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At least 865 records · Page 48

Bayesian inference in band excitation scanning probe microscopy for optimal dynamic model selection in imaging

The universal tendency in scanning probe microscopy (SPM) over the last two decades is to transition from simple 2D imaging to complex detection and spectroscopic imaging modes. The emergence of complex SPM engines brings forth the challenge of reliable data interpretation, i.e., conversion from detected signals to descriptors specific to tip–surface interactions and subsequently to material’s properties. In this work, we implemented a Bayesian inference approach for the analysis of the image formation mechanisms in band excitation SPM. Compared to the point estimates in classical functional fit approaches, Bayesian inference allows for the incorporation of extant knowledge of materials and probe behavior in the form of corresponding prior distribution and return the information on the material functionality in the form of readily interpretable posterior distributions. We explore the nonlinear mechanical behaviors spatially in a classical ferroelectric material, PbTiO 3 . We observe the non-trivial evolution of the Duffing stiffness term and the nonlinearity of the sample surface, determine spatial clustering of the nonlinear response, and perform a Landau analysis on predicting the nonlinear coefficient, which indicates that ferroelectric behavior can be a cause of the observed results. These observations suggest that the spectrum of anomalous behaviors at the ferroelectric domain walls may be broader than previously believed and can extend to non-conventional mechanical properties in addition to static and microwave conductance.

36 MATERIALS SCIENCE↗

The Open Flux Problem

The heliospheric magnetic field is of pivotal importance in solar and space physics. The field is rooted in the Sun’s photosphere, where it has been observed for many years. Global maps of the solar magnetic field based on full-disk magnetograms are commonly used as boundary conditions for coronal and solar wind models. Two primary observational constraints on the models are (1) the open field regions in the model should approximately correspond to coronal holes (CHs) observed in emission and (2) the magnitude of the open magnetic flux in the model should match that inferred from in situ spacecraft measurements. In this study, we calculate both magnetohydrodynamic and potential field source surface solutions using 14 different magnetic maps produced from five different types of observatory magnetograms, for the time period surrounding 2010 July. We have found that for all of the model/map combinations, models that have CH areas close to observations underestimate the interplanetary magnetic flux, or, conversely, for models to match the interplanetary flux, the modeled open field regions are larger than CHs observed in EUV emission. In an alternative approach, we estimate the open magnetic flux entirely from solar observations by combining automatically detected CHs for Carrington rotation 2098 with observatory synoptic magnetic maps. This approach also underestimates the interplanetary magnetic flux. Our results imply that either typical observatory maps underestimate the Sun’s magnetic flux, or a significant portion of the open magnetic flux is not rooted in regions that are obviously dark in EUV and X-ray emission.

79 ASTRONOMY AND ASTROPHYSICS↗

Evaluation and development of satellite inferences of convective storm intensity using combined case study analysis and thunderstorm model simulations

Major research accomplishments which were achieved during the first year of the grant are summarized. The research concentrated in the following areas: (1) an examination of observational requirements for predicting convective storm development and intensity as suggested by recent numerical experiments; (2) interpretation of recent 3D numerical experiments with regard to the relationship between overshooting tops and surface wind gusts; (3) the development of software for emulating satellite-inferred cloud properties using 3D cloud model predicted data; and (4) the development of a conceptual/semi-quantitative model of eastward propagating, mesoscale convective complexes forming to the lee of the Rocky Mountains.

Cotton, W. R.↗

Machine learning pipeline for denoising low signal-to-noise ratio and out-of-distribution transmission electron microscopy datasets

