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DOE OSTI2022

Learning functional priors and posteriors from data and physics

In this work, we develop a new Bayesian framework based on deep neural networks to be able to extrapolate in space-time using historical data and to quantify uncertainties arising from both noisy and gappy data in physical problems. Specifically, the proposed approach has two stages: (1) prior learning and (2) posterior estimation. At the first stage, we employ the physics-informed Generative Adversarial Networks (PI-GAN) to learn a functional prior either from a prescribed function distribution, e.g., Gaussian process, or from historical data and physics. At the second stage, we employ the Hamiltonian Monte Carlo (HMC) method to estimate the posterior in the latent space of PI-GANs. In addition, we use two different approaches to encode the physics: (1) automatic differentiation, used in the physicsinformed neural networks (PINNs) for scenarios with explicitly known partial differential equations (PDEs), and (2) operator regression using the deep operator network (DeepONet) for PDE-agnostic scenarios. We then test the proposed method for (1) meta-learning for one-dimensional regression, and forward/inverse PDE problems (combined with PINNs); (2) PDE-agnostic physical problems (combined with DeepONet), e.g., fractional diffusion as well as saturated stochastic (100-dimensional) flows in heterogeneous porous media; and (3) spatial-temporal regression problems, i.e., inference of a marine riser displacement field using experimental data from the Norwegian Deepwater Programme (NDP). The results demonstrate that the proposed approach can provide accurate predictions as well as uncertainty quantification given very limited scattered and noisy data, since historical data could be available to provide informative priors. In summary, the proposed method is capable of learning flexible functional priors, e.g., both Gaussian and non-Gaussian process, and can be readily extended to big data problems by enabling mini-batch training using stochastic HMC or normalizing flows since the latent space is generally characterized as low dimensional.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Time-of-Flight Estimation for Nondestructive Evaluation

Ultrasonic testing (UT) for nondestructive evaluation (NDE) is a critical entity necessary to resolve both the quality and precision questions of complex parts evolving from the classical approaches to the innovative additive manufacturing (AM) process. This modality provides the essential quantitative information for acceptance and potential flaw detectionof apart under investigation. A primary ingredient in UT besides the required precision robotic hardware for theacquisition of high-qualitymeasurement data is the underlying signal processing. It is here that much of the system performance capability resides. In this report,we discuss the basic steps in UT signal processing along with current capabilities that must be achieved in order to satisfy the criticaldemands of the various LLNL programs.In itsbasic foundations, signal processing is essentially the “extraction of critical information (signals) from noisy, uncertain data.” Clearly, in a perfect world the best signal processing is none---just make a reliable, noise-free, uncertainty-free, measurement. Unfortunately, even the best of systems is still straddled within the confines and limitations of physical instrumentation. With this in mind, we discuss the development of signal processing techniques toextract the desired UT information from noisy measurement data. We start with a discussion of a simple homogeneous representation of a “part” under investigation and its insonification by an ultrasonicexcitation from a physics-based perspective. Once developed, we briefly discussthe various choices of excitation signals and their tradeoffs.Next,we discuss a simulation approach employing simple models from the signal processing perspective and then move on to the development of the basic signal processing approach to ultrasonic signal processing all based on estimating the pulse arrival estimation. Starting with simple peak detection techniques, progressing to the processing workhorse so-called “matched-filter” and finally to the more sophisticated “model-based matched filter.”The underlying pre-and post-processing of noisy measurement data along with the application of these techniques are subsequently demonstrated on experimental ultrasonic data.Finally, we present some results for processing “weld” data when the ultrasonic excitation signal is not directly available.

