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At least 829 records · Page 46
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

A Review of Physics-Informed Machine Learning in Fluid Mechanics

Physics-informed machine-learning (PIML) enables the integration of domain knowledge with machine learning (ML) algorithms, which results in higher data efficiency and more stable predictions. This provides opportunities for augmenting—and even replacing—high-fidelity numerical simulations of complex turbulent flows, which are often expensive due to the requirement of high temporal and spatial resolution. In this review, we (i) provide an introduction and historical perspective of ML methods, in particular neural networks (NN), (ii) examine existing PIML applications to fluid mechanics problems, especially in complex high Reynolds number flows, (iii) demonstrate the utility of PIML techniques through a case study, and (iv) discuss the challenges and opportunities of developing PIML for fluid mechanics.

42 ENGINEERING↗
DOE OSTI2021

Higher-order particle representation for particle-in-cell simulations

In this paper we present an alternative approach to the representation of simulation particles for unstructured electrostatic and electromagnetic PIC simulations. In our modified PIC algorithm we represent particles as having a smooth shape function limited by some specified finite radius, r 0 . A unique feature of our approach is the representation of this shape by surrounding simulation particles with a set of virtual particles with delta shape, with fixed offsets and weights derived from Gaussian quadrature rules and the value of r 0 . As the virtual particles are purely computational, they provide the additional benefit of increasing the arithmetic intensity of traditionally memory bound particle kernels. The modified algorithm is implemented within Sandia National Laboratories' unstructured EMPIRE-PIC code, for electrostatic and electromagnetic simulations, using periodic boundary conditions. We show results for a representative set of benchmark problems, including electron orbit, a transverse electromagnetic wave propagating through a plasma, numerical heating, and a plasma slab expansion. In this work, good error reduction across all of the chosen problems is achieved as the particles are made progressively smoother, with the optimal particle radius appearing to be problem-dependent.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Classical symmetries and the Quantum Approximate Optimization Algorithm

Here, we study the relationship between the Quantum Approximate Optimization Algorithm (QAOA) and the underlying symmetries of the objective function to be optimized. Our approach formalizes the connection between quantum symmetry properties of the QAOA dynamics and the group of classical symmetries of the objective function. The connection is general and includes but is not limited to problems defined on graphs. We show a series of results exploring the connection and highlight examples of hard problem classes where a nontrivial symmetry subgroup can be obtained efficiently. In particular, we show how classical objective function symmetries lead to invariant measurement outcome probabilities across states connected by such symmetries, independent of the choice of algorithm parameters or number of layers. To illustrate the power of the developed connection, we apply machine learning techniques toward predicting QAOA performance based on symmetry considerations. We provide numerical evidence that a small set of graph symmetry properties suffices to predict the minimum QAOA depth required to achieve a target approximation ratio on the MaxCut problem, in a practically important setting where QAOA parameter schedules are constrained to be linear and hence easier to optimize.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A Scalable Space-Time Domain Decomposition Approach for Solving Large Scale Nonlinear Regularized Inverse Ill Posed Problems in 4D Variational Data Assimilation

We address the development of innovative algorithms designed to solve the strong-constraint Four Dimensional Variational Data Assimilation (4DVar DA) problems in large scale applications. We present a space-time decomposition approach which employs the whole domain decomposition, i.e. both along the spacial and temporal direction in the overlapping case, and the partitioning of both the solution and the operator. Starting from the global functional defined on the entire domain, we get to a sort of regularized local functionals on the set of sub domains providing the order reduction of both the predictive and the Data Assimilation models. The algorithm convergence is developed. Performance in terms of reduction of time complexity and algorithmic scalability is discussed on the Shallow Water Equations on the sphere. The number of state variables in the model, the number of observations in an assimilation cycle, as well as numerical parameters as the discretization step in time and in space domain are defined on the basis of discretization grid used by data available at repository Ocean Synthesis/Reanalysis Directory of Hamburg University.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

An adaptive and stability-promoting layerwise training approach for sparse deep neural network architecture