High-resolution transmission electron microscopy (HRTEM) is crucial for observing material’s structural and morphological evolution at Angstrom scales, but the electron beam can alter these processes. Devices such as CMOS-based direct-electron detectors operating in electron-counting mode can be utilized to substantially reduce the electron dosage. However, the resulting images often lead to a low signal-to-noise ratio, which requires frame integration that sacrifices temporal resolution. Several machine learning (ML) models have been recently developed to successfully denoise HRTEM images. Yet, these models are often computationally expensive, and their inference speeds on GPUs are outpaced by the imaging speed of advanced detectors, precluding in situ analysis. Furthermore, the performance of these denoising models on datasets with imaging conditions that deviate from the training datasets has not been evaluated. To mitigate these gaps, we propose a new self-supervised ML denoising pipeline specifically designed for time-series HRTEM images. This pipeline integrates a blind-spot convolution neural network with pre-processing and post-processing steps, including drift correction and low-pass filtering. Results demonstrate that our model outperforms various other ML and non-ML denoising methods in noise reduction and contrast enhancement, leading to improved visual clarity of atomic features. Additionally, the model is drastically faster than U-Net-based ML models and demonstrates excellent out-of-distribution generalization. The model’s computational inference speed is in the order of milliseconds per image, rendering it suitable for application in in-situ HRTEM experiments.

36 MATERIALS SCIENCE↗

A Bayesian Approach for Quantifying Data Scarcity when Modeling Human Behavior via Inverse Reinforcement Learning

Computational models that formalize complex human behaviors enable study and understanding of such behaviors. However, collecting behavior data required to estimate the parameters of such models is often tedious and resource intensive. Thus, estimating dataset size as part of data collection planning (also known as Sample Size Determination) is important to reduce the time and effort of behavior data collection while maintaining an accurate estimate of model parameters. In this paper, we present a sample size determination method based on Uncertainty Quantification (UQ) for a specific Inverse Reinforcement Learning (IRL) model of human behavior, in two cases: 1) pre-hoc experiment design—conducted in the planning stage before any data is collected, to guide the estimation of how many samples to collect; and 2) post-hoc dataset analysis—performed after data is collected, to decide if the existing dataset has sufficient samples and whether more data is needed. Here, we validate our approach in experiments with a realistic model of behaviors of people with Multiple Sclerosis (MS) and illustrate how to pick a reasonable sample size target. Our work enables model designers to perform a deeper, principled investigation of effects of dataset size on IRL.

97 MATHEMATICS AND COMPUTING↗

DS-TIDE: Harnessing Dynamical Systems for Efficient Time-Independent Differential Equation Solving

Time-Independent Differential Equations (TIDEs) are central to modeling equilibrium behavior across a wide range of scientific and engineering domains, from electrostatics to porous media flow. Conventional numerical solvers offer reliable solutions but incur significant computational costs due to fine-grained discretization and iterative procedures. Machine learning-based approaches address this by replacing iterative solving processes with one-time inference; however, their sophisticated models require extensive training resources that often exceed those of traditional solvers. Consequently, designing a TIDE solver that achieves high accuracy, broad applicability, and exceptional computational efficiency remains a fundamental challenge. In this paper, we propose DS-TIDE, a novel hardware solver that is inspired by, and subsequently leverages, the intrinsic connection between Dynamical Systems (DS) and Differential Equations (DEs) to efficiently and accurately solve TIDEs. DS-TIDE employs a CMOS-compatible DS-based processor, whose physical states evolve under carefully designed DE-driven dynamics and naturally converge to equilibrium -- the solution of the target TIDE -- within ~1µs on a ~1-watt DS-TIDE processor. To enhance expressivity, DS-TIDE incorporates Heterogeneous Dynamics with Temporal Layering (HDTL), which solves TIDEs through a three-stage DS evolution -- conditioning, solving, and decoding -- each governed by specialized dynamics. The entire evolution process is analogous to an infinitely deep neural network temporally unrolled, offering the system the capability of representing complex equations. Furthermore, DS-TIDE is equipped with an on-device DS-DE Auto-Alignment mechanism that dynamically adapts intrinsic hardware dynamics within milliseconds, effectively aligning the system’s dynamics to diverse target DEs. Experimental results across TIDEs from a wide range of scientific and engineering domains demonstrate that DS-TIDE achieves ~10^3× speedup, ~10^5× energy savings, and competitive or superior accuracy compared to state-of-the-art numerical and ML-based solvers.

