plug-and-play priors (PnP) is an image reconstruction framework that utilizes an image denoiser as an imaging prior. Unlike traditional regularized inversion, PnP does not require the prior to be expressible in the form of a regularization function. This flexibility enables PnP algorithms to exploit the most effective image denoisers, leading to their state-of-the-art performance in various imaging tasks. However, many powerful denoisers, such as the ones based on convolutional neural networks (CNNs), do not have tunable parameters that would allow controlling their influence within PnP. To address this issue, in this paper, we introduce a scaling parameter that adjusts the magnitude of the denoiser input and output. We theoretical justify the denoiser scaling from the perspectives of proximal optimization, statistical estimation, and consensus equilibrium. Finally, we provide numerical experiments demonstrating the ability of denoiser scaling to systematically improve the performance of PnP for denoising CNN priors that do not have explicitly tunable parameters.

Boosting↗

DOE OSTI2024

Increase in the effective viscosity of polyethylene under extreme nanoconfinement

Understanding polymer transport in nanopores is crucial for optimizing heterogeneously catalyzed processes in polymer upcycling and fabricating high-performance nanocomposite films and membranes. Although confined polymer dynamics have been extensively studied, the behavior of polyethylene (PE)—the most widely used commodity polymer—in pores smaller than 20 nm remains largely unexplored. We investigate the effects of extreme nanoconfinement on PE transport using capillary rise infiltration in silica nanoparticle packings with average pore radii ranging from ~1 to ~9 nm. Using in situ ellipsometry and the Lucas–Washburn model, we discover a previously unknown inverse relationship between effective viscosity (η eff ) and average pore radius (R pore ). Additonally, we determine that PE transport under these extreme conditions is primarily governed by physical confinement, rather than pore surface chemistry. We refine an existing theory to provide a generalized formalism to describe the polymer transport dynamics over a wide range of pore radii (from 1 nm and larger). Our results offer valuable insights for optimizing catalyst supports in polymer upcycling and improving infiltration processes for nanocomposite fabrication.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Autonomous Output‐Oriented Aerosol Jet Printing Enabled by Hybrid Machine Learning

Additive manufacturing (AM) is rapidly revolutionizing modern manufacturing with recent progress in advanced printing methods and improved properties of printed materials. However, traditional AM methods are limited by their input‐oriented nature, which demands tedious trial‐and‐error tuning of printing parameters to achieve desired output properties. Here, in this work, an output‐oriented artificial intelligence‐integrated AM (AIAM) method is reported that enables an user to specify desired output properties while the printer autonomously discovers the optimal input printing parameters by integrating hybrid machine learning models and in situ measurements. Based on a predictive mapping between the input printing parameters and the output properties of interests established with <20 experiments designed by active learning, inverse design tasks are performed to intelligently generate the printing parameter settings that lead to desired outcomes using reinforcement learning. This method is demonstrated by autonomous aerosol jet printing (AJP) of conductive polymer films and achieving user‐defined electrical resistances with an ultralow error of 3.7%. The AIAM method, with its output‐oriented nature, holds the potential to significantly improve the autonomy, predictability, efficiency, and accessibility of the AM processes, which will unlock new possibilities in the autonomous and intelligent printing of a broad range of functional materials and devices.

36 MATERIALS SCIENCE↗

DOE OSTI2023

CSPlib: A performance portable parallel software toolkit for analyzing complex kinetic mechanisms

Computational singular perturbation (CSP) is a method to analyze dynamical systems. It targets the decoupling of fast and slow dynamics using an alternate linear expansion of the right-hand side of the governing equations based on eigenanalysis of the associated Jacobian matrix. This representation facilitates diagnostic analysis, detection and control of stiffness, and the development of simplified models. For this work, we have implemented CSP in a C++ open-source library CSPlib using the Kokkos parallel programming model to address portability across diverse heterogeneous computing platforms, i.e., multi/many-core CPUs and GPUs. We describe the CSPlib implementation and present its computational performance across different computing platforms using several test problems. Specifically, we test the CSPlib performance for a constant pressure ignition reactor model on different architectures, including IBM Power 9, Intel Xeon Skylake, and NVIDIA V100 GPU. The size of the chemical kinetic mechanism is varied in these tests. As expected, the Jacobian matrix evaluation, the eigensolution of the Jacobian matrix, and matrix inversion are the most expensive computational tasks. When considering the higher throughput characteristic of GPUs, GPUs performs better for small matrices with higher occupancy rate. CPUs gain more advantages from the higher performance of well-tuned and optimized linear algebra libraries such as OpenBLAS.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Manifold Learning-Based Polynomial Chaos Expansions for High-Dimensional Surrogate Models

