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260 records · Page 15

All sources NASA NTRS DOE OSTI

DOE OSTI2020

nPINNs: nonlocal Physics-Informed Neural Networks for a parametrized nonlocal universal Laplacian operator. Algorithms and Applications

Physics-informed neural networks (PINNs) are effective in solving inverse problems based on differential and integro-differential equations with sparse, noisy, unstructured, and multifidelity data. PINNs incorporate all available information, including governing equations (reflecting physical laws), initial-boundary conditions, and observations of quantities of interest, into a loss function to be minimized, thus recasting the original problem into an optimization problem. In this paper, we extend PINNs to parameter and function inference for integral equations such as nonlocal Poisson and nonlocal turbulence models, and we refer to them as nonlocal PINNs (nPINNs). The contribution of the paper is three-fold. First, we propose a unified nonlocal Laplace operator, which converges to the classical Laplacian as one of the operator parameters, the nonlocal interaction radius δ goes to zero, and to the fractional Laplacian as δ goes to infinity. This universal operator forms a super-set of classical Laplacian and fractional Laplacian operators and, thus, has the potential to fit a broad spectrum of data sets. We provide theoretical convergence rates with respect to δ and verify them via numerical experiments. Second, we use nPINNs to estimate the two parameters, δ and α, characterizing the kernel of the unified operator. The strong non-convexity of the loss function yielding multiple (good) local minima reveals the occurrence of the operator mimicking phenomenon, that is, different pairs of estimated parameters could produce multiple solutions of comparable accuracy. Third, we propose another nonlocal operator with spatially variable order α(γ), which is more suitable for modeling turbulent Couette flow. Our results show that nPINNs can jointly infer this function as well as δ. More importantly, these parameters exhibit a universal behavior with respect to the Reynolds number, a finding that contributes to our understanding of nonlocal interactions in wall-bounded turbulence.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

nPINNs: Nonlocal physics-informed neural networks for a parametrized nonlocal universal Laplacian operator. Algorithms and applications

Physics-informed neural networks (PINNs) are effective in solving inverse problems based on differential and integro-differential equations with sparse, noisy, unstructured, and multifidelity data. PINNs incorporate all available information, including governing equations (reflecting physical laws), initial-boundary conditions, and observations of quantities of interest, into a loss function to be minimized, thus recasting the original problem into an optimization problem. In this paper, we extend PINNs to parameter and function inference for integral equations such as nonlocal Poisson and nonlocal turbulence models, and we refer to them as nonlocal PINNs (nPINNs). The contribution of the paper is three-fold. First, we propose a unified nonlocal Laplace operator, which converges to the classical Laplacian as one of the operator parameters, the nonlocal interaction radius $\delta$ goes to zero, and to the fractional Laplacian as $\delta$ goes to infinity. This universal operator forms a super-set of classical Laplacian and fractional Laplacian operators and, thus, has the potential to fit a broad spectrum of data sets. We also provide theoretical convergence rates with respect to $\delta$ and verify them via numerical experiments. Second, we use nPINNs to estimate the two parameters, $\delta$ and $\alpha$, characterizing the kernel of the unified operator. The strong non-convexity of the loss function yielding multiple (good) local minima reveals the occurrence of the operator mimicking phenomenon, that is, different pairs of estimated parameters could produce multiple solutions of comparable accuracy. Third, we propose another nonlocal operator with spatially variable order $\alpha(y)$, which is more suitable for modeling turbulent Couette flow. Our results show that nPINNs can jointly infer this function as well as $\delta$. More importantly, these parameters exhibit a universal behavior with respect to the Reynolds number, a finding that contributes to our understanding of nonlocal interactions in wall-bounded turbulence.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

On the Solution of ℓ 0 -Constrained Sparse Inverse Covariance Estimation Problems

The sparse inverse covariance matrix is used to model conditional dependencies between variables in a graphical model to fit a multivariate Gaussian distribution. Estimating the matrix from data are well known to be computationally expensive for large-scale problems. Sparsity is employed to handle noise in the data and to promote interpretability of a learning model. Although the use of a convex ℓ 1 regularizer to encourage sparsity is common practice, the combinatorial ℓ 0 penalty often has more favorable statistical properties. In this paper, we directly constrain sparsity by specifying a maximally allowable number of nonzeros, in other words, by imposing an ℓ 0 constraint. Here, we introduce an efficient approximate Newton algorithm using warm starts for solving the nonconvex ℓ 0 -constrained inverse covariance learning problem. Numerical experiments on standard data sets show that the performance of the proposed algorithm is competitive with state-of-the-art methods.