Liu, Chuan↗

DISSECTING MAGNETAR VARIABILITY WITH BAYESIAN HIERARCHICAL MODELS

Neutron stars are a prime laboratory for testing physical processes under conditions of strong gravity, high density, and extreme magnetic fields. Among the zoo of neutron star phenomena, magnetars stand out for their bursting behavior, ranging from extremely bright, rare giant flares to numerous, less energetic recurrent bursts. The exact trigger and emission mechanisms for these bursts are not known; favored models involve either a crust fracture and subsequent energy release into the magnetosphere, or explosive reconnection of magnetic field lines. In the absence of a predictive model, understanding the physical processes responsible for magnetar burst variability is difficult. Here, we develop an empirical model that decomposes magnetar bursts into a superposition of small spike-like features with a simple functional form, where the number of model components is itself part of the inference problem. The cascades of spikes that we model might be formed by avalanches of reconnection, or crust rupture aftershocks. Using Markov Chain Monte Carlo sampling augmented with reversible jumps between models with different numbers of parameters, we characterize the posterior distributions of the model parameters and the number of components per burst. We relate these model parameters to physical quantities in the system, and show for the first time that the variability within a burst does not conform to predictions from ideas of self-organized criticality. We also examine how well the properties of the spikes fit the predictions of simplified cascade models for the different trigger mechanisms.

79 ASTRONOMY AND ASTROPHYSICS↗

A Latent-Variable Formulation of the Poisson Canonical Polyadic Tensor Model: Maximum Likelihood Estimation and Fisher Information

We establish parameter inference for the Poisson canonical polyadic (PCP) tensor model through a latent-variable formulation. Our approach exploits the observation that any random PCP tensor can be derived by marginalizing an unobservable random tensor of one dimension larger. The loglikelihood of this larger dimensional tensor, referred to as the “complete” loglikelihood, is comprised of multiple rank one PCP loglikelihoods. Using this methodology, we first derive maximum likelihood estimators for the PCP model and demonstrate that several existing algorithms for fitting non-negative matrix and tensor factorizations are Expectation-Maximization algorithms. Next, we derive the observed and expected Fisher information matrices for the PCP model. The Fisher information provides us crucial insights into the well-posedness of the tensor model, such as the role that tensor rank plays in identifiability and indeterminacy. For the special case of rank one PCP models, we demonstrate that these results are greatly simplified.

97 MATHEMATICS AND COMPUTING↗

Approximate Bayesian Model Inversion for PDEs with Heterogeneous and State-Dependent Coefficients

We present two approximate Bayesian inference methods for parameter estimation in partial differential equation (PDE) models with space-dependent and state-dependent parameters. We demonstrate that these methods provide accurate and cost-effective alternatives to Markov Chain Monte Carlo simulation. We assume a parameterized Gaussian prior on the unknown functions, and approximate the posterior density by a parameterized multivariate Gaussian density. The parameters of the prior and posterior are estimated from sparse observations of the PDE model's states and the unknown functions themselves by maximizing the evidence lower bound (ELBO), a lower bound on the log marginal likelihood of the observations. The first method, Laplace-EM, employs the expectation maximization algorithm to maximize the ELBO, with a Laplace approximation of the posterior on the E-step, and minimization of a Kullback-Leibler divergence on the M-step. The second method, DSVI-EB, employs the doubly stochastic variational inference (DSVI) algorithm, in which the ELBO is maximized via gradient-based stochastic optimization, with nosiy gradients computed via simple Monte Carlo sampling and Gaussian backpropagation. We apply these methods to identifying diffusion coefficients in linear and nonlinear diffusion equations, and we find that both methods provide accurate estimates of posterior densities and the hyperparameters of Gaussian priors. While the Laplace-EM method is more accurate, it requires computing Hessians of the physics model. The DSVI-EB method is found to be less accurate but only requires gradients of the physics model.

approximate Bayesian inference, model inversion, v↗

Multiclass Classification Using Bayesian Multivariate Adaptive Regression Splines

We present a new Bayesian model for the problem of multiclass classification. In this model, the probabilities of class membership of a given observation are determined by the mean of a latent Gaussian distribution. The mean functions of this latent distribution consist of combinations of highly flexible basis functions of the inputs: multivariate adaptive regression splines (MARS), first developed for multiple regression. We use reversible jump Markov chain Monte Carlo to make inference on the classification model, including the number of basis functions. We compare the probabilistic classification performance of our proposed approach to existing methods on simulated and benchmark data, and compare uncertainty estimates on simulated data. Our proposed method compares favorably with existing Bayesian and frequentist multiclass classification methods in out-of-sample probabilistic classification, and uncertainty estimation of these probabilistic classifications. We examine the fit of the proposed method to a data set of hurricane storm surge levels near Delaware Bay, US, and conclude that sea level rise is a key contributor to damage delivered by storm surge.

