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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 OSTI2020

Short-depth circuits for efficient expectation-value estimation

The evaluation of expectation values Tr[$\rho \mathcal{O}$] for some pure state $\rho$ and Hermitian operator $\mathcal{O}$ is of central importance in a variety of quantum algorithms. Near-optimal techniques have been developed in the past and require a number of measurements N approaching the Heisenberg limit N = O(1/ ε) as a function of target accuracy ε. The use of quantum phase estimation (QPE) requires, however, long circuit depths C = O(1/ ε) making its implementation difficult on near-term noisy devices. The more direct strategy of operator averaging is usually preferred as it can be performed using N = O(1/ε 2 ) measurements and no additional gates aside from those needed for the state preparation. In this work we use a simple but realistic model to describe the bound state of a neutron and a proton (the deuteron) to show that the latter strategy can require an overly large number of measurements in order to achieve a prefixed relative target accuracy ε r . Further, we propose to overcome this problem using a single step of QPE and classical postprocessing. This approach leads to a circuit depth C = O (ε μ ) (with μ ≥ 0) and to a number of measurements N = O (1/ε 2 + ν ) for 0 < ν ≤ 1 and a much smaller prefactor. We provide detailed descriptions of two implementations of our strategy for ν = 1 and ν ≈ 0.5 and derive appropriate conditions that a particular problem instance has to satisfy in order for our method to provide an advantage.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Chapter 4 - Recent Advances in Identification of Differential Equations from Noisy Data: IDENT Review

Differential equations and numerical methods are extensively used to model various real-world phenomena in science and engineering. With modern developments, we aim to find the underlying differential equation from a single observation of time-dependent data. If we assume that the differential equation is a linear combination of various linear and nonlinear differential terms, then the identification problem can be formulated as solving a linear system. The goal then reduces to finding the optimal coefficient vector that best represents the time derivative of the given data. We review some recent works on the identification of differential equations. We find some common themes for the improved accuracy: (i) The formulation of linear system with proper denoising is important, (ii) how to utilize sparsity and model selection to find the correct coefficient support needs careful attention, and (iii) there are ways to improve the coefficient recovery. We present an overview and analysis of recent developments on the topic.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1985

Future possibilities in objective analysis and data assimilation for atmospheric dynamics

The role that dynamics plays in estimating the state of the atmosphere from incomplete and noisy data is reviewed. Objective analysis represents an attempt at relying mostly on the data and minimizing the role of dynamics in the estimation. Data assimilation tries to balance properly the roles of dynamical and observational information. Sequential estimation is presented as the proper framework for understanding this balance, and the Kalman filter as the ideal, optimal procedure for data assimilation. The optimal filter computes forecast error covariances of a given atmospheric model exactly, and hence data assimilation should be closely connected with predictability studies. This connection is described, and consequences drawn for currently active areas of the atmospheric and related sciences, namely, mesoscale meteorology, long range forecasting, and upper ocean dynamics. Possibilities offered by judicious data assimilation in understanding barotropic adjustment, a phenomenon that appears to play a crucial role in atmospheric behavior on the scale of weeks to months, and hence in long range forecasting are addressed.

Ghil, M.↗

NASA NTRS1999

A Comparative Study of Interferometric Regridding Algorithms

THe paper discusses regridding options: (1) The problem of interpolating data that is not sampled on a uniform grid, that is noisy, and contains gaps is a difficult problem. (2) Several interpolation algorithms have been implemented: (a) Nearest neighbor - Fast and easy but shows some artifacts in shaded relief images. (b) Simplical interpolator - uses plane going through three points containing point where interpolation is required. Reasonably fast and accurate. (c) Convolutional - uses a windowed Gaussian approximating the optimal prolate spheroidal weighting function for a specified bandwidth. (d) First or second order surface fitting - Uses the height data centered in a box about a given point and does a weighted least squares surface fit.