$\ell_0$-Constrained↗

DOE OSTI2026

Regional surrogates for predictive control of digital twins

Digital twins of complex systems must involve a model that is fast, generalizable, and usable for real-time control. For example, high-fidelity nonlinear multiphysics simulations can capture laser-material interactions, but are too slow for optimization or model predictive control (MPC). Reduced-order models, used to accelerate such computation, frequently fail to generalize to unseen inputs or control states. We show theoretically that this failure is intrinsic, i.e., that a learned model is non-unique outside the sampled subspace when its low-rank structure arises from limited excitation and clustered eigenvalues, rather than from a user-imposed truncation alone. Motivated by this result, we propose a control-ready regional surrogate-construction framework for both autonomous and nonautonomous dynamics; it employs Koopman lifting to represent nonlinearities, while preserving spatial locality. We illustrate our approach by constructing a control-ready surrogate for the digital twin of a thermal component of additive-manufacturing process. Our surrogate, localized in space through a von Neumann stencil, is learned from noisy high-fidelity simulations that emulate thermal-camera images collected during the manufacturing. It is linear in thermo-physically augmented states so that MPC reduces to a convex quadratic program. The surrogate requires no online correction, generalizes to unseen scan paths and power profiles of the laser, and is more than three orders of magnitude faster than a finite-difference solver. Furthermore, when the MPC sequence computed on the digital twin is applied to this solver, closed-loop temperature regulation is recovered, showing that the surrogate preserves control-relevant input-output behavior.

Data-driven model↗

DOE OSTI2020

Proppant embedment in coal and shale: Impacts of stress hardening and sorption

During methane production in CBM reservoirs, the influence of proppant embedment and permeability damage cannot be neglected – especially where the wall-rock is soft. Effective stresses are elevated during methane recovery, increasing both normal loading stress and confinement and simultaneously overprinting sorption-induced volumetric strains. Experiments and analytic modeling are conducted to define key mechanisms controlling these competitive effects. We independently measure overall sample compaction (external LVDT) and local strain (strain gauge) in the matrix to deconvolve proppant embedment in a propped fracture for different conditions of confining stress. The results show symptomatic behaviors of elastic (shale) and elastoplastic (coal) responses of embedment. Different from shale, the evolution of embedment is convex upwards with increased stress where indented depth increases more rapidly as loading stress increases under constant confinement. In addition, a stress-hardening effect is found to play a pivotal role in determining the characteristics of indentation, which are examined in terms of evolution profiles, deformation regimes, embedment slopes, curvatures, yield points and irreversible indentations. Based on the experimental observations a semianalytical model predicts indentation and the evolution of propped permeability under recreated in-situ stress conditions. A simplified case study is conducted to further illustrate the evolution of aperture and permeability of a propped fracture in CBM reservoirs. The modeling results suggest that proppant embedment is significantly overestimated if the variable stress-hardening (VSH) effect is neglected, especially when effective stress is large. Moreover, a decrease in indentation depth possibly occurs during late stage methane production, resulting in a reversal/recovery in fracture closure. This is because desorption-induced shrinkage becomes the predominant effect, causing an increase in aperture and a reduction in the indented volume of proppant. The resulting recovery in permeability implies that the propped coal fracture has the potential to optimally facilitate methane production as a pathway, even at high closure stresses generated by methane drainage.

01 COAL, LIGNITE, AND PEAT↗

DOE OSTI2023

Computational optimal transport for molecular spectra: The fully continuous case

Computational optimal transport is used to analyze the difference between pairs of continuous molecular spectra. It is demonstrated that transport distances which are derived from this approach may be a more appropriate measure of the difference between two continuous spectra than more familiar measures of distance under many common circumstances. Associated with the transport distances is the transport map which provides a detailed analysis of the difference between two molecular spectra and is a key component of our study of quantitative differences between two continuous spectra. The use of optimal transport for comparing molecular spectra is developed in detail here with a set of model spectra, so that the discussion is self-contained. The difference between the transport distance and more common definitions of distance is elucidated for some well-chosen examples and it is shown where transport distances may be very useful alternatives to standard definitions of distance. The transport distance between a theoretical and experimental electronic absorption spectrum for SO 2 is studied and it is shown how the theoretical spectrum can be modified to fit the experimental spectrum better adjusting the theoretical band origin and the resolution of the theoretical spectrum. In conclusion, this analysis includes the calculation of transport maps between the theoretical and experimental spectra suggesting future applications of the methodology.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2025