97 MATHEMATICS AND COMPUTING↗

Atomistic Method Applied to Computational Modeling of Surface Alloys

The formation of surface alloys is a growing research field that, in terms of the surface structure of multicomponent systems, defines the frontier both for experimental and theoretical techniques. Because of the impact that the formation of surface alloys has on surface properties, researchers need reliable methods to predict new surface alloys and to help interpret unknown structures. The structure of surface alloys and when, and even if, they form are largely unpredictable from the known properties of the participating elements. No unified theory or model to date can infer surface alloy structures from the constituents properties or their bulk alloy characteristics. In spite of these severe limitations, a growing catalogue of such systems has been developed during the last decade, and only recently are global theories being advanced to fully understand the phenomenon. None of the methods used in other areas of surface science can properly model even the already known cases. Aware of these limitations, the Computational Materials Group at the NASA Glenn Research Center at Lewis Field has developed a useful, computationally economical, and physically sound methodology to enable the systematic study of surface alloy formation in metals. This tool has been tested successfully on several known systems for which hard experimental evidence exists and has been used to predict ternary surface alloy formation (results to be published: Garces, J.E.; Bozzolo, G.; and Mosca, H.: Atomistic Modeling of Pd/Cu(100) Surface Alloy Formation. Surf. Sci., 2000 (in press); Mosca, H.; Garces J.E.; and Bozzolo, G.: Surface Ternary Alloys of (Cu,Au)/Ni(110). (Accepted for publication in Surf. Sci., 2000.); and Garces, J.E.; Bozzolo, G.; Mosca, H.; and Abel, P.: A New Approach for Atomistic Modeling of Pd/Cu(110) Surface Alloy Formation. (Submitted to Appl. Surf. Sci.)). Ternary alloy formation is a field yet to be fully explored experimentally. The computational tool, which is based on the BFS (Bozzolo, Ferrante, and Smith) method for the calculation of the energetics, consists of a small number of simple PCbased computer codes that deal with the different aspects of surface alloy formation. Two analysis modes are available within this package. The first mode provides an atom-by-atom description of real and virtual stages 1. during the process of surface alloying, based on the construction of catalogues of configurations where each configuration describes one possible atomic distribution. BFS analysis of this catalogue provides information on accessible states, possible ordering patterns, and details of island formation or film growth. More importantly, it provides insight into the evolution of the system. Software developed by the Computational Materials Group allows for the study of an arbitrary number of elements forming surface alloys, including an arbitrary number of surface atomic layers. The second mode involves large-scale temperature-dependent computer 2. simulations that use the BFS method for the energetics and provide information on the dynamic processes during surface alloying. These simulations require the implementation of Monte-Carlo-based codes with high efficiency within current workstation environments. This methodology capitalizes on the advantages of the BFS method: there are no restrictions on the number or type of elements or on the type of crystallographic structure considered. This removes any restrictions in the definition of the configuration catalogues used in the analytical calculations, thus allowing for the study of arbitrary ordering patterns, ultimately leading to the actual surface alloy structure. Moreover, the Monte Carlo numerical technique used for the large-scale simulations allows for a detailed visualization of the simulated process, the main advantage of this type of analysis being the ability to understand the underlying features that drive these processes. Because of the simplicity of the BFS method for e energetics used in these calculations, a detailed atom-by-atom analysis can be performed at any point in the simulation, providing necessary insight on the details of the process. The main objective of this research program is to develop a tool to guide experimenters in understanding and interpreting often unexpected results in alloy formation experiments. By reducing the computational effort without losing physical accuracy, we expect that powerful simulation tools will be developed in the immediate future, which will allow material scientists to easily visualize and analyze processes at a level not achievable experimentally.