Hensley, Scott↗

DOE OSTI2020

Automated Identification of Molecular Crystals’ Packing Motifs

Packing motifs—patterns in how molecules orient relative to one another in a crystal structure—are an important concept in many subdisciplines of materials science because of correlations observed between specific packing motifs and properties of interest. That said, packing motif data sets have remained small and noisy due to intensive manual labeling processes and insufficient labeling schemes. The most prominent labeling algorithms calculate relative interplanar angles of nearest neighbor molecules to determine the packing motif of a molecular crystal, but this simple approach can fail when neighbors are naively sampled isotropically around the crystal structure. To remedy this issue, here we propose an optimization algorithm, which rotates the molecular crystal structure to find representative molecules that inform the packing motif. We package this algorithm into an automated framework—Autopack—which both optimally rotates the crystal structure and labels the packing motif based on the appropriate neighboring molecules. In this work, we detail the Autopack framework and its performance, which shows improvements compared to previous state-of-the-art labeling methods, providing the first quantitative point of comparison for packing motif labeling algorithms. Furthermore, using Autopack (available at https://ipo.llnl.gov/technologies/software/autopack), we perform the first large-scale study of potential relationships between chemicals’ compositions and packing motifs, which shows that these relationships are more complex than previously hypothesized from studies that used only tens of polycyclic aromatic hydrocarbon molecules. Autopack’s capabilities help pose next steps for crystal engineering research focusing not only on a molecule’s adoption of a specific packing motif but also on new structure–property relationships.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2017

Some Mathematical and Geophysical Considerations in Radioisotope Dating Applications

Some quality considerations for use in isotopic dating are presented to identify and correct heretofore unidentified overestimate scenarios. These include to a lesser degree the statistical interpretation issues with linear-least-squares fitting results but more importantly the isotope effect in the individual components of the isochron coefficient ratios. By taking into consideration the isotope effect (differential mass diffusion rates) when measuring isotopic ratios from very old samples, the distribution dependency in the coefficient ratios will cause a bias if isotopic diffusion rates are not identical throughout a sample. The isotope effect is that isotopes having a smaller atomic mass will diffuse faster throughout a medium than will their heavier counterparts causing concentration gradients of their ratios even when there are no contributions from radioactive decay. The application to Rb/Sr dating is evaluated and shown to result in expected age overestimates when isotopic ratios are employed to linearize the isochron. A suggested method to test for this effect is argued to require rigorous statistical analysis. An associated optimal sampling technique would involve using single-grain etching. It is also shown that the only method to fully eliminate the isotope effect is to not use isotopic ratios at all in radioisotopic dating as the physics do not require the use of isotopic ratios for geochronological dating. However, without the ratios, the data are inherently noisy.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2016

Automated Dynamic Demand Response Implementation on a Micro-grid

In this paper, we describe a system for real-time automated Dynamic and Sustainable Demand Response with sparse data consumption prediction implemented on the University of Southern California campus microgrid. Supply side approaches to resolving energy supply-load imbalance do not work at high levels of renewable energy penetration. Dynamic Demand Response (D 2 R) is a widely used demand-side technique to dynamically adjust electricity consumption during peak load periods. Our D 2 R system consists of accurate machine learning based energy consumption forecasting models that work with sparse data coupled with fast and sustainable load curtailment optimization algorithms that provide the ability to dynamically adapt to changing supply-load imbalances in near real-time. Our Sustainable DR (SDR) algorithms attempt to distribute customer curtailment evenly across sub-intervals during a DR event and avoid expensive demand peaks during a few sub-intervals. It also ensures that each customer is penalized fairly in order to achieve the targeted curtailment. We develop near linear-time constant-factor approximation algorithms along with Polynomial Time Approximation Schemes (PTAS) for SDR curtailment that minimizes the curtailment error defined as the difference between the target and achieved curtailment values. Our SDR curtailment problem is formulated as an Integer Linear Program that optimally matches customers to curtailment strategies during a DR event while also explicitly accounting for customer strategy switching overhead as a constraint. We demonstrate the results of our D 2 R system using real data from experiments performed on the USC smartgrid and show that 1) our prediction algorithms can very accurately predict energy consumption even with noisy or missing data and 2) our curtailment algorithms deliver DR with extremely low curtailment errors in the 0.01-0.05 kWh range.