Novel artificial neural network model for instantaneous power losses and operational efficiency mapping of MW-scale vanadium redox flow battery for improved technoeconomic analysis

A novel data-driven, machine-learning-based method for modeling the instantaneous power losses of a distribution-sited 2 MW/8MWh vanadium redox flow battery (VRFB), a grid-scale electrochemical storage technology, is introduced and compared against benchmark empirical modeling approaches, including symmetric and asymmetric models, as well as a recent convex hull modeling approach. The novel loss modeling method introduces several advantages over the benchmark models and over simplistic efficiency estimates, the most significant of which is that the model can accurately reflect the stepwise and non-linear parasitic losses associated with the duty cycles of mechanical auxiliary systems like pump motor drives and blower fans. Residuals of the models are compared; the proposed data driven model features significantly improved accuracy over the benchmark models. The model's coefficient of determination is also improved relative to that of the benchmark models. Furthermore, a novel method for visualization of operational efficiency of the grid-scale storage technology is introduced. To demonstrate the benefits of the novel data-driven method for modeling the VRFB, the benchmark models and the proposed models are embedded into an Open DSS distribution network model to study two applications of the grid-scale electrical storage system: load leveling for grid support and energy arbitrage. This article demonstrates that the accuracy of the instantaneous power loss model significantly impacts the understanding of the state of charge of the VRFB. In turn, the accuracy of the efficiency modeling of the VRFB impacts the understanding of the potential economic value and technical benefits to the distribution network operators. In conclusion, the presented power loss modeling approach is, therefore, highly relevant for utility-stakeholders, battery asset owners, system engineers, system designers, and financial planners interested in evaluating or optimizing the operation of grid-scale VRFBs.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2026

Bio-inspired alula-based winglet design for enhanced heat transfer in high temperature fin-and-tube heat exchangers

Fin-and-tube heat exchangers (FTHEs) are widely used for high-temperature flue-gas heat recovery, but their performance is often limited by wake regions and non-uniform fin-surface temperatures. This study proposes and numerically evaluates four bio-inspired longitudinal vortex generator (VG) configurations in a high-temperature FTHE with flue-gas inlet temperature ∼1230 K: double-delta, curved double-delta, alula, and a new curved-alula geometry. The reference fin is not hydraulically plain; it already incorporates leading-edge separation columns and convex protrusions, so the alula-type winglets are assessed as downstream add-ons acting on a strongly disturbed flow. In a second step, perforations (one, two and three circular holes) are introduced into the curved-alula VGs to further tailor the flow field. Three-dimensional simulations with the Shear Stress Transpor (SST) $k - ω$ model, temperature-dependent flue-gas properties and conjugate conduction are carried out for gas-side Reynolds numbers $Re_g ≈ 8.0$ x $10^2 - 3.6$ x $10^3$ (mass flow rates 0.5 – 2.5 g/s), and the designs are compared in terms of surface heat flux, Nusselt number, friction factor and hydrothermal performance factor (HTPF). For this already-promoted fin, the additional downstream winglets provide moderate, incremental hydrothermal gains. At the highest Reynolds number, the best non-perforated design (curved-alula) increases surface heat flux from 1630.9 to 1794.7 kW/m² (∼ 10 % gain) and the Nusselt number from 227.6 to 242.6 (∼ 7 % gain), while the friction factor rises from 0.26 to about 0.30, yielding HTPF values close to unity (∼ 0.9 – 1.0). Introducing circular perforations into the curved-alula winglets acts mainly as a wake-bleeding refinement: the three-hole configuration provides a heat flux of 1824.7 kW/m² and a pressure drop of 127.9 Pa, with HTPF in the range ∼ 1.03 – 1.14 and a small (∼ 1 – 3 %) improvement over the solid curved-alula design. Flow-field analysis shows that the perforated curved-alula VGs shrink tube-wake regions, thin the thermal boundary layer and homogenize the fin-surface temperature (outlet-gas temperature ∼ 510 – 520 K and fin-surface temperature ∼ 420 – 421 K for the three-hole case). An optimal flue-gas mass flow rate of ∼ 1 g/s ($Re_g ≈ 1.5$ x $10^3$) is identified, beyond which additional heat-transfer gains are offset by rapidly increasing pressure losses. Overall, the results highlight that initial fin geometry and VG placement are as important as VG shape: alula-based winglets are expected to yield larger relative gains on simpler flat-fin layouts or when positioned closer to the fin leading edge and tube

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