Bozzolo, Guillermo H.↗

Numerical study of a micro flow reactor at engine pressures: Flames with repetitive extinction and ignition and simulations with a reduced chemical model

Combustion in a narrow channel with an imposed temperature gradient is studied numerically at elevated pressure with engine-relevant fuels. Here, the focus is placed on unsteady flames with repetitive extinction and ignition (FREI) to determine the potential of this regime for fuel testing and calibration of reduced chemical mechanisms. First, it is shown that the FREI regime does occur at elevated pressures for sufficiently small tube diameters. The sensitivity of the extinction and ignition temperatures to low-temperature chemistry is found to be significantly enhanced at 25 bar compared to atmospheric conditions. The ignition and extinction temperatures differ by up to 100 K between PRF mixtures with varying octane numbers. Ternary mixtures of iso-octane/n-heptane/toluene and iso-octane/n-heptane/ethanol at similar research and motor octane numbers are also studied. Second, the potential of using data from the micro flow reactor to infer reaction rates is assessed. A reduced chemical mechanism combining a small fuel-dependent submechanism with a detailed fuel-independent submechanism for the core species chemistry is used for that purpose. Only the most sensitive fuel-dependent reactions are inferred. the calibrated reduced model is compared to a detailed model and good agreement in ignition delay times and laminar flame speeds is observed. Finally, this illustrates the potential of a micro flow reactor with a controlled temperature profile to test fuels and infer kinetic data.

33 ADVANCED PROPULSION SYSTEMS↗

Uncertainty quantification for incident helium flux in plasma-exposed tungsten

In this work, the surface response of a tungsten plasma-facing component was simulated by a cluster-dynamics code, Xolotl, with a focus on quantifying the impact of uncertainty in one of the input parameters to Xolotl, namely, the incident helium flux. The simulated conditions involve a tungsten surface exposed to 100 eV helium ion implantations with a flux of either 4 × 10 22 or 4 × 10 25 He m -2 s -1 . Furthermore, two sources were used to describe the implanted helium depth distribution in tungsten, either molecular dynamics (MD) or a binary collision approximation code, the stopping and range of ions in matter (SRIM). The aim of this work is to evaluate and examine uncertain predictions on the helium retention based on these two different modeling methodologies that either neglect electronic energy loss or the crystalline structure of the solid, respectively. An embedded model-form error approach was pursued here in order to arrive at predictions that account for variability due to the two different data sources, and the impact of this model-form uncertainty in incident helium flux on Xolotl output was presented for the two implantation fluxes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

FAST VARIABILITY AND MILLIMETER/IR FLARES IN GRMHD MODELS OF Sgr A* FROM STRONG-FIELD GRAVITATIONAL LENSING

We explore the variability properties of long, high-cadence general relativistic magnetohydrodynamic (GRMHD) simulations across the electromagnetic spectrum using an efficient, GPU-based radiative transfer algorithm. We focus on both standard and normal evolution (SANE) and magnetically arrested disk (MAD) simulations with parameters that successfully reproduce the time-averaged spectral properties of Sgr A* and the size of its image at 1.3 mm. We find that the SANE models produce short-timescale variability with amplitudes and power spectra that closely resemble those inferred observationally. In contrast, MAD models generate only slow variability at lower flux levels. Neither set of models shows any X-ray flares, which most likely indicates that additional physics, such as particle acceleration mechanisms, need to be incorporated into the GRMHD simulations to account for them. The SANE models show strong, short-lived millimeter/infrared (IR) flares, with short (≲1 hr) time lags between the millimeter and IR wavelengths, that arise from the combination of short-lived magnetic flux tubes and strong-field gravitational lensing near the horizon. Such events provide a natural explanation for the observed IR flares with no X-ray counterparts.