This work presents a two-stage adaptive framework for progressively developing deep neural network (DNN) architectures that generalize well for a given training data set. In the first stage, a layerwise training approach is adopted where a new layer is added each time and trained independently by freezing parameters in the previous layers. We impose desirable structures on the DNN by employing manifold regularization, sparsity regularization, and physics-informed terms. We introduce a ε – δ – stability-promoting concept as a desirable property for a learning algorithm and show that employing manifold regularization yields a ε – δ stability-promoting algorithm. Further, we also derive the necessary conditions for the trainability of a newly added layer and investigate the training saturation problem. In the second stage of the algorithm (post-processing), a sequence of shallow networks is employed to extract information from the residual produced in the first stage, thereby improving the prediction accuracy. Numerical investigations on prototype regression and classification problems demonstrate that the proposed approach can outperform fully connected DNNs of the same size. Moreover, by equipping the physics-informed neural network (PINN) with the proposed adaptive architecture strategy to solve partial differential equations, we numerically show that adaptive PINNs not only are superior to standard PINNs but also produce interpretable hidden layers with provable stability. As a result, we also apply our architecture design strategy to solve inverse problems governed by elliptic partial differential equations.

42 ENGINEERING↗
DOE OSTI2021

Striving to translate shale physics across ten orders of magnitude: What have we learned?

Shales will play an important role in the successful transition of energy from fossil-based resources to renewables in the coming decades. Aside from being a significant source of low-carbon intensity fuels, like natural gas, they also serve as geologic seals of subsurface formations that may be used to isolate nuclear waste, sequester CO 2 , or store intermittent energy (e.g., solar hydrogen). Despite their importance, shales pose significant engineering and environmental challenges due to their nanoporous structure and extreme heterogeneity that spans at least ~10 orders of magnitude in spatial scale. Two challenges inhibit a system-level understanding: (1) the physics of fluid flow and phase behavior in shales are poorly understood due to the dominant molecular interactions between minerals and fluids under confinement, and (2) the apparent lack of scale separation that prevents a reliable (closed) description of the physics at any single scale of observation. In this review, we focus on the latter issue and discuss scale translation, which in its broadest sense is transforming data or simulations from one spatiotemporal scale to another. While effective scale translation is not exclusive to shales, but all geologic porous media, the need for it is especially acute in shales given their high degree of heterogeneity. Classical theories like homogenization, while indispensable, fail when scales are not separated. Other methods, like numerical upscaling, scale-translate in only one direction: small to large, but not the reverse, called downscaling. However, the confluence of advances in three areas are bringing challenging problems such as shales within reach: increased computational power and scalable algorithms; high-resolution imaging and multi-modal data acquisition; and machine learning to process massive amounts of data. While these advances equip geoscientists with a wide array of experimental and computational tools, no individual tool can probe the entire gamut of heterogeneity in shales. Their effective use, therefore, requires an ability to bridge between various data types obtained at different scales. The aim of this review is to present a coherent account of computational and experimental methods that may be used to achieve just that, i.e., to perform scale translation. We provide a broader definition of scale translation, one that transcends classical homogenization and upscaling methods, but is consistent with them and accommodates notions like downscaling and data translation. After a brief introduction to homogenization, we review hybrid methods, numerical upscaling and its recent extensions, multiscale computing, high-resolution imaging, and machine learning. We place particular emphasis on multiscale computing and propose an algorithmic framework to bridge between the pore (micro) and Darcy (macro) scales. Throughout the paper, we draw comparisons between the various methods and highlight their (often hidden) similarities, differences, benefits, and pitfalls. We finally conclude with two case studies on shales that exemplify some of the methods presented.

58 GEOSCIENCES↗
DOE OSTI2021

An extended numerical manifold method for unsaturated soil-water interaction analysis at micro-scale