Kuppannagari, Sanmukh R.↗

DOE OSTI2023

Quantum machine learning with differential privacy

Abstract Quantum machine learning (QML) can complement the growing trend of using learned models for a myriad of classification tasks, from image recognition to natural speech processing. There exists the potential for a quantum advantage due to the intractability of quantum operations on a classical computer. Many datasets used in machine learning are crowd sourced or contain some private information, but to the best of our knowledge, no current QML models are equipped with privacy-preserving features. This raises concerns as it is paramount that models do not expose sensitive information. Thus, privacy-preserving algorithms need to be implemented with QML. One solution is to make the machine learning algorithm differentially private, meaning the effect of a single data point on the training dataset is minimized. Differentially private machine learning models have been investigated, but differential privacy has not been thoroughly studied in the context of QML. In this study, we develop a hybrid quantum-classical model that is trained to preserve privacy using differentially private optimization algorithm. This marks the first proof-of-principle demonstration of privacy-preserving QML. The experiments demonstrate that differentially private QML can protect user-sensitive information without signficiantly diminishing model accuracy. Although the quantum model is simulated and tested on a classical computer, it demonstrates potential to be efficiently implemented on near-term quantum devices [noisy intermediate-scale quantum (NISQ)]. The approach’s success is illustrated via the classification of spatially classed two-dimensional datasets and a binary MNIST classification. This implementation of privacy-preserving QML will ensure confidentiality and accurate learning on NISQ technology.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Hypothesis tests on Rayleigh wave radiation pattern shapes: a theoretical assessment of idealized source screening

SUMMARY Shallow seismic sources excite Rayleigh wave ground motion with azimuthally dependent radiation patterns. We place binary hypothesis tests on theoretical models of such radiation patterns to screen cylindrically symmetric sources (like explosions) from non-symmetric sources (like non-vertical dip-slip or non-VDS faults). These models for data include sources with several unknown parameters, contaminated by Gaussian noise and embedded in a layered half-space. The generalized maximum likelihood ratio tests that we derive from these data models produce screening statistics and decision rules that depend on measured, noisy ground motion at discrete sensor locations. We explicitly quantify how the screening power of these statistics increase with the size of any dip-slip and strike-slip components of the source, relative to noise (faulting signal strength) and how they vary with network geometry. As applications of our theory, we apply these tests to (1) find optimal sensor locations that maximize the probability of screening non-circular radiation patterns and (2) invert for the largest non-VDS faulting signal that could be mistakenly attributed to an explosion with damage, at a particular attribution probability. Finally, we quantify how certain errors that are sourced by opening cracks increase screening rate errors. While such theoretical solutions are ideal and require future validation, they remain important in underground explosion monitoring scenarios because they provide fundamental physical limits on the discrimination power of tests that screen explosive from non-VDS faulting sources.

58 GEOSCIENCES↗

DOE OSTI2024

Approximate Dynamic Programming With Enhanced Off-Policy Learning for Coordinating Distributed Energy Resources

Herein this paper proposes an innovative approximate dynamic programming (ADP) method for distributed energy resource coordination with the loss of life of battery energy storage system (BESS) explicitly modeled. The dispatch policy is designed to account for both calendrical and cyclical aging effects on BESS, explicitly modeling the impacts of ambient temperature on BESS lifespan. The proposed ADP employs an adaptive critic method and enhanced off-policy deterministic policy gradient (DPG) strategy, addressing the limitations of the on-policy gradient-based ADP approaches, including inadequate exploration, low data usage, and computational complexity. In particular, a customized policy is proposed to guide the algorithm to explore some promising decisions and thereby improve exploration capability and learning efficiency compared to conventional DPG-based learning approaches, which may struggle to find a global optimum due to random noisy action-based exploration or require expert demonstration with extra effort. The proposed method is illustrated using the IEEE 123-node system and compared with the existing ADP methods to prove solution accuracy and demonstrate the effects of incorporating degradation models into control design. Case studies showed that the proposed ADP effectively coordinates DERs with a 10 times smaller optimization gap compared to existing methods, and the incorporation of the BESS life loss model ensures the expected lifespan and results in significant cost savings.