In this work we introduce a manifold learning-based method for uncertainty quantification (UQ) in systems describing complex spatiotemporal processes. Our first objective is to identify the embedding of a set of high-dimensional data representing quantities of interest of the computational or analytical model. For this purpose, we employ Grassmannian diffusion maps, a two-step nonlinear dimension reduction technique which allows us to reduce the dimensionality of the data and identify meaningful geometric descriptions in a parsimonious and inexpensive manner. Polynomial chaos expansion is then used to construct a mapping between the stochastic input parameters and the diffusion coordinates of the reduced space. An adaptive clustering technique is proposed to identify an optimal number of clusters of points in the latent space. The similarity of points allows us to construct a number of geometric harmonic emulators which are finally utilized as a set of inexpensive pretrained models to perform an inverse map of realizations of latent features to the ambient space and thus perform accurate out-of-sample predictions. Thus, the proposed method acts as an encoder-decoder system which is able to automatically handle very high-dimensional data while simultaneously operating successfully in the small-data regime. The method is demonstrated on two benchmark problems and on a system of advection-diffusion-reaction equations which model a first-order chemical reaction between two species. In all test cases, the proposed method is able to achieve highly accurate approximations which ultimately lead to the significant acceleration of UQ tasks.

42 ENGINEERING↗

DOE OSTI2018

Adjoint-based Calibration of Plasticity Model Parameters from Digital Image Correlation Data

Parameter estimation for mechanical models of plastic deformation utilized in nuclear weapons systems is a laborious process for both experimentalists and constitutive modelers and is critical to producing meaningful numerical predictions. In this work we derive an adjoint-based optimization approach for a stabilized, large-deformation J 2 plasticity model that is considerably more computationally efficient but no less accurate than current state of the art methods. Unlike most approaches to model calibration, we drive the inversion procedure with full-field deformation data that can be experimentally measured through established digital image or volume correlation techniques. We present numerical results for two and three dimensional model problems and comment on various directions of future research.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

DOE OSTI2022

Physics constrained learning for data-driven inverse modeling from sparse observations

Deep neural networks (DNN) have been used to model nonlinear relations between physical quantities. Those DNNs are embedded in physical systems described by partial differential equations (PDE) and trained by minimizing a loss function that measures the discrepancy between predictions and observations in some chosen norm. This loss function often includes the PDE constraints as a penalty term when only sparse observations are available. As a result, the PDE is only satisfied approximately by the solution. However, the penalty term typically slows down the convergence of the optimizer for stiff problems. We present a new approach that trains the embedded DNNs while numerically satisfying the PDE constraints. We develop an algorithm that enables differentiating both explicit and implicit numerical solvers in reverse-mode automatic differentiation. This allows the gradients of the DNNs and the PDE solvers to be computed in a unified framework. We demonstrate that our approach enjoys faster convergence and better stability in relatively stiff problems compared to the penalty method. Furthermore, our approach allows for the potential to solve and accelerate a wide range of data-driven inverse modeling, where the physical constraints are described by PDEs and need to be satisfied accurately.

97 MATHEMATICS AND COMPUTING↗

NASA NTRSDate not supplied

OCO-2 Satellite-imposed Constraints on Terrestrial Biospheric CO2 Flux over South Asia

The spatiotemporal variability of terrestrial biospheric carbon dioxide (CO2) flux over South Asia is poorly understood. The inverse model “top-down” CO2 flux estimates which rely on atmospheric CO2 observational data are impeded by sparse in situ measurements over this region. The Orbiting Carbon Observatory 2 (OCO-2) provides much needed global retrievals of column-average CO2 dry-air mole fraction (XCO2) with the finest spatial and temporal resolution and highest sensitivity to surface fluxes available to-date. This study conducted global inverse model simulations as part of the second OCO-2 Multi-model Intercomparison Project assimilating version 9 of the OCO-2 XCO2 retrievals in land nadir (LN) and land glint (LG) observing modes and global in situ (IS) measurements. The four-dimensional variational assimilation system with the GEOS-Chem global chemical transport model was used to estimate CO2 fluxes from 2015 to 2018. We then assessed the spatiotemporal variability of optimized CO2 Net ecosystem Exchange (NEE) fluxes aggregated over the South Asia region. The most robust result found by assimilating OCO-2 observations was the constraints imposed on the seasonal cycle of terrestrial biospheric fluxes over South Asia. The seasonality of South Asian NEE estimated by assimilating OCO-2 or global IS data showed a larger seasonal cycle compared to the current understanding of NEE in this region (represented by the prior NEE used in the model). The satellite-in situ joint inversion (IS + LN + LG) led to land flux seasonal amplitude (absolute magnitude of the difference between peak and trough of monthly mean values over a year) of 4.0 PgC yr-1, compared to the prior model (1.5 PgC yr-1). Moreover, OCO-2 data imposed a phase shift in the seasonal cycle, resulting in a large CO2 source in April and a large uptake in September. Most of the features in the seasonal cycle imposed by OCO-2 data are in agreement with previous “top-down” studies assimilating regional aircraft observations. Nevertheless, we recommend a closer examination of the novel features highlighted by the OCO-2 column data over South Asia in future studies by conducting regional inverse modelling with denser in situ and vertically-resolved regional observations along with satellite data.