To investigate unsaturated soil-water interaction at micro-scale, this work extends the numerical manifold method (NMM) by incorporating a soil-water coupling model considering specific capillary water distribution and capillary force calculation. The soil skeleton is constructed by a soil skeleton generation algorithm with random polygons. To more realistically capture the interaction between soil grains and capillary water, a capillary mechanics-based geometric algorithm is proposed to iteratively calculate the capillary water distribution. The capillary forces corresponding to the capillary water distribution are calculated based on the Young-Laplace equation. The proposed capillary water solving framework is first verified by reproducing the soil-water characteristic curve and the capillary water distribution of an ideal contact-disk model against analytical solutions. To further validate the ability of the capillary water solving framework to predict hydraulic behavior of the real soil, a laboratory test on the Toyoura sand is reproduced numerically. Then an ideal direct shear test is performed to further validate the two-way soil-water coupling procedure, in which a comparison between the numerical and analytical results regarding the shear strength and matric suction is presented. Finally, microscopic hydraulic and compression tests are conducted on two soil specimens with the same porosity and mean grain diameter but different uniformity coefficients. The results elucidate that the extended method is a potential tool to explore unsaturated soil behaviors at micro-scale.

58 GEOSCIENCES↗
DOE OSTI2024

A multi-algorithm approach for modeling coastal wetland eco-geomorphology

Coastal wetlands play an important role in the global water and biogeochemical cycles. Climate change makes it more difficult for these ecosystems to adapt to the fluctuation in sea levels and other environmental changes. Given the importance of eco-geomorphological processes for coastal wetland resilience, many eco-geomorphology models differing in complexity and numerical schemes have been developed in recent decades. However, their divergent estimates of the response of coastal wetlands to climate change indicate that substantial structural uncertainties exist in these models. To investigate the structural uncertainty of coastal wetland eco-geomorphology models, we developed a multi-algorithm model framework of eco-geomorphological processes, such as mineral accretion and organic matter accretion, within a single hydrodynamics model. The framework is designed to explore possible ways to represent coastal wetland eco-geomorphology in Earth system models and reduce the related uncertainties in global applications. We tested this model framework at three representative coastal wetland sites: two saltmarsh wetlands (Venice Lagoon and Plum Island Estuary) and a mangrove wetland (Hunter Estuary). Through the model–data comparison, we showed the importance of using a multi-algorithm ensemble approach for more robust predictions of the evolution of coastal wetlands. We also found that more observations of mineral and organic matter accretion at different elevations of coastal wetlands and evaluation of the coastal wetland models at different sites in diverse environments can help reduce the model uncertainty.

58 GEOSCIENCES↗
DOE OSTI2020

Block Krylov Subspace Methods for Functions of Matrices II: Modified Block FOM

We analyze an expansion of the generalized block Krylov subspace framework of [Electron. Trans. Numer. Anal., 47 (2017), pp. 100--126]. This expansion allows the use of low-rank modifications of the matrix projected onto the block Krylov subspace and contains, as special cases, the block GMRES method and the new block Radau--Arnoldi method. Within this general setting, we present results that extend the interpolation property from the nonblock case to a matrix polynomial interpolation property for the block case, and we relate the eigenvalues of the projected matrix to the latent roots of these matrix polynomials. Some error bounds for these modified block FOM methods for solving linear systems are presented. We then show how cospatial residuals can be preserved in the case of families of shifted linear block systems. This result is used to derive computationally practical restarted algorithms for block Krylov approximations that compute the action of a matrix function on a set of several vectors simultaneously. Finally, we prove some error bounds and present numerical results showing that two modifications of FOM, the block harmonic and the block Radau--Arnoldi methods for matrix functions, can significantly improve the convergence behavior.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Resilient Hierarchical Networked Control Systems: Secure Controls for Critical Locations and at Edge

Integration of information and communication technology (ICT) offers new opportunities in improving the management and operation of critical infrastructures such as power systems as it allows connection of different sensors and control components via a communication network, leading to the so-called networked control systems (NCS). However, the use of open and pervasive ICT such as the Internet or wireless communication technologies comes at a price of making NCS vulnerable to cyber intrusions/attacks which may cause physical damage. Here, this chapter presents control algorithms to ensure resilient and safe operation of NCS under unknown cyberattacks. Specifically, a variant of dynamic watermarking strategies is presented by embedding encoding/decoding components of chaotic signals into the NCS for secure control for critical locations where the measurement/control signals are transmitted to/from the control center via a communication network. In addition, resilient cooperative control algorithms are discussed to ensure safe operation at edge of the NCS which consists of a large number of distributed controllable devices. Several numerical examples are provided to illustrate the proposed control strategies.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗
DOE OSTI2023