24 POWER TRANSMISSION AND DISTRIBUTION↗

NASA NTRS1986

Sequential estimation and satellite data assimilation in meteorology and oceanography

The central theme of this review article is the role that dynamics plays in estimating the state of the atmosphere and of the ocean from incomplete and noisy data. Objective analysis and inverse methods represent an attempt at relying mostly on the data and minimizing the role of dynamics in the estimation. Four-dimensional data assimilation tries to balance properly the roles of dynamical and observational information. Sequential estimation is presented as the proper framework for understanding this balance, and the Kalman filter as the ideal, optimal procedure for data assimilation. The optimal filter computes forecast error covariances of a given atmospheric or oceanic model exactly, and hence data assimilation should be closely connected with predictability studies. This connection is described, and consequences drawn for currently active areas of the atmospheric and oceanic sciences, namely, mesoscale meteorology, medium and long-range forecasting, and upper-ocean dynamics.

Ghil, M.↗

NASA NTRS2011

Towards an Optimal Noise Versus Resolution Trade-Off in Wind Scatterometry

This paper approaches the noise versus resolution trade-off in wind scatterometry from a field-wise retrieval perspective. Theoretical considerations are discussed and practical implementation using a MAP estimator is applied to the Sea-Winds scatterometer. The approach is compared to conventional approaches as well as numerical weather predictions. The new approach incorporates knowledge of the wind spectrum to reduce the impact of components of the wind signal that are expected to be noisy.

scatterometer↗

DOE OSTI2017

Compressive Classification for TEM-EELS

Acquiring atomic-resolution images of beam sensitive materials or under dynamic conditions (e.g. operando STEM) is very difficult and requires precise dose fractioning to minimize the dose delivered to the sample and acquire the data more rapidly than dynamics present. Typical methods of low-dose STEM imaging include adjusting the beam current, dwell-time, and probe Scanning transmission electron microscopy (STEM) is used routinely to obtain atomic-resolution images of a small selection of radiation tolerant materials under stable conditions.size. All three of these determine the dose over a spatial area in STEM. Recently, compressive sensing [1] has been applied to electron microscopy. The computational imaging method of inpainting [2] has been proposed as a method to reduce dose and increase acquisition speed for STEM. Inpainting is a technique to recover missing pixels in an image. By skipping pixels (randomly) during acquisition, a fourth dose-control mechanism is realized [3]. A few implementations of randomly-subsampled STEM exist (e.g., [4]). To make the concepts of compressive sensing accessible to the microscopy community we begin with an example using atomic resolution images of a GaAs crystal (see Figure 1). Because the crystal is periodic it has a sparse representation in reciprocal space. In fact, a sparse representation is a key component of compressive sensing. If an image is sub-sampled randomly we find that the Fourier transform remains sparse, but becomes increasing noisy as less and less data is acquired. Yet, by finding the peaks in the reciprocal image and removing the noise it is possible to recover atomic resolution images with only 1% of the pixels. Figure 1 shows the reconstruction process for GaAs sub-sampled at 50%, 10%, 5%, and 1%. Periodic images form a special class for which the optimal sampling approach (according to CS theory) is a random selection of pixels. For non-periodic images, such as those arising in in-situ STEM, methods such as dictionary learning are necessary [2,5]. The data can be compressed in time for TEM [5] or pixels can be skipped randomly for STEM. There are several issues that arise in developing a random scan for STEM [4] and a coded aperture for TEM. The remainder of the talk will address these issues. References: [1] E Candes and M Wakin. Signal Processing Magazine, IEEE. 2(25) (2008), pp. 21. [2] A Stevens, Pu Y, Sun Y, et al. Artificial Intelligence & Statistics (AISTATS), 2017. [3] A Stevens, H Yang, L Carin et al. Microscopy 63(1), (2014), pp. 41. [4] L Kovarik, A Stevens, A Liyu et al. Appl. Phys. Lett. 109, 164102 (2016). [5] A Stevens, L Kovarik, P Abellan et al. Adv. Structural and Chemical Imaging 1(10), (2015), pp. 1. [6] Supported by the Chemical Imaging, Signature Discovery, and Analytics in Motion Initiatives at PNNL. PNNL is operated by Battelle Memorial Inst. for the US DOE; contract DE-AC05-76RL01830.