42 ENGINEERING↗

DOE OSTI2020

MOSAIC: a joint modeling methodology for combined circadian and non-circadian analysis of multi-omics data

Abstract Motivation Circadian rhythms are approximately 24-h endogenous cycles that control many biological functions. To identify these rhythms, biological samples are taken over circadian time and analyzed using a single omics type, such as transcriptomics or proteomics. By comparing data from these single omics approaches, it has been shown that transcriptional rhythms are not necessarily conserved at the protein level, implying extensive circadian post-transcriptional regulation. However, as proteomics methods are known to be noisier than transcriptomic methods, this suggests that previously identified arrhythmic proteins with rhythmic transcripts could have been missed due to noise and may not be due to post-transcriptional regulation. Results To determine if one can use information from less-noisy transcriptomic data to inform rhythms in more-noisy proteomic data, and thus more accurately identify rhythms in the proteome, we have created the Multi-Omics Selection with Amplitude Independent Criteria (MOSAIC) application. MOSAIC combines model selection and joint modeling of multiple omics types to recover significant circadian and non-circadian trends. Using both synthetic data and proteomic data from Neurospora crassa, we showed that MOSAIC accurately recovers circadian rhythms at higher rates in not only the proteome but the transcriptome as well, outperforming existing methods for rhythm identification. In addition, by quantifying non-circadian trends in addition to circadian trends in data, our methodology allowed for the recognition of the diversity of circadian regulation as compared to non-circadian regulation. Availability and implementation MOSAIC’s full interface is available at https://github.com/delosh653/MOSAIC. An R package for this functionality, mosaic.find, can be downloaded at https://CRAN.R-project.org/package=mosaic.find. Supplementary information Supplementary data are available at Bioinformatics online.

De los Santos, Hannah↗

DOE OSTI2021

Towards robust autonomous impedance spectroscopy analysis: A calibrated hierarchical Bayesian approach for electrochemical impedance spectroscopy (EIS) inversion

Distribution-based analyses, such as the distribution of relaxation times (DRT) and the distribution of diffusion times (DDT), present model-free alternatives to equivalent circuit modeling for analysis of electrochemical impedance spectroscopy (EIS) data. However, reconstructing such distributions from noisy impedance data is an ill-posed problem that must be solved with specialized inversion algorithms, requiring careful control and tuning. Furthermore, most inversion algorithms developed to date can only solve problems of limited complexity. Herein, we present a new hierarchical Bayesian method for EIS inversion, leveraging efficient algorithms for optimization and Hamiltonian Monte Carlo (HMC) sampling to solve models of arbitrary complexity. We overcome the challenge of ad-hoc parameter tuning by encoding intrinsic characteristics of the DRT and DDT into flexible prior distributions and “pre-calibrating” the model to simulated data. This approach is versatile, highly robust to noise, and provides quantitative estimates of both the error structure of the data and the uncertainty in the recovered distributions. The model is validated with simulated data to demonstrate accurate recovery of the DRT and the DDT. The method also shows promise for simultaneous recovery of multiple distributions, raising the intriguing possibility of semi-autonomous EIS analysis and ad-hoc model construction. Finally, the practical utility of the method is illustrated with experimental data. Throughout, we draw comparisons to several recently published EIS inversion methodologies.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Operator learning for predicting multiscale bubble growth dynamics

We report simulating and predicting multiscale problems that couple multiple physics and dynamics across many orders of spatiotemporal scales is a great challenge that has not been investigated systematically by deep neural networks (DNNs). Herein, we develop a framework based on operator regression, the so-called deep operator network (DeepONet), with the long-term objective to simplify multiscale modeling by avoiding the fragile and time-consuming “hand-shaking” interface algorithms for stitching together heterogeneous descriptions of multiscale phenomena. To this end, as a first step, we investigate if a DeepONet can learn the dynamics of different scale regimes, one at the deterministic macroscale and the other at the stochastic microscale regime with inherent thermal fluctuations. Specifically, we test the effectiveness and accuracy of the DeepONet in predicting multirate bubble growth dynamics, which is described by a Rayleigh–Plesset (R–P) equation at the macroscale and modeled as a stochastic nucleation and cavitation process at the microscale by dissipative particle dynamics (DPD). First, we generate data using the R–P equation for multirate bubble growth dynamics caused by randomly time-varying liquid pressures drawn from Gaussian random fields (GRFs). Our results show that properly trained DeepONets can accurately predict the macroscale bubble growth dynamics and can outperform long short-term memory networks. We also demonstrate that the DeepONet can extrapolate accurately outside the input distribution using only very few new measurements. Subsequently, we train the DeepONet with DPD data corresponding to stochastic bubble growth dynamics. Although the DPD data are noisy and we only collect sparse data points on the trajectories, the trained DeepONet model is able to predict accurately the mean bubble dynamics for time-varying GRF pressures. Taken together, our findings demonstrate that DeepONets can be employed to unify the macroscale and microscale models of the multirate bubble growth problem, hence providing new insight into the role of operator regression via DNNs in tackling realistic multiscale problems and in simplifying modeling with heterogeneous descriptions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Identifying crack tip position and stress intensity factors from displacement data