A new approach to color-coherent parton evolution

We present a simple parton-shower model that replaces the explicit angular ordering of the coherent branching formalism with a differentially accurate simulation of soft-gluon radiation by means of a non-trivial dependence of the splitting functions on azimuthal angles. We introduce a global kinematics mapping and provide an analytic proof that it satisfies the criteria for next-to leading logarithmic accuracy. In the new algorithm, initial and final state evolution are treated on the same footing. We provide an implementation for final-state evolution in the numerical code ALARIC and present a first comparison to experimental data.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Analysis of the ratio of ℓ 1 and ℓ 2 norms in compressed sensing

We study the ratio of ℓ 1 and ℓ 2 norms ( ℓ 1 / ℓ 2 ) as a sparsity-promoting objective in compressed sensing. We first propose a novel criterion that guarantees that an s-sparse signal is the local minimizer of the ℓ 1 / ℓ 2 objective; our criterion is interpretable and useful in practice. We also give the first uniform recovery condition using a geometric characterization of the null space of the measurement matrix, and show that this condition is satisfied for a class of random matrices. We also present analysis on the robustness of the procedure when noise pollutes data. Numerical experiments are provided that compare ℓ 1 / ℓ 2 with some other popular non-convex methods in compressed sensing. Finally, we propose a novel initialization approach to accelerate the numerical optimization procedure. We call this initialization approach support selection, and we demonstrate that it empirically improves the performance of existing ℓ 1 / ℓ 2 algorithms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A comprehensive modeling of falling film evaporators subject to vapor flow, pass arrangements, and refrigerants

Improving the heat transfer performance of falling film evaporators is a crucial step for improving the energy efficiency of the heat pump or refrigeration systems. This study conducts a numerical investigation for the practical-scale falling film evaporator based on the epsilon–NTU method with an updated heat transfer correlation. The algorithm was validated with lab-scale and real-scale falling film evaporator experimental results, and the prediction reaches a mean absolute deviation of 12.5%. Here, the parametric study encompasses eight refrigerants: R-134a, R-410A, R-600a, R-717, R-1270, R-152a, R-1234yf, and R-1234ze(E). The results indicate that vaporization enthalpy of refrigerant is a key property in selecting an appropriate working fluid because it helps minimize severe heat transfer degradation caused by dry-out. Additionally, the vapor-flow–induced heat transfer degradation can be predicted using the critical Weber number. Furthermore, the trade-off between extending the tube length and increasing the number of tubes for heat transfer improvement is discussed. Finally, different two-pass arrangements show deviations of less than 4 %.

Dry-out↗
DOE OSTI2023

Enabling site-specific well leakage risk estimation during geologic carbon sequestration using a modular deep-learning-based wellbore leakage model

Geologic carbon sequestration (GCS) is a promising technology for mitigating net carbon emissions and growing climate concern by storing CO 2 in reservoirs. Oil and gas brownfields are an attractive option for CO 2 storage, but these sites have many historical wellbores from petroleum production and can be a potential leakage pathway for CO 2 or formation brine. Therefore, risk management of GCS operations requires an assessment of potential well leakage. Due to the high uncertainty of the system, stochastic approaches are ideal for quantifying the range of risk behaviors, but they must be computationally efficient in the face of complex physics. Here, we develop a new physics-centric deep learning wellbore model to predict the leakage of CO 2 and brine through leaky wellbores. Multi-physics numerical simulations were used to generate data sets, and physics-informed features were introduced. Neural networks were optimized with an automated searching algorithm. Feature analysis quantifies the impact of each feature on model prediction and confirms the role of physics-inspired parameters. The model shows high predictive performance across a wide range of geologic and injection conditions and well attributes. In conclusion, a case study illustrates how the model is applied to assess well leakage in GCS operations.