OCO-2↗

NASA NTRS1985

A methodology for designing robust multivariable nonlinear feedback control systems

This paper presents an outline of a methodology for the design of nonlinear dynamic compensators for nonlinear multivariable systems with guarantees of closed-loop stability, robustness, and performance. The method is an extension of the Linear-Quadratic-Gaussian with Loop-Transfer-Recovery (LQG/LTR) methodology for linear systems, thus hinging upon the idea of constructing an approximate nonlinear inverse operator for the plant. A major feature of the method is a unification of both the state-space and Input-Output formulations. The major results of the paper are: (1) Properties of the solution of certain optimal control problems; (2) New results on nonlinear estimation, including a new nonlinear observer with certain guaranteed properties; (3) The Loop Operator Recovery (LOR) procedure, and (4) Inclusion of command-following and disturbance rejection with a goal of a closed-loop stable, robust system.

Grunberg, D. B.↗

NASA NTRS2016

An Optimal-Estimation-Based Aerosol Retrieval Algorithm Using OMI Near-UV Observations

An optimal-estimation(OE)-based aerosol retrieval algorithm using the OMI (Ozone Monitoring Instrument) near-ultraviolet observation was developed in this study. The OE-based algorithm has the merit of providing useful estimates of errors simultaneously with the inversion products. Furthermore, instead of using the traditional lookup tables for inversion, it performs online radiative transfer calculations with the VLIDORT (linearized pseudo-spherical vector discrete ordinate radiative transfer code) to eliminate interpolation errors and improve stability. The measurements and inversion products of the Distributed Regional Aerosol Gridded Observation Network campaign in northeast Asia (DRAGON NE-Asia 2012) were used to validate the retrieved aerosol optical thickness (AOT) and single scattering albedo (SSA). The retrieved AOT and SSA at 388 nm have a correlation with the Aerosol Robotic Network (AERONET) products that is comparable to or better than the correlation with the operational product during the campaign. The OEbased estimated error represented the variance of actual biases of AOT at 388 nm between the retrieval and AERONET measurements better than the operational error estimates. The forward model parameter errors were analyzed separately for both AOT and SSA retrievals. The surface reflectance at 388 nm, the imaginary part of the refractive index at 354 nm, and the number fine-mode fraction (FMF) were found to be the most important parameters affecting the retrieval accuracy of AOT, while FMF was the most important parameter for the SSA retrieval. The additional information provided with the retrievals, including the estimated error and degrees of freedom, is expected to be valuable for relevant studies. Detailed advantages of using the OE method were described and discussed in this paper.

Air Pollution↗

DOE OSTI2022

Iterative subspace algorithms for finite-temperature solution of Dyson equation

One-particle Green’s functions obtained from the self-consistent solution of the Dyson equation can be employed in the evaluation of spectroscopic and thermodynamic properties for both molecules and solids. However, typical acceleration techniques used in the traditional quantum chemistry self-consistent algorithms cannot be easily deployed for the Green’s function methods because of a non-convex grand potential functional and a non-idempotent density matrix. Moreover, the optimization problem can become more challenging due to the inclusion of correlation effects, changing chemical potential, and fluctuations of the number of particles. In this paper, we study acceleration techniques to target the self-consistent solution of the Dyson equation directly. We use the direct inversion in the iterative subspace (DIIS), the least-squared commutator in the iterative subspace (LCIIS), and the Krylov space accelerated inexact Newton method (KAIN). We observe that the definition of the residual has a significant impact on the convergence of the iterative procedure. Based on the Dyson equation, we generalize the concept of the commutator residual used in DIIS and LCIIS and compare it with the difference residual used in DIIS and KAIN. The commutator residuals outperform the difference residuals for all considered molecular and solid systems within both GW and GF2. For a number of bond-breaking problems, we found that an easily obtained high-temperature solution with effectively suppressed correlations is a very effective starting point for reaching convergence of the problematic low-temperature solutions through a sequential reduction of temperature during calculations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Enhancing membrane performance for CO 2 capture from flue gas with ultrahigh MW polyvinylamine