Fracture prognosis and characterization efforts require knowledge of crack tip position and the Stress Intensity Factors (SIFs) acting in the vicinity of the crack. Here, in this work, we present an efficient numerical approach to infer both of these characteristics under a consistent theoretical framework from noisy, unstructured displacement data. The novel approach utilizes the separability of the asymptotic linear elastic fracture mechanics fields to expedite the search for crack tip position and is particularly useful for noisy displacement data. The manuscript begins with an assessment of the importance of accurately locating crack tip position when quantifying the SIFs from displacement data. Next, the proposed separability approach for quickly inferring crack tip position is introduced. Comparing to the widely used displacement correlation approach, the performance of the separability approach is assessed. Cases involving both noisy data and systematic deviation from the asymptotic linear elastic fracture mechanics model are considered, e.g. inelastic material behavior and finite geometries. An open source python implementation of the proposed approach is available for use by those doing field and laboratory work involving digital image correlation and simulations, e.g. finite element, discrete element, molecular dynamics and peridynamics, where the crack tip position is not explicitly defined.

36 MATERIALS SCIENCE↗

DOE OSTI2023

IPN Absorption Coefficients

The dataset contains aerosol light absorption and scattering coefficients measured by three single-wavelength Integrated Photoacoustic Nephelometers (IPN). The absorption coefficients were measured at 405, 721, and 1047 nm, while the scattering coefficients were measured at 405 and 721 nm. The single scattering albedo (SSA) at 405 and 721 nm were also calculated from the IPN measurements. The three IPNs shared a common inlet without impactor/cyclone in July; in August, a PM2.5 cyclone inlet was installed to reduce measurement noise and improve data quality. The 721-nm IPN experienced laser shutdown issues, causing missing of a large fraction of the 721-nm measurements, especially in July. As described before, the 721-nm laser issue was less frequent in August after the cyclone installation, improving the data completeness and quality. The IPN raw data were noisy, making identifying patterns and trends difficult; therefore, the hourly average data are recommended over the raw data. The hourly average data were cross-checked with the filter-based TAP and PSAP measurements, which showed that their patterns, trends, and peaks matched. However, due to the differences in working mechanisms and principles of the filter-based and photoacoustic particle-phase instruments, the IPN measurements are lower than the filter-based measurements despite that they have consistent patterns, trends, and peaks.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Convergence Analysis for an Online Data-Driven Feedback Control Algorithm

This paper presents convergence analysis of a novel data-driven feedback control algorithm designed for generating online controls based on partial noisy observational data. The algorithm comprises a particle filter-enabled state estimation component, estimating the controlled system’s state via indirect observations, alongside an efficient stochastic maximum principle-type optimal control solver. By integrating weak convergence techniques for the particle filter with convergence analysis for the stochastic maximum principle control solver, we derive a weak convergence result for the optimization procedure in search of optimal data-driven feedback control. Numerical experiments are performed to validate the theoretical findings.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Propagating sample variance uncertainties in redshift calibration: simulations, theory, and application to the COSMOS2015 data