58 GEOSCIENCES↗
DOE OSTI2021

Rotor blade imbalance fault detection for variable-speed marine current turbines via generator power signal analysis

Marine hydrokinetic (MHK) turbines extract renewable energy from oceanic environments. However, due to the harsh conditions that these turbines operate in, system performance naturally degrades over time. Thus, ensuring efficient condition-based maintenance is imperative towards guaranteeing reliable operation and reduced costs for marine hydrokinetic power. This work proposes a novel framework aimed at identifying and classifying the severity of rotor blade pitch imbalance faults experienced by marine current turbines (MCTs). In the framework, a Continuous Morlet Wavelet Transform (CMWT) is first utilized to acquire the wavelet coefficients encompassed within the 1P frequency range of the turbine's rotor shaft. From these coefficients, several statistical indices are tabulated into a six-dimensional feature space. Next, Principle Component Analysis (PCA) is employed on the resulting feature space for dimensionality reduction, and then the application of a K-Nearest Neighbor (KNN) machine learning algorithm is utilized for fault detection and severity classification. The effectiveness of the proposed framework is validated using a high-fidelity MCT numerical simulation platform, where results demonstrate that the presence of a pitch imbalance fault can be accurately detected 100% of the time and correctly classified based upon severity more than 97% of the time.

42 ENGINEERING↗
DOE OSTI2021

A Simple Criterion for Feasibility of Heat Integration between Distillation Streams Based on Relative Volatilities

In a multicomponent distillation configuration, there are numerous sources and sinks of heat, and a potential way to reduce the heat duty requirement is to perform heat integration. Unfortunately, an algorithmic search of the optimal heat integration opportunities is intractable when the required temperatures of intermediate streams are computed via complex models. Instead, in this work, we introduce pressure-scaled pseudo relative volatility, a new metric to compare stream temperatures. Here, we justify the use of pseudo relative volatility by proving that this variable is a monotonically increasing function of the liquid fraction in a saturated mixture stream. Using this metric, we derive a shortcut criterion to check the feasibility of various heat integration opportunities, such as thermal coupling via heat transfer (TCH). The advantage of this approach is that it circumvents the need for explicit temperatures and instead relies on composition, component relative volatilities, and pressure—quantities that are readily available in shortcut models for optimization of distillation configurations. Leveraging this fact, we propose a new optimization framework that identifies feasible TCHs that we consider within the formulation while minimizing the total heat duty of a distillation configuration. We demonstrate, on a few examples, that our formulation can identify heat duty efficient configurations, some of which are multieffect configurations. Using this methodology, we discover configurations that are not only simpler than the fully thermally coupled (FTC) configuration but also have a much lower heat duty.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2022

Thermodynamics of correlated electrons in a magnetic field

The Hofstadter–Hubbard model captures the physics of strongly correlated electrons in an applied magnetic field, which is relevant to many recent experiments on Moiré materials. Few large-scale, numerically exact simulations exists for this model. In this work, we simulate the Hubbard–Hofstadter model using the determinant quantum Monte Carlo (DQMC) algorithm. We report the field and Hubbard interaction strength dependence of charge compressibility, fermion sign, local moment, magnetic structure factor, and specific heat. The gross structure of magnetic Bloch bands and band gaps determined by the non-interacting Hofstadter spectrum is preserved in the presence of U. Incompressible regions of the phase diagram have improved fermion sign. At half filling and intermediate and larger couplings, a strong orbital magnetic field delocalizes electrons and reduces the effect of Hubbard U on thermodynamic properties of the system.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Beyond Limber: efficient computation of angular power spectra for galaxy clustering and weak lensing

Angular two-point statistics of large-scale structure observables are important cosmological probes. To reach the high accuracy required by the statistical precision of future surveys, some of these statistics may need to be computed without the commonly employed Limber approximation; the exact computation however requires integration over Bessel functions, and a brute-force evaluation is slow to converge. Here, we present a new method based on our generalized FFTLog algorithm for the efficient computation of angular power spectra beyond the Limber approximation. The new method significantly simplifies the calculation and improves the numerical speed and stability. It is easily extended to handle integrals involving derivatives of Bessel functions, making it equally applicable to numerically more challenging cases such as contributions from redshift-space distortions and Doppler effects. We implement our method for galaxy clustering and galaxy-galaxy lensing power spectra. We find that using the Limber approximation for galaxy clustering in future analyses like LSST Year 1 and DES Year 6 may cause significant biases in cosmological parameters, indicating that going beyond the Limber approximation is necessary for these analyses.

weak gravitational lensing↗