Membranes for post-combustion CO 2 capture are required to have a high CO 2 permeance due to the limited driving force. For facilitated transport membranes synthesized with polyvinylamine (PVAm), a defect-free selective layer of <200 nm is usually required to render sufficient permeance with high CO 2 /N 2 selectivity. In order to meet such a demand through the knife-coating process, the coating solution needs to have a high viscosity at a relatively low concentration to minimize its penetration into the substrate. The demand was met by synthesizing PVAm with an ultrahigh molecular weight (MW) via inverse emulsion polymerization (IEP) in this study. Compared to solution polymerization, IEP isolates the reaction in inverse micelles suspended in a continuous organic phase, which allows excellent dissipation of the heat generated by the reaction and reduces gel formation drastically. The polymerization parameters, including monomer concentration, initiator concentration, and reaction temperature, were investigated to obtain the optimal MW of PVAm for membrane performance. As compared to solution polymerization, IEP enhanced the MW of PVAm from 1.2 to 12.7 MDa, which minimized the penetration of the coating solution into the substrate and hence the extra mass transfer resistance. The effect of MW and degree of hydrolysis of PVAm on the membrane transport properties were studied. Furthermore, by employing PVAm with a MW of 12.7 MDa to strengthen the polymer matrix, the loading of piperazine glycinate in the membrane was increased up to 85 wt.%. In conclusion, the resultant membrane achieved a CO 2 permeance of 839 GPU and a CO 2 /N 2 selectivity of 161 at the typical flue gas temperature of 57°C.

20 FOSSIL-FUELED POWER PLANTS↗

DOE OSTI2019

Folding and Assembly of Short α, β, γ -Hybrid Peptides: Minor Variations in Sequence and Drastic Differences in Higher-Level Structures

Multilevel protein structures typically involve polypeptides of sufficient lengths. Here we report the folding and assembly of seven short tetrapeptides sharing the same types of α-, β-, and aromatic γ-amino acid residues. These are two sets of hybrid peptides, with three members in one set and four in the other, having complementary hydrogen-bonding sequences that were hypothesized to pair into linear H-bonded duplexes. However, instead of undergoing the anticipated pairing, the initially examined three oligomers, 1 and 2a or 2b, differing only in their central αβ hybrid dipeptide sequence, do not associate with each other and exhibit distinctly different folding behavior. Experiments based on NMR and mass spectrometry, along with computational studies and systematic inference, reveal that oligomer 1 folds into an expanded β-turn containing an unusual hybrid α/β-amino acid sequence composed of glycine and β-alanine, two α- and β-amino acid residues that are conformationally most flexible, and peptides 2a and 2b adopt a noncanonical, extended helical conformation and dimerize into double helices undergoing rapid conformational exchange or helix inversion. The different central dipeptide sequences, αβ vs βα, result in drastically different intramolecular H-bonding patterns that are responsible for the observed folding behavior of 1 and 2. The revealed turn and double helix have few natural or synthetic counterparts, and provide novel and unique folding prototypes based on which chiral α- and β-amino acids are incorporated. The resultant derivatives 1a, 1b, 2c, and 2d follow the same folding and assembling behavior and demonstrate the generality of this system with the formation of expanded β-turns and double helices with enhanced folding stabilities, hampered helix inversion, as well as defined and dominant helical sense. This work has demonstrated the unique capability of synthetic foldamers in generating structures with fascinating folding and assembling behavior. As a result, the revealed systems offer ample opportunity for further structural optimization and applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Laser-heated capillary discharge plasma waveguides for electron acceleration to 8 GeV