ABSTRACT Cosmological analyses of galaxy surveys rely on knowledge of the redshift distribution of their galaxy sample. This is usually derived from a spectroscopic and/or many-band photometric calibrator survey of a small patch of sky. The uncertainties in the redshift distribution of the calibrator sample include a contribution from shot noise, or Poisson sampling errors, but, given the small volume they probe, they are dominated by sample variance introduced by large-scale structures. Redshift uncertainties have been shown to constitute one of the leading contributions to systematic uncertainties in cosmological inferences from weak lensing and galaxy clustering, and hence they must be propagated through the analyses. In this work, we study the effects of sample variance on small-area redshift surveys, from theory to simulations to the COSMOS2015 data set. We present a three-step Dirichlet method of resampling a given survey-based redshift calibration distribution to enable the propagation of both shot noise and sample variance uncertainties. The method can accommodate different levels of prior confidence on different redshift sources. This method can be applied to any calibration sample with known redshifts and phenotypes (i.e. cells in a self-organizing map, or some other way of discretizing photometric space), and provides a simple way of propagating prior redshift uncertainties into cosmological analyses. As a worked example, we apply the full scheme to the COSMOS2015 data set, for which we also present a new, principled SOM algorithm designed to handle noisy photometric data. We make available a catalogue of the resulting resamplings of the COSMOS2015 galaxies.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Error-mitigated data-driven circuit learning on noisy quantum hardware

Application-level benchmarks measure how well a quantum device performs meaningful calculations. In the case of parameterized circuit training, the computational task is the preparation of a target quantum state via optimization over a loss landscape. This is complicated by various sources of noise, fixed hardware connectivity, and generative modeling, the choice of target distribution. Gradient-based training has become a useful benchmarking task for noisy intermediate-scale quantum computers because of the additional requirement that the optimization step uses the quantum device to estimate the loss function gradient. In this work, we use gradient-based data-driven circuit learning to qualitatively evaluate the performance of several superconducting platform devices and present results that show how error mitigation can improve the training of quantum circuit Born machines with 28 tunable parameters.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Quantification of neural networks uncertainties with applications to SAFARI-1 axial neutron flux profiles

Deep Neural Networks (DNNs) have been widely used as a data-driven modelling tool in nuclear engineering. However, as a Machine Learning model, Artificial Neural Network (ANN) predictions are subjected to uncertainties originating from the noise in training data, incomplete coverage of the domain, and imperfect neural network architectures. In this work, we target at quantifying the prediction/approximation uncertainties of ANNs using Monte Carlo Dropout (MCD), as well as Bayesian Neural Networks (BNNs) which are solved by variational inference. With a demonstration problem in which neural networks are used to predict the assembly axial neutron flux profiles, the results have shown that the three different neural network models (regular DNNs, DNNs solved with MCD and BNNs) can produce results that agree very well among each other and with the measurement data, on cycles that are not used in the training process. Besides the excellent generalization capability, the uncertainty bands produced by MCD and BNN agree very well, and in general, they can fully envelop the noisy measurement data points. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2023

Encoding nonlinear and unsteady aerodynamics of limit cycle oscillations using nonlinear sparse Bayesian learning

This article investigates the applicability of a recently proposed, nonlinear sparse Bayesian learning (NSBL) algorithm to identify and estimate the complex aerodynamics of limit cycle oscillations. NSBL provides a semi-analytical framework for determining the data-optimal sparse model nested within a (potentially) over-parameterized model. This is particularly relevant to nonlinear dynamical systems where modelling approaches involve the use of physics-based and data-driven components. In such cases, the data-driven components, where analytical descriptions of the physical processes are not readily available, are often prone to overfitting, meaning that the empirical aspects of these models will often involve the calibration of an unnecessarily large number of parameters. While an overparameterized model may fit the observed data well, such models may be inadequate for making predictions in regimes that are different from those wherein the data were recorded. In view of this, it is desirable to not only calibrate the model parameters, but also identify the optimal compromise between data fit and model complexity. In this article, we exhibit the optimal model discovery for an aeroelastic system wherein the structural dynamics are well-known and described by a differential equation model, coupled with a semi-empirical aerodynamic model for laminar separation flutter, resulting in low-amplitude limit cycle oscillations (LCO). To illustrate the performance of the algorithm, in this article, we use synthetic data and demonstrate the ability of the algorithm to correctly rediscover the optimal model and model parameters, given a known data-generating model. The synthetic data are generated from a forward simulation of a known differential equation model with parameters selected so as to mimic the dynamics observed in wind-tunnel experiments. Subsequently, we demonstrate the performance of the algorithm for model selection using noisy LCO data from wind tunnel experiments. As there is no ground truth available for the experimental data case, we provide a comparison between NSBL and Bayesian model selection to validate the results, and demonstrate the use of NSBL as an efficient alternative to traditional methods.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Seismic Characterization of the Blue Mountain Geothermal Field