Hao, Weituo↗

NASA NTRS1974

A self-reorganizing digital flight control system for aircraft

This paper presents a design method for digital self-reorganizing control systems which is optimally tolerant of failures in aircraft sensors. The functions of this system are accomplished with software instead of the popular and costly technique of hardware duplication. The theoretical development, based on M-ary hypothesis testing, results in a bank of M Kalman filters operating in parallel in the failure detection logic. A moving window of the innovations of each Kalman filter drives the detection logic to decide the failure state of the system. The detection logic also selects the optimal state estimate (for control logic) from the bank of Kalman filters. The design process is applied to the design of a self-reorganizing control system for a current configuration of the space shuttle orbiter at Mach 5 and 120,000 feet. The failure detection capabilities of the system are demonstrated using a real-time simulation of the system with noisy sensors.

Montgomery, R. C.↗

DOE OSTI2017

Compositing Ground Penetrating Radar Scans of Differing Frequencies for Better Depth Perception

Methods developed to reduce interference in a noisy environment, be it radar target responses or effective communications in the presence of noise for mobile phone users, are vital in delivering a clear usable signal. The methods used to render a cleaner signal can also be used to combine signals of various frequencies. Ground Penetrating Radar (GPR) scans over the same area are no exception. This paper explores using an optimization problem solver, the Expectation Maximization (EM) Algorithm, to define the weights to use to combine multiple GPR scans at different frequencies over the same target area. This approach exploits the Gaussian Mixture Model (GMM) feature of the EM algorithm to produce a cleaner image at depth. Our method demonstrates a measured improvement toward producing a cleaner image.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

NeuroSEM: A hybrid framework for simulating multiphysics problems by coupling PINNs and spectral elements

Multiphysics problems that are characterized by complex interactions among fluid dynamics, heat transfer, structural mechanics, and electromagnetics, are inherently challenging due to their coupled nature. While experimental data on certain state variables may be available, integrating these data with numerical solvers remains a significant challenge. Physics-informed neural networks (PINNs) have shown promising results in various engineering disciplines, particularly in handling noisy data and solving inverse problems in partial differential equations (PDEs). However, their effectiveness in forecasting nonlinear phenomena in multiphysics regimes, particularly involving turbulence, is yet to be fully established. Here, this study introduces NeuroSEM, a hybrid framework integrating PINNs with the highfidelity Spectral Element Method (SEM) solver, Nektar++. NeuroSEM leverages the strengths of both PINNs and SEM, providing robust solutions for multiphysics problems. PINNs are trained to assimilate data and model physical phenomena in specific subdomains, which are then integrated into the Nektar++ solver. We demonstrate the efficiency and accuracy of NeuroSEM for thermal convection in cavity flow and flow past a cylinder. The framework effectively handles data assimilation by addressing those subdomains and state variables where the data is available. We applied NeuroSEM to the Rayleigh-B´enard convection system, including cases with missing thermal boundary conditions and noisy datasets. Finally, we applied the proposed NeuroSEM framework to real particle image velocimetry (PIV) data to capture flow patterns characterized by horseshoe vortical structures. Our results indicate that NeuroSEM accurately models the physical phenomena and assimilates the data within the specified subdomains. The framework’s plug-and-play nature facilitates its extension to other multiphysics or multiscale problems. Furthermore, NeuroSEM is optimized for efficient execution on emerging integrated GPU-CPU architectures. This hybrid approach enhances the accuracy and efficiency of simulations, making it a powerful tool for tackling complex engineering challenges in various scientific domains.

42 ENGINEERING↗

NASA NTRS1986

Efficient identification of critical stresses in structures subject to dynamic loads

Optimum structural design problems generally employ constraints which are parametric in terms of space and time variables. A parametric constraint may be replaced by equivalent critical point constraints at its local minima for optimization applications. In complex structures, accurate identification of such critical points is computationally expensive due to the cost of finite element analyses. Three techniques are described for efficiently and accurately identifying critical points for space- and time-dependent parametric constraints. An adaptive search technique and a spline interpolation technique are developed for exactly known response. A least squares spline approximation is suggested for noisy behavior. A helicopter tail-boom structure subjected to transient loading is used as an example to demonstrate the techniques described. All three techniques are shown to be computationally efficient for critical point identification and the least squares approximation also removes noise from the data. The case of multiple constraints per element is shown to be particularly suited to the use of spline techniques.

Haftka, R. T.↗