A plasma channel created by the combination of a capillary discharge and inverse Bremsstrahlung laser heating enabled the generation of electron bunches with energy up to 7.8 GeV in a laser-driven plasma accelerator. The capillary discharge created an initial plasma channel and was used to tune the plasma temperature, which optimized laser heating. Although optimized colder initial plasma temperatures reduced the ionization degree, subsequent ionization from the heater pulse created a fully ionized plasma on-axis. The heater pulse duration was chosen to be longer than the hydrodynamic timescale of ≈ 1 ns, such that later temporal slices were more efficiently guided by the channel created by the front of the pulse. Here, simulations are presented which show that this thermal self-guiding of the heater pulse enabled channel formation over 20 cm. The post-heated channel had lower on-axis density and increased focusing strength compared to relying on the discharge alone, which allowed for guiding of relativistically intense laser pulses with a peak power of 0.85 PW and wakefield acceleration over 15 diffraction lengths. Electrons were injected into the wake in multiple buckets and times, leading to several electron bunches with different peak energies. To create single electron bunches with low energy spread, experiments using localized ionization injection inside a capillary discharge waveguide were performed. A single injected bunch with energy 1.6 GeV, charge 38 pC, divergence 1 mrad, and relative energy spread below 2% full-width half-maximum was produced in a 3.3 cm-long capillary discharge waveguide. This development shows promise for mitigation of energy spread and future high efficiency staged acceleration experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1995

Optimization methods, flux conserving methods for steady state Navier-Stokes equation

Navier-Stokes equation as discretized by new flux conserving method proposed by Chang and Scott results in the system: vector F(vector x) = 0, where F is a vector valued function. The Optimization method we use is based on Quasi-Newton methods: given a nonlinear function vector F(vector x) = 0, we solve, Delta(vector x) = -BF(vector x), where Delta(vector x) is the correction term and B is the inverse Jacobian of F(x). Then, iteratively, vector(x(sub (i+1))) = vector(x (sub i)) + alpha.Delta(vector x(sub i)), where alpha is a line search correction term determined by a line search routine. We use the BFCG's update the Jacobian matrix B(sub k) at each iteration. It is well known that B(sub k) approaches B(*) at the solution X(*). This algorithm has several advantages over the Newton-Raphson method. For example, we do not need to calculate the Jacobian matrix at each iteration which is computationally very expensive.

Adeyeye, John↗

DOE OSTI2017

Bianisotropic metamaterial

The topology of the elements of a metamaterial can be engineered from its desired electromagnetic constitutive tensor using an inverse group theory method. Therefore, given a desired electromagnetic response and a generic metamaterial elemental design, group theory is applied to predict the various ways that the element can be arranged in three dimensions to produce the desired functionality. An optimizer can then be applied to an electromagnetic modeling tool to fine tune the values of the electromagnetic properties of the resulting metamaterial topology.

36 MATERIALS SCIENCE↗

DOE OSTI2015

SU-E-I-09: The Impact of X-Ray Scattering On Image Noise for Dedicated Breast CT

Purpose: To quantify the impact of detected x-ray scatter on image noise in flat panel based dedicated breast CT systems and to determine the optimal scanning geometry given practical trade-offs between radiation dose and scatter reduction. Methods: Four different uniform polyethylene cylinders (104, 131, 156, and 184 mm in diameter) were scanned as the phantoms on a dedicated breast CT scanner developed in our laboratory. Both stationary projection imaging and rotational cone-beam CT imaging was performed. For each acquisition type, three different x-ray beam collimations were used (12, 24, and 109 mm measured at isocenter). The aim was to quantify image noise properties (pixel variance, SNR, and image NPS) under different levels of x-ray scatter, in order to optimize the scanning geometry. For both projection images and reconstructed CT images, individual pixel variance and NPS were determined and compared. Noise measurement from the CT images were also performed with different detector binning modes and reconstruction matrix sizes. Noise propagation was also tracked throughout the intermediate steps of cone-beam CT reconstruction, including the inverse-logarithmic process, Fourier-filtering before backprojection. Results: Image noise was lower in the presence of higher scatter levels. For the 184 mm polyethylene phantom, the image noise (measured in pixel variance) was ∼30% lower with full cone-beam acquisition compared to a narrow (12 mm) fan-beam acquisition. This trend is consistent across all phantom sizes and throughout all steps of CT image reconstruction. Conclusion: From purely a noise perspective, the cone-beam geometry (i.e. the full cone-angle acquisition) produces lower image noise compared to the lower-scatter fan-beam acquisition for breast CT. While these results are relevant in homogeneous phantoms, the full impact of scatter on noise in bCT should involve contrast-to-noise-ratio measurements in heterogeneous phantoms if the goal is to optimize the scanning geometry for dedicated breast CT. This work was supported by a grant from the National Institute for Biomedical Imaging and Bioengineering (R01 EB002138)

60 APPLIED LIFE SCIENCES↗