Subsurface characterization is crucial for geothermal energy exploration and production. Yet hydrothermal reservoirs usually reside in highly fractured and faulted zones where accurate characterization is very challenging because of low signal-to-noise ratios of land seismic data and lack of coherent reflection signals. We perform an active-source seismic characterization for the Blue Mountain geothermal field in Nevada using active seismic data to reveal the elastic medium property complexity and fault distribution at this field. We first employ an unsupervised machine learning method to attenuate groundroll and near-surface guided-wave noise and enhance coherent reflection and scattering signals from noisy seismic data. We then build a smooth initial P-wave velocity model based on an existing magnetotellurics survey result, and use 3D first-arrival traveltime tomography to refine the initial velocity model. We then derive a set of elastic wave velocities and anisotropic parameters using elastic full-waveform inversion, and obtain PP and PS images using elastic reverse-time migration. We identify major faults by analyzing the variations of seismic velocities and anisotropy parameters, and reveal mid- to small-scale faults by applying a supervised machine learning method to the seismic migration images. Our characterization reveals complex velocity heterogeneities and anisotropies, as well as faults, with a high spatial resolution. These results can provide valuable information for optimal placement of future injection and production wells to increase geothermal energy production at the Blue Mountain geothermal power plant.

58 GEOSCIENCES↗

DOE OSTI2021

Sea Surface Salinity Reemergence in an Updated North Atlantic In Situ Salinity Dataset

Monthly sea surface salinity (SSS) fields are constructed from observations, using objective mapping on a 1° x 1° grid in the Atlantic between 30°S and 50°N in the 1970-2016 period in an update of the dataset of Reverdin et al. Data coverage is heterogeneous, with increased density in 2002 when Argo floats become available, high density along Voluntary Observing Ship lines, and low density south of 10°S. Using lag correlation, the seasonal reemergence of SSS anomalies is investigated between 20° and 50°N in 5° x 5° boxes during the 1993-2016 period, both locally and remotely following the displacements of the deep mixed-layer waters estimated from virtual float trajectories derived from the daily AVISO surface geostrophic currents. Although SSS data are noisy, local SSS reemergence is detected in about half of the boxes, notably in the northeast and southeast, while little reemergence is seen in the central and part of the eastern subtropical gyre. In the same period, sea surface temperature (SST) reemergence is found only slightly more frequently, reflecting the short data duration. However, taking geostrophic advection into account degrades the detection of remote SSS and even SST reemergence. When anomalies are averaged over broader areas, robust evidence of a second and third SSS reemergence peak is found in the northeastern and southeastern parts of the domain, indicating long cold-season persistence of large-scale SSS anomalies, while only a first SST reemergence is seen. Finally, an oceanic reanalysis is used to confirm that the correlation analysis indeed reflects the reemergence of subsurface salinity anomalies.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Temporally-consistent koopman autoencoders for forecasting dynamical systems

Absence of sufficiently high-quality data often poses a key challenge in data-driven modeling of high-dimensional spatio-temporal dynamical systems. Koopman Autoencoders (KAEs) harness the expressivity of deep neural networks (DNNs), the dimension reduction capabilities of autoencoders, and the spectral properties of the Koopman operator to learn a reduced-order feature space with simpler, linear dynamics. However, the effectiveness of KAEs is hindered by limited and noisy training datasets, leading to poor generalizability. To address this, we introduce the Temporally-Consistent Koopman Autoencoder (tcKAE), designed to generate accurate long-term predictions even with limited and noisy training data. This is achieved through a consistency regularization term that enforces prediction coherence across different time steps, thus enhancing the robustness and generalizability of tcKAE over existing models. We provide analytical justification for this approach based on Koopman spectral theory and empirically demonstrate tcKAE’s superior performance over state-of-the-art KAE models across a variety of test cases, including simple pendulum oscillations, kinetic plasma, and fluid flow data.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Analysis techniques for blob properties from gas puff imaging data