79 ASTRONOMY AND ASTROPHYSICS↗

Global electric field determination in the Earth's outer magnetosphere using energetic charged particles

Although many properties of the Earth's magnetosphere have been measured and quantified in the past 30 years since it was discovered, one fundamental measurement (for zeroth order MHD equilibrium) has been made infrequently and with poor spatial coverage - the global electric field. This oversight is due in part to the neglect of theorists. However, there is renewed interest in the convection electric field because it is now realized to be central to many magnetospheric processes, including the global MHD equilibrium, reconnection rates, Region 2 Birkeland currents, magnetosphere ionosphere coupling, ring current and radiation belt transport, substorm injections, and several acceleration mechanisms. Unfortunately the standard experimental methods have not been able to synthesize a global field (excepting the pioneering work of McIlwain's geostationary models) and we are left with an overly simplistic theoretical field, the Volland-Stern electric field model. Single point measurements of the plasmapause were used to infer the appropriate amplitudes of this model, parameterized by K(sub p). Although this result was never intended to be the definitive electric field model, it has gone nearly unchanged for 20 years. The analysis of current data sets requires a great deal more accuracy than can be provided by the Volland-Stern model. The variability of electric field shielding has not been properly addressed although effects of penetrating magnetospheric electric fields has been seen in mid-and low-latitude ionospheric data sets. The growing interest in substorm dynamics also requires a much better assessment of the electric fields responsible for particle injections. Thus we proposed and developed algorithms for extracting electric fields from particle data taken in the Earth's magnetosphere. As a test of the effectiveness of these new techniques, we analyzed data taken by the AMPTE/CCE spacecraft in equatorial orbit from 1984 to 1989.

Eastman, Timothy E.↗

Toward a dynamic-thermodynamic assimilation of satellite surface temperature in numerical atmospheric models

An assimilation technique is described in which satellite-observed surface skin temperature tendencies are used in a model surface energy budget so that the predicted rate of temperature change in the model more closely agrees with the satellite observations. Both visible and infrared GOES satellite data are used in the assimilation. The technique is based on analytically recovering surface moisture from similarity expressions derived from an evapotranspiration residual obtained as a difference between the unadjusted model evapotranspiration and the satellite-inferred evapotranspiration. The technique has application in regional-scale models where surface parameters such as root zone moisture, soil moisture, etc., are unknown. It is assumed that the largest error in the surface energy budget is in the evapotranspiration term. Two tests are given for the technique, first, a one-dimensional test against FIFE data and, second, a three-dimensional test over Oklahoma. In these cases the technique appears to correctly adjust the model response to agree better with observations.

Mcnider, Richard T.↗

The Role of Gravity Waves in Generating Equatorial Oscillations in Modulating Atmospheric Tides

We discuss a Numerical Spectral Mode (NSM) that extends from the ground up into the thermosphere and incorporates Hines' Doppler spread parameterization (DSP) for small scale gravity waves (GW). This model is applied to describe the seasonal variations in the mean zonal circulation, the semi-annual and quasi-biennial oscillations (SAO and QBO), as well as the tides and planetary waves in the middle atmosphere. Initial results showed that this model can reproduce the salient features observed, including the QBO extending into the upper mesosphere inferred from UARS measurements. The model has now been extended to simulate also: (a) the zonal circulation of the lower stratosphere and upper troposphere, and (b) the upwelling at equatorial latitudes associated with the Brewer Dobsen circulation that affects the dynamics significantly as pointed out by Dunkerton. Upward vertical winds increase the period of the QBO observed from the ground. To compensate for that, one needs to increase in the model the eddy diffusivity and the GW momentum flux, bringing the latter closer to values recommended in the DSP. This development is conducive to extending the QBO and SAO to higher latitudes through global scale momentum redistribution. Multi-year interannual oscillations are generated through wave filtering by the solar driven annual oscillation in the zonal circulation. In a 3D version of the model, wave momentum is absorbed and dissipated by tides and planetary waves. A somewhat larger GW source (well within the DSP range) is then required to generate realistic QBO and SAO amplitudes. Since GW momentum is deposited in the altitude regime of increasing winds, the amplitude of the diurnal tide is amplified and its vertical wavelength is reduced at altitudes between 70 and 120 km. Wave filtering by the mean zonal circulation causes the GW flux to peak during equinox, and this produces a large semi-annual variation in the tide that has been observed on UARS. Without the diurnal tide, the semidiurnal tide would also be modulated in this way. But the diurnal tide filters out the GW preferentially during equinox, so that the semidiurnal tide tends to peak during solstice. Under the influence of GW, the tides are modulated significantly by planetary waves that are generated preferentially during solstice in part due to baroclinic instability.

Mayr, H. G.↗