Filamentary structures, also known as blobs, are a prominent feature of turbulence and transport at the edge of magnetically confined plasmas. They cause cross-field particle and energy transport and are, therefore, of interest in tokamak physics and, more generally, nuclear fusion research. Several experimental techniques have been developed to study their properties. Among these, measurements are routinely performed with stationary probes, passive imaging, and, in more recent years, Gas Puff Imaging (GPI). In this work, we present different analysis techniques developed and used on 2D data from the suite of GPI diagnostics in the Tokamak à Configuration Variable, featuring different temporal and spatial resolutions. Although specifically developed to be used on GPI data, these techniques can be employed to analyze 2D turbulence data presenting intermittent, coherent structures. We focus on size, velocity, and appearance frequency evaluation with, among other methods, conditional averaging sampling, individual structure tracking, and a recently developed machine learning algorithm. We describe in detail the implementation of these techniques, compare them against each other, and comment on the scenarios to which these techniques are best applied and on the requirements that the data must fulfill in order to yield meaningful results.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Bayesian learning with Gaussian processes for low-dimensional representations of time-dependent nonlinear systems

This work presents a data-driven method for learning low-dimensional time-dependent physics-based surrogate models whose predictions are endowed with uncertainty estimates. We use the operator inference approach to model reduction that poses the problem of learning low-dimensional model terms as a regression of state space data and corresponding time derivatives by minimizing the residual of reduced system equations. Standard operator inference models perform well with accurate training data that are dense in time, but producing stable and accurate models when the state data are noisy and/or sparse in time remains a challenge. Another challenge is the lack of uncertainty estimation for the predictions from the operator inference models. Our approach addresses these challenges by incorporating Gaussian process surrogates into the operator inference framework to (1) probabilistically describe uncertainties in the state predictions and (2) procure analytical time derivative estimates with quantified uncertainties. The formulation leads to a generalized least-squares regression and, ultimately, reduced-order models that are described probabilistically with a closed-form expression for the posterior distribution of the operators. The resulting probabilistic surrogate model propagates uncertainties from the observed state data to reduced-order predictions. Furthermore, we demonstrate the method is effective for constructing low-dimensional models of two nonlinear partial differential equations representing a compressible flow and a nonlinear diffusion–reaction process, as well as for estimating the parameters of a low-dimensional system of nonlinear ordinary differential equations representing compartmental models in epidemiology.

Data-driven model reduction↗

DOE OSTI2024

Design, Detection, and Countermeasure of Frequency Spectrum Attack and Its Impact on Long Short-Term Memory Load Forecasting and Microgrid Energy Management

This paper introduces a frequency-domain false data injection attack called Frequency Spectrum Attack (FSA) and explores its effects on load forecasting and the energy management system (EMS) in a microgrid. The FSA analyzes time-series signals in the frequency domain to identify patterns in their frequency spectrum. It learns the distribution of dominant frequencies in a dataset of healthy signals. Subsequently, it manipulates the amplitudes of dominant frequencies within this healthy distribution, ensuring a stealthy attack against statistical analysis of the signal spectrum. We evaluated the performance of FSA on LSTM, a state-of-the-art network for load forecasting. The results show that FSA can triple the Mean Absolute Error (MAE) of predictions compared to the normal case and increase it by 70% compared to noise injection attacks. Furthermore, FSA indirectly enhances battery utilization in the EMS by 45%. We then proposed a detection method that combines statistical analysis and machine-learning-based classification techniques with features. The model effectively distinguishes FSA from healthy and noisy signals, achieving an accuracy of 98.7% and an F1-score of 98.1% on a load dataset, covering healthy, FSA, and noisy load data. Finally, a countermeasure was introduced based on the statistical analysis of the frequency spectrum of healthy signals to mitigate the impact of FSA. This countermeasure successfully reduces the MAE of the attacked model from 0.135 to 0.053, validating its effectiveness in mitigating FSA.

Nazeri, Amirhossein↗